Agda
A dependently typed functional programming language and proof assistant http://wiki.portal.chalmers.se/agda/
Version on this page:  [email protected]:5 
LTS Haskell 12.26:  2.5.4.2 
Stackage Nightly 20180928:  2.5.4.1 
Latest on Hackage:  2.6.1 
Module documentation for 2.5.3
[email protected]:7ac9cac6f799207bdf292608aeab2c1e142e74ee4c61da0cda18de44ca4d9e32,27800
 Agda
 Agda.Auto
 Agda.Benchmarking
 Agda.Compiler
 Agda.Compiler.Backend
 Agda.Compiler.CallCompiler
 Agda.Compiler.Common
 Agda.Compiler.JS
 Agda.Compiler.MAlonzo
 Agda.Compiler.ToTreeless
 Agda.Compiler.Treeless
 Agda.Compiler.Treeless.AsPatterns
 Agda.Compiler.Treeless.Builtin
 Agda.Compiler.Treeless.Compare
 Agda.Compiler.Treeless.EliminateDefaults
 Agda.Compiler.Treeless.EliminateLiteralPatterns
 Agda.Compiler.Treeless.Erase
 Agda.Compiler.Treeless.GuardsToPrims
 Agda.Compiler.Treeless.Identity
 Agda.Compiler.Treeless.NormalizeNames
 Agda.Compiler.Treeless.Pretty
 Agda.Compiler.Treeless.Simplify
 Agda.Compiler.Treeless.Subst
 Agda.Compiler.Treeless.Uncase
 Agda.Compiler.Treeless.Unused
 Agda.ImpossibleTest
 Agda.Interaction
 Agda.Interaction.BasicOps
 Agda.Interaction.CommandLine
 Agda.Interaction.EmacsCommand
 Agda.Interaction.EmacsTop
 Agda.Interaction.FindFile
 Agda.Interaction.Highlighting
 Agda.Interaction.Imports
 Agda.Interaction.InteractionTop
 Agda.Interaction.Library
 Agda.Interaction.MakeCase
 Agda.Interaction.Monad
 Agda.Interaction.Options
 Agda.Interaction.Response
 Agda.Interaction.SearchAbout
 Agda.Main
 Agda.Syntax
 Agda.Syntax.Abstract
 Agda.Syntax.Common
 Agda.Syntax.Concrete
 Agda.Syntax.Fixity
 Agda.Syntax.IdiomBrackets
 Agda.Syntax.Info
 Agda.Syntax.Internal
 Agda.Syntax.Literal
 Agda.Syntax.Notation
 Agda.Syntax.Parser
 Agda.Syntax.Parser.Alex
 Agda.Syntax.Parser.Comments
 Agda.Syntax.Parser.Layout
 Agda.Syntax.Parser.LexActions
 Agda.Syntax.Parser.Lexer
 Agda.Syntax.Parser.Literate
 Agda.Syntax.Parser.LookAhead
 Agda.Syntax.Parser.Monad
 Agda.Syntax.Parser.Parser
 Agda.Syntax.Parser.StringLiterals
 Agda.Syntax.Parser.Tokens
 Agda.Syntax.Position
 Agda.Syntax.Reflected
 Agda.Syntax.Scope
 Agda.Syntax.Translation
 Agda.Syntax.Treeless
 Agda.Termination
 Agda.TheTypeChecker
 Agda.TypeChecking
 Agda.TypeChecking.Abstract
 Agda.TypeChecking.CheckInternal
 Agda.TypeChecking.CompiledClause
 Agda.TypeChecking.Constraints
 Agda.TypeChecking.Conversion
 Agda.TypeChecking.Coverage
 Agda.TypeChecking.Datatypes
 Agda.TypeChecking.DeadCode
 Agda.TypeChecking.DisplayForm
 Agda.TypeChecking.DropArgs
 Agda.TypeChecking.Empty
 Agda.TypeChecking.Errors
 Agda.TypeChecking.EtaContract
 Agda.TypeChecking.Forcing
 Agda.TypeChecking.Free
 Agda.TypeChecking.Functions
 Agda.TypeChecking.Implicit
 Agda.TypeChecking.Injectivity
 Agda.TypeChecking.InstanceArguments
 Agda.TypeChecking.Irrelevance
 Agda.TypeChecking.Level
 Agda.TypeChecking.LevelConstraints
 Agda.TypeChecking.MetaVars
 Agda.TypeChecking.Monad
 Agda.TypeChecking.Monad.Base
 Agda.TypeChecking.Monad.Benchmark
 Agda.TypeChecking.Monad.Builtin
 Agda.TypeChecking.Monad.Caching
 Agda.TypeChecking.Monad.Closure
 Agda.TypeChecking.Monad.Constraints
 Agda.TypeChecking.Monad.Context
 Agda.TypeChecking.Monad.Debug
 Agda.TypeChecking.Monad.Env
 Agda.TypeChecking.Monad.Imports
 Agda.TypeChecking.Monad.Local
 Agda.TypeChecking.Monad.MetaVars
 Agda.TypeChecking.Monad.Mutual
 Agda.TypeChecking.Monad.Open
 Agda.TypeChecking.Monad.Options
 Agda.TypeChecking.Monad.Sharing
 Agda.TypeChecking.Monad.Signature
 Agda.TypeChecking.Monad.SizedTypes
 Agda.TypeChecking.Monad.State
 Agda.TypeChecking.Monad.Statistics
 Agda.TypeChecking.Monad.Trace
 Agda.TypeChecking.Patterns
 Agda.TypeChecking.Polarity
 Agda.TypeChecking.Positivity
 Agda.TypeChecking.Pretty
 Agda.TypeChecking.Primitive
 Agda.TypeChecking.ProjectionLike
 Agda.TypeChecking.Quote
 Agda.TypeChecking.ReconstructParameters
 Agda.TypeChecking.RecordPatterns
 Agda.TypeChecking.Records
 Agda.TypeChecking.Reduce
 Agda.TypeChecking.Rewriting
 Agda.TypeChecking.Rules
 Agda.TypeChecking.Serialise
 Agda.TypeChecking.SizedTypes
 Agda.TypeChecking.Substitute
 Agda.TypeChecking.SyntacticEquality
 Agda.TypeChecking.Telescope
 Agda.TypeChecking.Unquote
 Agda.TypeChecking.Warnings
 Agda.TypeChecking.With
 Agda.Utils
 Agda.Utils.AssocList
 Agda.Utils.Bag
 Agda.Utils.Benchmark
 Agda.Utils.BiMap
 Agda.Utils.Char
 Agda.Utils.Cluster
 Agda.Utils.Either
 Agda.Utils.Empty
 Agda.Utils.Environment
 Agda.Utils.Except
 Agda.Utils.Favorites
 Agda.Utils.FileName
 Agda.Utils.Function
 Agda.Utils.Functor
 Agda.Utils.Geniplate
 Agda.Utils.Graph
 Agda.Utils.Graph.AdjacencyMap
 Agda.Utils.Hash
 Agda.Utils.HashMap
 Agda.Utils.Haskell
 Agda.Utils.IO
 Agda.Utils.IORef
 Agda.Utils.Impossible
 Agda.Utils.IndexedList
 Agda.Utils.Lens
 Agda.Utils.List
 Agda.Utils.ListT
 Agda.Utils.Map
 Agda.Utils.Maybe
 Agda.Utils.Memo
 Agda.Utils.Monad
 Agda.Utils.Monoid
 Agda.Utils.Null
 Agda.Utils.Parser
 Agda.Utils.PartialOrd
 Agda.Utils.Permutation
 Agda.Utils.Pointer
 Agda.Utils.Pretty
 Agda.Utils.SemiRing
 Agda.Utils.Singleton
 Agda.Utils.Size
 Agda.Utils.String
 Agda.Utils.Suffix
 Agda.Utils.Three
 Agda.Utils.Time
 Agda.Utils.Trie
 Agda.Utils.Tuple
 Agda.Utils.TypeLevel
 Agda.Utils.Update
 Agda.Utils.VarSet
 Agda.Utils.Warshall
 Agda.Version
 Agda.VersionCommit
Agda 2
Table of contents:
 Documentation
 Prerequisites
 Installing Agda
 Configuring the Emacs mode
 Installing Emacs under Windows
Note that this README only discusses installation of Agda, not its standard library. See the Agda Wiki for information about the library.
Documentation
Prerequisites
You need recent versions of the following programs:
 GHC: http://www.haskell.org/ghc/
 cabalinstall: http://www.haskell.org/cabal/
 Alex: http://www.haskell.org/alex/
 Happy: http://www.haskell.org/happy/
 cpphs: http://projects.haskell.org/cpphs/
 GNU Emacs: http://www.gnu.org/software/emacs/
You should also make sure that programs installed by cabalinstall are on your shell’s search path.
For instructions on installing a suitable version of Emacs under Windows, see below.
NonWindows users need to ensure that the development files for the C libraries zlib and ncurses are installed (see http://zlib.net and http://www.gnu.org/software/ncurses/). Your package manager may be able to install these files for you. For instance, on Debian or Ubuntu it should suffice to run
aptget install zlib1gdev libncurses5dev
as root to get the correct files installed.
Optionally one can also install the ICU
library, which is used to implement the countclusters
flag. Under
Debian or Ubuntu it may suffice to install libicudev
. Once the ICU
library is installed one can hopefully enable the countclusters
flag by giving the fenableclustercounting
flag to cabal install
. Note that make install
by default enables
fenableclustercounting
.
Note on GHC’s CPP language extension
Recent versions of Clang’s preprocessor don’t work well with Haskell. In order to get some dependencies to build, you may need to set up Cabal to have GHC use cpphs by default. You can do this by adding
programdefaultoptions
ghcoptions: pgmPcpphs optPcpp
to your .cabal/config file. (You must be using cabal >= 1.18. Note that some packages may not compile with this option set.)
You don’t need to set this option to install Agda from the current development source; Agda.cabal now uses cpphs.
Installing Agda
There are several ways to install Agda:
Using a binary package prepared for your platform
Recommended if such a package exists. See the Agda Wiki.
Using a released source package from Hackage
Install the prerequisites mentioned above, then run the following commands:
cabal update
cabal install Agda
agdamode setup
The last command tries to set up Emacs for use with Agda. As an alternative you can copy the following text to your .emacs file:
(loadfile (let ((codingsystemforread 'utf8))
(shellcommandtostring "agdamode locate")))
It is also possible (but not necessary) to compile the Emacs mode’s files:
agdamode compile
This can, in some cases, give a noticeable speedup.
WARNING: If you reinstall the Agda mode without recompiling the Emacs Lisp files, then Emacs may continue using the old, compiled files.
Using the development version of the code
You can obtain tarballs of the development version from the Agda Wiki, or clone the repository.
Install the prerequisites discussed in Prerequisites.
Then, either:
(1a) Run the following commands in the toplevel directory of the Agda source tree to install Agda:
cabal update
cabal install
(1b) Run agdamode setup
to set up Emacs for use with Agda. Alternatively,
add the following text to your .emacs file:
(loadfile (let ((codingsystemforread 'utf8))
(shellcommandtostring "agdamode locate")))
It is also possible (but not necessary) to compile the Emacs mode’s files:
agdamode compile
This can, in some cases, give a noticeable speedup.
WARNING: If you reinstall the Agda mode without recompiling the Emacs Lisp files, then Emacs may continue using the old compiled files.
(2) Or, you can try to install Agda (including a compiled Emacs mode) by running the following command:
make install
Configuring the Emacs mode
If you want to you can customise the Emacs mode. Just start Emacs and type the following:
Mx loadlibrary RET agda2mode RET
Mx customizegroup RET agda2 RET
This is useful if you want to change the Agda search path, in which case you should change the agda2includedirs variable.
If you want some specific settings for the Emacs mode you can add them to agda2modehook. For instance, if you do not want to use the Agda input method (for writing various symbols like ∀≥ℕ→π⟦⟧) you can add the following to your .emacs:
(addhook 'agda2modehook
'(lambda ()
; If you do not want to use any input method:
(deactivateinputmethod)
; (In some versions of Emacs you should use
; inactivateinputmethod instead of
; deactivateinputmethod.)
; If you want to use the X input method:
(setinputmethod "X")))
Note that, on some systems, the Emacs mode changes the default font of the current frame in order to enable many Unicode symbols to be displayed. This only works if the right fonts are available, though. If you want to turn off this feature, then you should customise the agda2fontsetname variable.
Installing Emacs under Windows
A precompiled version of Emacs 24.3, with the necessary mathematical fonts, is available at http://homepage.cs.uiowa.edu/~astump/agda/
Hacking on Agda
Head to HACKING
Changes
Release notes for Agda version 2.5.3
Installation and infrastructure

Added support for GHC 8.0.2 and 8.2.1.

Removed support for GHC 7.6.3.

Markdown support for literate Agda [PR #2357].
Files ending in
.lagda.md
will be parsed as literate Markdown files. Code blocks start with
```
or```agda
in its own line, and end with```
, also in its own line.  Code blocks which should be typechecked by Agda but should not be visible
when the Markdown is rendered may be enclosed in HTML comment delimiters
(
<!
and>
).  Code blocks which should be ignored by Agda, but rendered in the final document may be indented by four spaces.
 Note that inline code fragments are not supported due to the difficulty of interpreting their indentation level with respect to the rest of the file.
 Code blocks start with
Language
Pattern matching

Dot patterns.
The dot in front of an inaccessible pattern can now be skipped if the pattern consists entirely of constructors or literals. For example:
open import Agda.Builtin.Bool data D : Bool → Set where c : D true f : (x : Bool) → D x → Bool f true c = true
Before this change, you had to write
f .true c = true
. 
Withclause patterns can be replaced by _ [Issue #2363]. Example:
test : Nat → Set test zero with zero test _  _ = Nat test (suc x) with zero test _  _ = Nat
We do not have to spell out the pattern of the parent clause (
zero
/suc x
) in the withclause if we do not need the pattern variables. Note thatx
is not in scope in the withclause!A more elaborate example, which cannot be reduced to an ellipsis
...
:record R : Set where coinductive  disallow matching field f : Bool n : Nat data P (r : R) : Nat → Set where fTrue : R.f r ≡ true → P r zero nSuc : P r (suc (R.n r)) data Q : (b : Bool) (n : Nat) → Set where true! : Q true zero suc! : ∀{b n} → Q b (suc n) test : (r : R) {n : Nat} (p : P r n) → Q (R.f r) n test r nSuc = suc! test r (fTrue p) with R.f r test _ (fTrue ())  false test _ _  true = true!  underscore instead of (isTrue _)

Pattern matching lambdas (also known as extended lambdas) can now be nullary, mirroring the behaviour for ordinary function definitions. [Issue #2671]
This is useful for case splitting on the result inside an expression: given
record _×_ (A B : Set) : Set where field π₁ : A π₂ : B open _×_
one may case split on the result (Cc Cc RET) in a hole
λ { → {!!}}
of type A × B to produce
λ { .π₁ → {!!} ; .π₂ → {!!}}

Records with a field of an empty type are now recognized as empty by Agda. In particular, they can be matched against with an absurd pattern (). For example:
data ⊥ : Set where record Empty : Set where field absurdity : ⊥ magic : Empty → ⊥ magic ()

Injective pragmas.
Injective pragmas can be used to mark a definition as injective for the pattern matching unifier. This can be used as a version of
injectivetypeconstructors
that only applies to specific datatypes. For example:open import Agda.Builtin.Equality data Fin : Nat → Set where zero : {n : Nat} → Fin (suc n) suc : {n : Nat} → Fin n → Fin (suc n) {# INJECTIVE Fin #} Fininjective : {m n : Nat} → Fin m ≡ Fin n → m ≡ n Fininjective refl = refl
Aside from datatypes, this pragma can also be used to mark other definitions as being injective (for example postulates).

Metavariables can no longer be instantiated during case splitting. This means Agda will refuse to split instead of taking the first constructor it finds. For example:
open import Agda.Builtin.Nat data Vec (A : Set) : Nat → Set where nil : Vec A 0 cons : {n : Nat} → A → Vec A n → Vec A (suc n) foo : Vec Nat _ → Nat foo x = {!x!}
In Agda 2.5.2, case splitting on
x
produced the single clausefoo nil = {!!}
, but now Agda refuses to split.
Reflection

New TC primitive:
debugPrint
.debugPrint : String → Nat → List ErrorPart → TC ⊤
This maps to the internal function
reportSDoc
. Debug output is enabled with thev
flag at the command line, or in anOPTIONS
pragma. For instance, givingv a.b.c:10
enables printing fromdebugPrint "a.b.c.d" 10 msg
. In the Emacs mode, debug output ends up in the*Agda debug*
buffer.
Builtins

BUILTIN REFL is now superfluous, subsumed by BUILTIN EQUALITY [Issue #2389].

BUILTIN EQUALITY is now more liberal [Issue #2386]. It accepts, among others, the following new definitions of equality:
 Nonuniverse polymorphic: data _≡_ {A : Set} (x : A) : A → Set where refl : x ≡ x  ... with explicit argument to refl; data _≡_ {A : Set} : (x y : A) → Set where refl : {x : A} → x ≡ x  ... even visible data _≡_ {A : Set} : (x y : A) → Set where refl : (x : A) → x ≡ x  Equality in a different universe than domain:  (also with explicit argument to refl) data _≡_ {a} {A : Set a} (x : A) : A → Set where refl : x ≡ x
The standard definition is still:
 Equality in same universe as domain: data _≡_ {a} {A : Set a} (x : A) : A → Set a where refl : x ≡ x
Miscellaneous

Rule change for omitted toplevel module headers. [Issue #1077]
If your file is named
Bla.agda
, then the following content is rejected.foo = Set module Bla where bar = Set
Before the fix of this issue, Agda would add the missing module header
module Bla where
at the top of the file. However, in this particular case it is more likely the user put the declarationfoo = Set
before the module start in error. Now you get the errorIllegal declaration(s) before toplevel module
if the following conditions are met:

There is at least one nonimport declaration or nontoplevel pragma before the start of the first module.

The module has the same name as the file.

The module is the only module at this level (may have submodules, of course).
If you should see this error, insert a toplevel module before the illegal declarations, or move them inside the existing module.

Emacs mode

New warnings:

Unreachable clauses give rise to a simple warning. They are highlighted in gray.

Incomplete patterns are nonfatal warnings: it is possible to keep interacting with the file (the reduction will simply be stuck on arguments not matching any pattern). The definition with incomplete patterns are highlighted in wheat.


Clauses which do not hold definitionally are now highlighted in white smoke.

Fewer commands have the side effect that the buffer is saved.

Aborting commands.
Now one can (try to) abort an Agda command by using
Cc Cx Ca
or a menu entry. The effect is similar to that of restarting Agda (Cc Cx Cr
), but some state is preserved, which could mean that it takes less time to reload the module.Warning: If a command is aborted while it is writing data to disk (for instance .agdai files or Haskell files generated by the GHC backend), then the resulting files may be corrupted. Note also that external commands (like GHC) are not aborted, and their output may continue to be sent to the Emacs mode.

New bindings for the Agda input method:

All the bold digits are now available. The naming scheme is
\Bx
for digitx
. 
Typing
\:
you can now get a whole slew of colons.(The Agda input method originally only bound the standard unicode colon, which looks deceptively like the normal colon.)


Case splitting now preserves underscores. [Issue #819]
data ⊥ : Set where test : {A B : Set} → A → ⊥ → B test _ x = {! x !}
Splitting on
x
yieldstest _ ()

Interactively expanding ellipsis. [Issue #2589] An ellipsis in a withclause can be expanded by splitting on “variable” “.” (dot).
test0 : Nat → Nat test0 x with zero ...  q = {! . !}  Cc Cc
Splitting on dot here yields:
test0 x  q = ?

New command to check an expression against the type of the hole it is in and see what it elaborates to. [Issue #2700] This is useful to determine e.g. what solution typeclass resolution yields. The command is bound to
Cc C;
and respects theCu
modifier.record Pointed (A : Set) : Set where field point : A it : ∀ {A : Set} {{x : A}} → A it {{x}} = x instance _ = record { point = 3  4 } _ : Pointed Nat _ = {! it !}  Cu Cu Cc C;
yields
Goal: Pointed Nat Elaborates to: record { point = 0 }

If
agda2give
is called with a prefix, then giving is forced, i.e., the safety checks are skipped, including positivity, termination, and double typechecking. [Issue #2730]Invoke forced giving with key sequence
Cu Cc CSPC
.
Library management

The
name
field in an.agdalib
file is now optional. [Issue #2708]This feature is convenient if you just want to specify the dependencies and include pathes for your local project in an
.agdalib
file.Naturally, libraries without names cannot be depended on.
Compiler backends

Unified compiler pragmas
The compiler pragmas (
COMPILED
,COMPILED_DATA
, etc.) have been unified across backends into two new pragmas:{# COMPILE <Backend> <Name> <Text> #} {# FOREIGN <Backend> <Text> #}
The old pragmas still work, but will emit a warning if used. They will be removed completely in Agda 2.6.
The translation of old pragmas into new ones is as follows:
Old New {# COMPILED f e #}
{# COMPILE GHC f = e #}
{# COMPILED_TYPE A T #}
{# COMPILE GHC A = type T #}
{# COMPILED_DATA A D C1 .. CN #}
`{# COMPILE GHC A = data D (C1 {# COMPILED_DECLARE_DATA #}
obsolete, removed {# COMPILED_EXPORT f g #}
{# COMPILE GHC f as g #}
{# IMPORT M #}
{# FOREIGN GHC import qualified M #}
{# HASKELL code #}
{# FOREIGN GHC code #}
{# COMPILED_UHC f e #}
{# COMPILE UHC f = e #}
{# COMPILED_DATA_UHC A D C1 .. CN #}
`{# COMPILE UHC A = data D (C1 {# IMPORT_UHC M #}
{# FOREIGN UHC __IMPORT__ M #}
{# COMPILED_JS f e #}
{# COMPILE JS f = e #}

GHC Haskell backend
The COMPILED pragma (and the corresponding COMPILE GHC pragma) is now also allowed for functions. This makes it possible to have both an Agda implementation and a native Haskell runtime implementation.
The GHC file header pragmas
LANGUAGE
,OPTIONS_GHC
, andINCLUDE
inside aFOREIGN GHC
pragma are recognized and printed correctly at the top of the generated Haskell file. [Issue #2712] 
UHC compiler backend
The UHC backend has been moved to its own repository [https://github.com/agda/agdauhc] and is no longer part of the Agda distribution.

Haskell imports are no longer transitively inherited from imported modules.
The (now deprecated) IMPORT and IMPORT_UHC pragmas no longer cause import statements in modules importing the module containing the pragma.
The same is true for the corresponding FOREIGN pragmas.

Support for standalone backends.
There is a new API in
Agda.Compiler.Backend
for creating standalone backends using Agda as a library. This allows prospective backend writers to experiment with new backends without having to change the Agda code base.
HTML backend

Anchors for identifiers (excluding bound variables) are now the identifiers themselves rather than just the file position [Issue #2604].
Symbolic anchors look like
<a id="test1"> <a id="M.bla">
while other anchors just give the character position in the file:
<a id="42">
Toplevel module names do not get a symbolic anchor, since the position of a toplevel module is defined to be the beginning of the file.
Example:
module Issue2604 where  Character position anchor test1 : Set₁  Issue2604.html#test1 test1 = bla where bla = Set  Character position anchor test2 : Set₁  Issue2604.html#test2 test2 = bla where bla = Set  Character position anchor test3 : Set₁  Issue2604.html#test3 test3 = bla module M where  Issue2604.html#M bla = Set  Issue2604.html#M.bla module NamedModule where  Issue2604.html#NamedModule test4 : Set₁  Issue2604.html#NamedModule.test4 test4 = M.bla module _ where  Character position anchor test5 : Set₁  Character position anchor test5 = M.bla

Some generated HTML files now have different file names [Issue #2725].
Agda now uses an encoding that amounts to first converting the module names to UTF8, and then percentencoding the resulting bytes. For instance, HTML for the module
Σ
is placed in%CE%A3.html
.
LaTeX backend

The LaTeX backend now handles indentation in a different way [Issue #1832].
A constraint on the indentation of the first token t on a line is determined as follows:
 Let T be the set containing every previous token (in any code block) that is either the initial token on its line or preceded by at least one whitespace character.
 Let S be the set containing all tokens in T that are not shadowed by other tokens in T. A token t₁ is shadowed by t₂ if t₂ is further down than t₁ and does not start to the right of t₁.
 Let L be the set containing all tokens in S that start to the left of t, and E be the set containing all tokens in S that start in the same column as t.
 The constraint is that t must be indented further than every token in L, and aligned with every token in E.
Note that if any token in L or E belongs to a previous code block, then the constraint may not be satisfied unless (say) the
AgdaAlign
environment is used in an appropriate way.If custom settings are used, for instance if
\AgdaIndent
is redefined, then the constraint discussed above may not be satisfied. (Note that the meaning of the\AgdaIndent
command’s argument has changed, and that the command is now used in a different way in the generated LaTeX files.)Examples:

Here
C
is indented further thanB
:postulate A B C : Set

Here
C
is not (necessarily) indented further thanB
, becauseX
shadowsB
:postulate A B : Set X C : Set
The new rule is inspired by, but not identical to, the one used by lhs2TeX’s poly mode (see Section 8.4 of the manual for lhs2TeX version 1.17).

Some spacing issues [#2353, #2441, #2733, #2740] have been fixed.

The user can now control the typesetting of (certain) individual tokens by redefining the
\AgdaFormat
command. Example:\usepackage{ifthen} % Insert extra space before some tokens. \DeclareRobustCommand{\AgdaFormat}[2]{% \ifthenelse{ \equal{#1}{≡⟨} \OR \equal{#1}{≡⟨⟩} \OR \equal{#1}{∎} }{\ }{}#2}
Note the use of
\DeclareRobustCommand
. The first argument to\AgdaFormat
is the token, and the second argument the thing to be typeset. 
One can now instruct the agda package not to select any fonts.
If the
nofontsetup
option is used, then some font packages are loaded, but specific fonts are not selected:\usepackage[nofontsetup]{agda}

The height of empty lines is now configurable [#2734].
The height is controlled by the length
\AgdaEmptySkip
, which by default is\baselineskip
. 
The alignment feature regards the string
+̲
, containing+
and a combining character, as having length two. However, it seems more reasonable to treat it as having length one, as it occupies a single column, if displayed “properly” using a monospace font. The new flagcountclusters
is an attempt at fixing this. When this flag is enabled the backend counts “extended grapheme clusters” rather than code points.Note that this fix is not perfect: a single extended grapheme cluster might be displayed in different ways by different programs, and might, in some cases, occupy more than one column. Here are some examples of extended grapheme clusters, all of which are treated as a single character by the alignment algorithm:
│ │ │+̲│ │Ö̂│ │நி│ │ᄀힰᇹ│ │ᄀᄀᄀᄀᄀᄀힰᇹᇹᇹᇹᇹᇹ│ │ │
Note also that the layout machinery does not count extended grapheme clusters, but code points. The following code is syntactically correct, but if
countclusters
is used, then the LaTeX backend does not align the twofield
keywords:record +̲ : Set₁ where field A : Set field B : Set
The
countclusters
flag is not enabled in all builds of Agda, because the implementation depends on the ICU library, the installation of which could cause extra trouble for some users. The presence of this flag is controlled by the Cabal flagenableclustercounting
. 
A faster variant of the LaTeX backend: QuickLaTeX.
When this variant of the backend is used the toplevel module is not typechecked, only scopechecked. This implies that some highlighting information is not available. For instance, overloaded constructors are not resolved.
QuickLaTeX can be invoked from the Emacs mode, or using
agda latex onlyscopechecking
. If the module has already been typechecked successfully, then this information is reused; in this case QuickLaTeX behaves like the regular LaTeX backend.The
onlyscopechecking
flag can also be used independently, but it is perhaps unclear what purpose that would serve. (The flag can currently not be combined withhtml
,dependencygraph
orvim
.) The flag is not allowed in safe mode.
Pragmas and options

The
safe
option is now a valid pragma.This makes it possible to declare a module as being part of the safe subset of the language by stating
{# OPTIONS safe #}
at the top of the corresponding file. Incompatibilities between thesafe
option and other options or language constructs are nonfatal errors. 
The
nomain
option is now a valid pragma.One can now suppress the compiler warning about a missing main function by putting
{# OPTIONS nomain #}
on top of the file.

New commandline option and pragma
warning=MODE
(orW MODE
) for setting the warning mode. Current options arewarn
for displaying warnings (default)error
for turning warnings into errorsignore
for not displaying warnings
List of fixed issues
For 2.5.3, the following issues have been fixed (see bug tracker):
 #142: Inherited dot patterns in with functions are not checked
 #623: Error message points to importing module rather than imported module
 #657: Yet another display form problem
 #668: Ability to stop, or restart, typechecking somehow
 #705: confusing error message for ambiguous datatype module name
 #719: Error message for duplicate module definition points to external module instead of internal module
 #776: Unsolvable constraints should give error
 #819: Casesplitting doesn’t preserve underscores
 #883: Rewrite loses type information
 #899: Instance search fails if there are several definitionally equal values in scope
 #1077: problem with module syntax, with parametric module import
 #1126: Port optimizations from the Epic backend
 #1175: Internal Error in Auto
 #1544: Positivity polymorphism needed for compositional positivity analysis
 #1611: Interactive splitting instantiates meta
 #1664: Add Reflection primitives to expose precedence and fixity
 #1817: Solvable size constraints reported as unsolvable
 #1832: Insufficient indentation in LaTeXrendered Agda code
 #1834: Copattern matching: order of clauses should not matter here
 #1886: Second copies of telescopes not checked?
 #1899: Positivity checker does not treat datatypes and record types in the same way
 #1975: Typeincorrect instantiated overloaded constructor accepted in pattern
 #1976: Typeincorrect instantiated projection accepted in pattern
 #2035: Matching on string causes solver to fail with internal error
 #2146: Unicode syntax for instance arguments
 #2217: Abort Agda without losing state
 #2229: Absence or presence of toplevel module header affects scope
 #2253: Wrong scope error for abstract constructors
 #2261: Internal error in Auto/CaseSplit.hs:284
 #2270: Printer does not use sections.
 #2329: Size solver does not use type
Size< i
to gain the necessary information  #2354: Interaction between instance search, size solver, and ordinary constraint solver.
 #2355: Literate Agda parser does not recognize TeX comments
 #2360: With clause stripping chokes on ambiguous projection
 #2362: Printing of parent patterns when withclause does not match
 #2363: Allow underscore in withclause patterns
 #2366: Withclause patterns renamed in error message
 #2368: Internal error after refining a tactic @ MetaVars.hs:267
 #2371: Shadowed module parameter crashes interaction
 #2372: problems when instances are declared with inferred types
 #2374: Ambiguous projection pattern could be disambiguated by visibility
 #2376: Termination checking interacts badly with etacontraction
 #2377: open public is useless before module header
 #2381: Search (
Cc Cz
) panics on pattern synonyms  #2386: Relax requirements of BUILTIN EQUALITY
 #2389: BUILTIN REFL not needed
 #2400: LaTeX backend error on LaTeX comments
 #2402: Parameters not dropped when reporting incomplete patterns
 #2403: Termination checker should reduce arguments in structural order check
 #2405: instance search failing in parameterized module
 #2408: DLub sorts are not serialized
 #2412: Problem with checking with sized types
 #2413: Agda crashes on [email protected] pattern
 #2415: Size solver reports “inconsistent upper bound” even though there is a solution
 #2416: Cannot give size as computed by solver
 #2422: Overloaded inherited projections don’t resolve
 #2423: Inherited projection on lhs
 #2426: On just warning about missing cases
 #2429: Irrelevant lambda should be accepted when relevant lambda is expected
 #2430: Another regression related to parameter refinement?
 #2433: rebindLocalRewriteRules readds global rewrite rules
 #2434: Exact split analysis is too strict when matching on eta record constructor
 #2441: Incorrect alignement in latex using the new ACM format
 #2444: Generalising compiler pragmas
 #2445: The LaTeX backend is slow
 #2447: Cache loaded interfaces even if a type error is encountered
 #2449: Agda depends on additional C library icu
 #2451: Agda panics when attempting to rewrite a typeclass Eq
 #2456: Internal error when postulating instance
 #2458: Regression: Agda2.5.3 loops where Agda2.5.2 passes
 #2462: Overloaded postfix projection does not resolve
 #2464: Eta contraction for irrelevant functions breaks subject reduction
 #2466: Case split to make hidden variable visible does not work
 #2467: REWRITE without BUILTIN REWRITE crashes
 #2469: “Partial” pattern match causes segfault at runtime
 #2472: Regression related to the auto command
 #2477: Sized data type analysis brittle, does not reduce size
 #2478: Multiply defined labels on the user manual (pdf)
 #2479: “Occurs check” error in generated Haskell code
 #2480: Agda accepts incorrect (?) code, subject reduction broken
 #2482: Wrong counting of data parameters with newstyle mutual blocks
 #2483: Files are sometimes truncated to a size of 201 bytes
 #2486: Imports via FOREIGN are not transitively inherited anymore
 #2488: Instance search inhibits holes for instance fields
 #2493: Regression: Agda seems to loop when expression is given
 #2494: Instance fields sometimes have incorrect goal types
 #2495: Regression: termination checker of Agda2.5.3 seemingly loops where Agda2.5.2 passes
 #2500: Adding fields to a record can cause Agda to reject previous definitions
 #2510: Wrong error with –nopatternmatching
 #2517: “Not a variable error”
 #2518: CopatternReductions in TreeLess
 #2523: The documentation of
withoutK
is outdated  #2529: Unable to install Agda on Windows.
 #2537: case splitting with ‘with’ creates {_} instead of replicating the arguments it found.
 #2538: Internal error when parsing aspattern
 #2543: Case splitting with ellipsis produces spurious parentheses
 #2545: Race condition in api tests
 #2549: Rewrite rule for higher path constructor does not fire
 #2550: Internal error in Agda.TypeChecking.Substitute
 #2552: Let bindings in module telescopes crash Agda.Interaction.BasicOps
 #2553: Internal error in Agda.TypeChecking.CheckInternal
 #2554: More flexible sizeassignment in successor style
 #2555: Why does the positivity checker care about nonrecursive occurrences?
 #2558: Internal error in Warshall Solver
 #2560: Internal Error in Reduce.Fast
 #2564: Nonexactsplit highlighting makes other highlighting disappear
 #2568: agda2infertypemaybetoplevel (in hole) does not respect “singlesolution” requirement of instance resolution
 #2571: Record pattern translation does not eta contract
 #2573: Rewrite rules fail depending on unrelated changes
 #2574: No link attached to module without toplevel name
 #2575: Internal error, related to caching
 #2577: deBruijn fail for higher order instance problem
 #2578: Catchall clause face used incorrectly for parent with pattern
 #2579: Import statements with module instantiation should not trigger an error message
 #2580: Implicit absurd match is NonVariant, explicit not
 #2583: Wrong de Bruijn index introduced by absurd pattern
 #2584: Duplicate warning printing
 #2585: Definition by copatterns not modulo eta
 #2586: “λ where” with single absurd clause not parsed
 #2588:
agda latex
produces invalid LaTeX when there are block comments  #2592: Internal Error in Agda/TypeChecking/Serialise/Instances/Common.hs
 #2597: Inline record definitions confuse the reflection API
 #2602: Debug output messes up AgdaInfo buffer
 #2603: Internal error in MetaVars.hs
 #2604: Use QNames as anchors in generated HTML
 #2605: HTML backend generates anchors for whitespace
 #2606: Check that LHS of a rewrite rule doesn’t reduce is too strict
 #2612:
exactsplit
documentation is outdated and incomplete  #2613: Parametrised modules, withabstraction and termination
 #2620: Internal error in auto.
 #2621: Case splitting instantiates meta
 #2626: triggered internal error with sized types in MetaVars module
 #2629: Exact splitting should not complain about absurd clauses
 #2631: docs for auto aren’t clear on how to use flags/options
 #2632: some flags to auto dont seem to work in current agda 2.5.2
 #2637: Internal error in Agda.TypeChecking.Pretty, possibly related to sized types
 #2639: Performance regression, possibly related to the size solver
 #2641: Required instance of FromNat when compiling imported files
 #2642: Records with duplicate fields
 #2644: Wrong substitution in expandRecordVar
 #2645: Agda accepts postulated fields in a record
 #2646: Only warn if fixities for undefined symbols are given
 #2649: Empty list of “previous definition” in duplicate definition error
 #2652: Added a new variant of the colon to the Agda input method
 #2653: agdamode: “cannot refine” inside instance argument even though term to be refined typechecks there
 #2654: Internal error on result splitting without –postfixprojections
 #2664: Segmentation fault with compiled programs using mutual record
 #2665: Documentation: Record update syntax in wrong location
 #2666: Internal error at Agda/Syntax/Abstract/Name.hs:113
 #2667: Panic error on unbound variable.
 #2669: Interaction: incorrect field variable name generation
 #2671: Feature request: nullary pattern matching lambdas
 #2679: Internal error at “Typechecking/Abstract.hs:133” and “TypeChecking/Telescope.hs:68”
 #2682: What are the rules for projections of abstract records?
 #2684: Bad error message for abstract constructor
 #2686: Abstract constructors should be ignored when resolving overloading
 #2690: [regression?] Agda engages in deep search instead of immediately failing
 #2700: Add a command to check against goal type (and normalise)
 #2703: Regression: Internal error for underapplied indexed constructor
 #2705: The GHC backend might diverge in infinite file creation
 #2708: Why is the
name
field in .agdalib files mandatory?  #2710: Type checker hangs
 #2712: Compiler Pragma for headers
 #2714: Option –nomain should be allowed as filelocal option
 #2717: internal error at DisplayForm.hs:197
 #2718: Interactive ‘give’ doesn’t insert enough parenthesis
 #2721: WithoutK doesn’t prevent heterogeneous conflict between literals
 #2723: Unreachable clauses in definition by copattern matching trip clause compiler
 #2725: File names for generated HTML files
 #2726: Old regression related to with
 #2727: Internal errors related to rewrite
 #2729: Regression: case splitting uses variable name variants instead of the unused original names
 #2730: Command to give in spite of termination errors
 #2731: Agda fails to build with happy 1.19.6
 #2733: Avoid some uses of \AgdaIndent?
 #2734: Make height of empty lines configurable
 #2736: Segfault using Alex 3.2.2 and cpphs
 #2740: Indenting every line of code should be a noop
Release notes for Agda version 2.5.2
Installation and infrastructure

Modular support for literate programming
Literate programming support has been moved out of the lexer and into the
Agda.Syntax.Parser.Literate
module.Files ending in
.lagda
are still interpreted as literate TeX. The extension.lagda.tex
may now also be used for literate TeX files.Support for more literate code formats and extensions can be added modularly.
By default,
.lagda.*
files are opened in the Emacs mode corresponding to their last extension. One may switch to and from Agda mode manually. 
reStructuredText
Literate Agda code can now be written in reStructuredText format, using the
.lagda.rst
extension.As a general rule, Agda will parse code following a line ending in
::
, as long as that line does not start with..
. The module name must match the path of the file in the documentation, and must be given explicitly. Several files have been converted already, for instance:language/mixfixoperators.lagda.rst
tools/compilers.lagda.rst
Note that:
 Code blocks inside an rST comment block will be typechecked by Agda, but not rendered in the documentation.
 Code blocks delimited by
.. codeblock:: agda
will be rendered in the final documenation, but not typechecked by Agda.  All lines inside a codeblock must be further indented than the first line of the code block.
 Indentation must be consistent between code blocks. In other words, the file as a whole must be a valid Agda file if all the literate text is replaced by white space.

Documentation testing
All documentation files in the
doc/usermanual
directory that end in.lagda.rst
can be typechecked by runningmake usermanualtest
, and also as part of the general test suite. 
Support installation through Stack
The Agda sources now also include a configuration for the stack install tool (tested through continuous integration).
It should hence be possible to repeatably build any future Agda version (including unreleased commits) from source by checking out that version and running
stack install
from the checkout directory. By using repeatable builds, this should keep selecting the same dependencies in the face of new releases on Hackage.For further motivation, see Issue #2005.

Removed the
test
commandline optionThis option ran the internal testsuite. This testsuite was implemented using Cabal supports for testsuites. [Issue #2083].

The
nodefaultlibraries
flag has been split into two flags [Issue #1937]nodefaultlibraries
: Ignore the defaults file but still look for local.agdalib
filesnolibraries
: Don’t use any.agdalib
files (the previous behaviour ofnodefaultlibraries
).

If
agda
was built insidegit
repository, then theversion
flag will display the hash of the commit used, and whether the tree wasdirty
(i.e. there were uncommited changes in the working directory). Otherwise, only the version number is shown.
Language

Dot patterns are now optional
Consider the following program
data Vec (A : Set) : Nat → Set where [] : Vec A zero cons : ∀ n → A → Vec A n → Vec A (suc n) vmap : ∀ {A B} n → (A → B) → Vec A n → Vec B n vmap .zero f [] = [] vmap .(suc m) f (cons m x xs) = cons m (f x) (vmap m f xs)
If we don’t care about the dot patterns they can (and could previously) be replaced by wildcards:
vmap : ∀ {A B} n → (A → B) → Vec A n → Vec B n vmap _ f [] = [] vmap _ f (cons m x xs) = cons m (f x) (vmap m f xs)
Now it is also allowed to give a variable pattern in place of the dot pattern. In this case the variable will be bound to the value of the dot pattern. For our example:
vmap : ∀ {A B} n → (A → B) → Vec A n → Vec B n vmap n f [] = [] vmap n f (cons m x xs) = cons m (f x) (vmap m f xs)
In the first clause
n
reduces tozero
and in the second clausen
reduces tosuc m
. 
Module parameters can now be refined by pattern matching
Previously, pattern matches that would refine a variable outside the current lefthand side was disallowed. For instance, the following would give an error, since matching on the vector would instantiate
n
.module _ {A : Set} {n : Nat} where f : Vec A n → Vec A n f [] = [] f (x ∷ xs) = x ∷ xs
Now this is no longer disallowed. Instead
n
is bound to the appropriate value in each clause. 
Withabstraction now abstracts also in module parameters
The change that allows pattern matching to refine module parameters also allows withabstraction to abstract in them. For instance,
module _ (n : Nat) (xs : Vec Nat (n + n)) where f : Nat f with n + n f  nn = ?  xs : Vec Nat nn
Note: Any function argument or lambdabound variable bound outside a given function counts as a module parameter.
To prevent abstraction in a parameter you can hide it inside a definition. In the above example,
module _ (n : Nat) (xs : Vec Nat (n + n)) where ys : Vec Nat (n + n) ys = xs f : Nat f with n + n f  nn = ?  xs : Vec Nat nn, ys : Vec Nat (n + n)

Aspatterns [Issue #78].
Aspatterns (
@
patterns) are finally working and can be used to name a pattern. The name has the same scope as normal pattern variables (i.e. the righthand side, where clause, and dot patterns). The name reduces to the value of the named pattern. For example::module _ {A : Set} (_<_ : A → A → Bool) where merge : List A → List A → List A merge xs [] = xs merge [] ys = ys merge [email protected](x ∷ xs₁) [email protected](y ∷ ys₁) = if x < y then x ∷ merge xs₁ ys else y ∷ merge xs ys₁

Idiom brackets.
There is new syntactic sugar for idiom brackets:
( e a1 .. an )
expands topure e <*> a1 <*> .. <*> an
The desugaring takes place before scope checking and only requires names
pure
and_<*>_
in scope. Idiom brackets work well with operators, for instance( if a then b else c )
desugars topure if_then_else_ <*> a <*> b <*> c
Limitations:

The toplevel application inside idiom brackets cannot include implicit applications, so
( foo {x = e} a b )
is illegal. In the casee
is pure you can write( (foo {x = e}) a b )
which desugars topure (foo {x = e}) <*> a <*> b

Binding syntax and operator sections cannot appear immediately inside idiom brackets.


Layout for pattern matching lambdas.
You can now write pattern matching lambdas using the syntax
λ where false → true true → false
avoiding the need for explicit curly braces and semicolons.

Overloaded projections [Issue #1944].
Ambiguous projections are no longer a scope error. Instead they get resolved based on the type of the record value they are eliminating. This corresponds to constructors, which can be overloaded and get disambiguated based on the type they are introducing. Example:
module _ (A : Set) (a : A) where record R B : Set where field f : B open R public record S B : Set where field f : B open S public
Exporting
f
twice from bothR
andS
is now allowed. Then,r : R A f r = a s : S A f s = f r
disambiguates to:
r : R A R.f r = a s : S A S.f s = R.f r
If the type of the projection is known, it can also be disambiguated unapplied.
unapplied : R A > A unapplied = f

Postfix projections [Issue #1963].
Agda now supports a postfix syntax for projection application. This style is more in harmony with copatterns. For example:
record Stream (A : Set) : Set where coinductive field head : A tail : Stream A open Stream repeat : ∀{A} (a : A) → Stream A repeat a .head = a repeat a .tail = repeat a zipWith : ∀{A B C} (f : A → B → C) (s : Stream A) (t : Stream B) → Stream C zipWith f s t .head = f (s .head) (t .head) zipWith f s t .tail = zipWith f (s .tail) (t .tail) module Fib (Nat : Set) (zero one : Nat) (plus : Nat → Nat → Nat) where {# TERMINATING #} fib : Stream Nat fib .head = zero fib .tail .head = one fib .tail .tail = zipWith plus fib (fib .tail)
The thing we eliminate with projection now is visibly the head, i.e., the leftmost expression of the sequence (e.g.
repeat
inrepeat a .tail
).The syntax overlaps with dot patterns, but for type correct left hand sides there is no confusion: Dot patterns eliminate function types, while (postfix) projection patterns eliminate record types.
By default, Agda prints systemgenerated projections (such as by etaexpansion or case splitting) prefix. This can be changed with the new option:
{# OPTIONS postfixprojections #}
Result splitting in extended lambdas (aka pattern lambdas) always produces postfix projections, as prefix projection pattern do not work here: a prefix projection needs to go left of the head, but the head is omitted in extended lambdas.
dup : ∀{A : Set}(a : A) → A × A dup = λ{ a → ? }
Result splitting (
Cc Cc RET
) here will yield:dup = λ{ a .proj₁ → ? ; a .proj₂ → ? }

Projection parameters [Issue #1954].
When copying a module, projection parameters will now stay hidden arguments, even if the module parameters are visible. This matches the situation we had for constructors since long. Example:
module P (A : Set) where record R : Set where field f : A open module Q A = P A
Parameter
A
is now hidden inR.f
:test : ∀{A} → R A → A test r = R.f r
Note that a module parameter that corresponds to the record value argument of a projection will not be hidden.
module M (A : Set) (r : R A) where open R A r public test' : ∀{A} → R A → A test' r = M.f r

Eager insertion of implicit arguments [Issue #2001]
Implicit arguments are now (again) eagerly inserted in lefthand sides. The previous behaviour of inserting implicits for where blocks, but not righthand sides was not type safe.

Module applications can now be eta expanded/contracted without changing their behaviour [Issue #1985]
Previously definitions exported using
open public
got the incorrect type for underapplied module applications.Example:
module A where postulate A : Set module B (X : Set) where open A public module C₁ = B module C₂ (X : Set) = B X
Here both
C₁.A
andC₂.A
have type(X : Set) → Set
. 
Polarity pragmas.
Polarity pragmas can be attached to postulates. The polarities express how the postulate’s arguments are used. The following polarities are available:
_
: Unused.++
: Strictly positive.+
: Positive.
: Negative.*
: Unknown/mixed.Polarity pragmas have the form
{# POLARITY name <zero or more polarities> #}
and can be given wherever fixity declarations can be given. The listed polarities apply to the given postulate’s arguments (explicit/implicit/instance), from left to right. Polarities currently cannot be given for module parameters. If the postulate takes n arguments (excluding module parameters), then the number of polarities given must be between 0 and n (inclusive).
Polarity pragmas make it possible to use postulated type formers in recursive types in the following way:
postulate ∥_∥ : Set → Set {# POLARITY ∥_∥ ++ #} data D : Set where c : ∥ D ∥ → D
Note that one can use postulates that may seem benign, together with polarity pragmas, to prove that the empty type is inhabited:
postulate _⇒_ : Set → Set → Set lambda : {A B : Set} → (A → B) → A ⇒ B apply : {A B : Set} → A ⇒ B → A → B {# POLARITY _⇒_ ++ #} data ⊥ : Set where data D : Set where c : D ⇒ ⊥ → D notinhabited : D → ⊥ notinhabited (c f) = apply f (c f) inhabited : D inhabited = c (lambda notinhabited) bad : ⊥ bad = notinhabited inhabited
Polarity pragmas are not allowed in safe mode.

Declarations in a
where
block are now private. [Issue #2101] This means thatf ps = body where decls
is now equivalent to
f ps = body where private decls
This changes little, since the
decls
were anyway not in scope outsidebody
. However, it makes a difference for abstract definitions, because private type signatures can see through abstract definitions. Consider:record Wrap (A : Set) : Set where field unwrap : A postulate P : ∀{A : Set} → A → Set abstract unnamedWhere : (A : Set) → Set unnamedWhere A = A where  the following definitions are private! B : Set B = Wrap A postulate b : B test : P (Wrap.unwrap b)  succeeds
The
abstract
is inherited inwhere
blocks from the parent (here: functionunnamedWhere
). Thus, the definition ofB
is opaque and the type equationB = Wrap A
cannot be used to check type signatures, not even of abstract definitions. Thus, checking the typeP (Wrap.unwrap b)
would fail. However, iftest
is private, abstract definitions are translucent in its type, and checking succeeds. With the implemented change, allwhere
definitions are private, in this caseB
,b
, andtest
, and the example succeeds.Nothing changes for the named forms of
where
,module M where module _ where
For instance, this still fails:
abstract unnamedWhere : (A : Set) → Set unnamedWhere A = A module M where B : Set B = Wrap A postulate b : B test : P (Wrap.unwrap b)  fails

Private anonymous modules now work as expected [Issue #2199]
Previously the
private
was ignored for anonymous modules causing its definitions to be visible outside the module containing the anonymous module. This is no longer the case. For instance,module M where private module _ (A : Set) where Id : Set Id = A foo : Set → Set foo = Id open M bar : Set → Set bar = Id  Id is no longer in scope here

Pattern synonyms are now expanded on left hand sides of DISPLAY pragmas [Issue #2132]. Example:
data D : Set where C c : D g : D → D pattern C′ = C {# DISPLAY C′ = C′ #} {# DISPLAY g C′ = c #}
This now behaves as:
{# DISPLAY C = C′ #} {# DISPLAY g C = c #}
Expected error for
test : C ≡ g C test = refl
is thus:
C′ != c of type D

The builtin floats have new semantics to fix inconsistencies and to improve crossplatform portability.

Float equality has been split into two primitives.
primFloatEquality
is designed to establish decidable propositional equality whileprimFloatNumericalEquality
is intended for numerical computations. They behave as follows:primFloatEquality NaN NaN = True primFloatEquality 0.0 0.0 = False primFloatNumericalEquality NaN NaN = False primFloatNumericalEquality 0.0 0.0 = True
This change fixes an inconsistency, see [Issue #2169]. For further detail see the user manual.

Floats now have only one
NaN
value. This is necessary for proper Float support in the JavaScript backend, as JavaScript (and some other platforms) only support oneNaN
value. 
The primitive function
primFloatLess
was renamedprimFloatNumericalLess
.


Added new primitives to builtin floats:

Anonymous declarations [Issue #1465].
A module can contain an arbitrary number of declarations named
_
which will scopedchecked and typechecked but won’t be made available in the scope (nor exported). They cannot introduce arguments on the LHS (but one can use lambdaabstractions on the RHS) and they cannot be defined by recursion._ : Set → Set _ = λ x → x
Rewriting
 The REWRITE pragma can now handle several names. E.g.:
{# REWRITE eq1 eq2 #}
Reflection

You can now use macros in reflected terms [Issue #2130].
For instance, given a macro
macro sometactic : Term → TC ⊤ sometactic = ...
the term
def (quote sometactic) []
represents a call to the macro. This makes it a lot easier to compose tactics. 
The reflection machinery now uses normalisation less often:

Macros no longer normalise the (automatically quoted) term arguments.

The TC primitives
inferType
,checkType
andquoteTC
no longer normalise their arguments. 
The following deprecated constructions may also have been changed:
quoteGoal
,quoteTerm
,quoteContext
andtactic
.


New TC primitive:
withNormalisation
.To recover the old normalising behaviour of
inferType
,checkType
,quoteTC
andgetContext
, you can wrap them inside a call towithNormalisation true
:withNormalisation : ∀ {a} {A : Set a} → Bool → TC A → TC A

New TC primitive:
reduce
.reduce : Term → TC Term
Reduces its argument to weak head normal form.

Added new TC primitive:
isMacro
[Issue #2182]isMacro : Name → TC Bool
Returns
true
if the name refers to a macro, otherwisefalse
. 
The
recordtype
constructor now has an extra argument containing information about the record type’s fields:data Definition : Set where … recordtype : (c : Name) (fs : List (Arg Name)) → Definition …
Type checking

Files with open metas can be imported now [Issue #964]. This should make simultaneous interactive development on several modules more pleasant.
Requires option:
allowunsolvedmetas
Internally, before serialization, open metas are turned into postulates named
unsolved#meta.<nnn>
where
<nnn>
is the internal meta variable number. 
The performance of the compiletime evaluator has been greatly improved.

Fixed a memory leak in evaluator (Issue #2147).

Reduction speed improved by an order of magnitude and is now comparable to the performance of GHCi. Still callbyname though.


The detection of types that satisfy K added in Agda 2.5.1 has been rolled back (see Issue #2003).

Etaequality for record types is now only on after the positivity checker has confirmed it is safe to have it. Etaequality for unguarded inductive records previously lead to looping of the type checker. [See Issue #2197]
record R : Set where inductive field r : R loops : R loops = ?
As a consequence of this change, the following example does not typecheck any more:
mutual record ⊤ : Set where test : ∀ {x y : ⊤} → x ≡ y test = refl
It fails because the positivity checker is only run after the mutual block, thus, etaequality for
⊤
is not available when checking test.One can declare etaequality explicitly, though, to make this example work.
mutual record ⊤ : Set where etaequality test : ∀ {x y : ⊤} → x ≡ y test = refl

Records with instance fields are now eta expanded before instance search.
For instance, assuming
Eq
andOrd
with boolean functions_==_
and_<_
respectively,record EqAndOrd (A : Set) : Set where field {{eq}} : Eq A {{ord}} : Ord A leq : {A : Set} {{_ : EqAndOrd A}} → A → A → Bool leq x y = x == y  x < y
Here the
EqAndOrd
record is automatically unpacked before instance search, revealing the componentEq
andOrd
instances.This can be used to simulate superclass dependencies.

Overlappable record instance fields.
Instance fields in records can be marked as overlappable using the new
overlap
keyword:record Ord (A : Set) : Set where field _<_ : A → A → Bool overlap {{eqA}} : Eq A
When instance search finds multiple candidates for a given instance goal and they are all overlappable it will pick the leftmost candidate instead of refusing to solve the instance goal.
This can be use to solve the problem arising from shared “superclass” dependencies. For instance, if you have, in addition to
Ord
above, aNum
record that also has anEq
field and want to write a function requiring bothOrd
andNum
, anyEq
constraint will be solved by theEq
instance from whichever argument that comes first.record Num (A : Set) : Set where field fromNat : Nat → A overlap {{eqA}} : Eq A lessOrEqualFive : {A : Set} {{NumA : Num A}} {{OrdA : Ord A}} → A → Bool lessOrEqualFive x = x == fromNat 5  x < fromNat 5
In this example the call to
_==_
will use theeqA
field fromNumA
rather than the one fromOrdA
. Note that these may well be different. 
Instance fields can be left out of copattern matches [Issue #2288]
Missing cases for instance fields (marked
{{
}}
) in copattern matches will be solved using instance search. This makes defining instances with superclass fields much nicer. For instance, we can defineNat
instances ofEq
,Ord
andNum
from above as follows:instance EqNat : Eq Nat _==_ {{EqNat}} n m = eqNat n m OrdNat : Ord Nat _<_ {{OrdNat}} n m = lessNat n m NumNat : Num Nat fromNat {{NumNat}} n = n
The
eqA
fields ofOrd
andNum
are filled in using instance search (withEqNat
in this case). 
Limited instance search depth [Issue #2269]
To prevent instance search from looping on bad instances (see Issue #1743) the search depth of instance search is now limited. The maximum depth can be set with the
instancesearchdepth
flag and the default value is500
.
Emacs mode

New command
Cu Cu Cc Cn
: Useshow
to display the result of normalisation.Calling
Cu Cu Cc Cn
on an expressione
(in a hole or at top level) normalisesshow e
and prints the resulting string, or an error message if the expression does not normalise to a literal string.This is useful when working with complex data structures for which you have defined a nice
Show
instance.Note that the name
show
is hardwired into the command. 
Changed feature: Interactively split result.
Makecase (
Cc Cc
) with no variables will now either introduce function arguments or do a copattern split (or fail).This is as before:
test : {A B : Set} (a : A) (b : B) → A × B test a b = ?  expected:  proj₁ (test a b) = {!!}  proj₂ (test a b) = {!!} testFun : {A B : Set} (a : A) (b : B) → A × B testFun = ?  expected:  testFun a b = {!!}
This is has changed:
record FunRec A : Set where field funField : A → A open FunRec testFunRec : ∀{A} → FunRec A testFunRec = ?  expected (since 20160503):  funField testFunRec = {!!}  used to be:  funField testFunRec x = {!!}

Changed feature: Split on hidden variables.
Makecase (
Cc Cc
) will no longer split on the given hidden variables, but only make them visible. (Splitting can then be performed in a second go.)test : ∀{N M : Nat} → Nat → Nat → Nat test N M = {!.N N .M!}
Invoking splitting will result in:
test {N} {M} zero M₁ = ? test {N} {M} (suc N₁) M₁ = ?
The hidden
.N
and.M
have been brought into scope, the visibleN
has been split upon. 
Nonfatal errors/warnings.
Nonfatal errors and warnings are now displayed in the info buffer and do not interrupt the typechecking of the file.
Currently termination errors, unsolved metavariables, unsolved constraints, positivity errors, deprecated BUILTINs, and empty REWRITING pragmas are nonfatal errors.

Highlighting for positivity check failures
Negative occurences of a datatype in its definition are now highlighted in a way similar to termination errors.

The abbrev for codata was replaced by an abbrev for code environments.
If you type
c Cx '
(on a suitably standard setup), then Emacs will insert the following text:\begin{code}<newline> <cursor><newline>\end{code}<newline>.

The LaTeX backend can now be invoked from the Emacs mode.
Using the compilation command (
Cc Cx Cc
).The flag
latexdir
can be used to set the output directory (by default:latex
). Note that if this directory is a relative path, then it is interpreted relative to the “project root”. (When the LaTeX backend is invoked from the command line the path is interpreted relative to the current working directory.) Example: If the moduleA.B.C
is located in the file/foo/A/B/C.agda
, then the project root is/foo/
, and the default output directory is/foo/latex/
. 
The compilation command (
Cc Cx Cc
) now by default asks for a backend.To avoid this question, set the customisation variable
agda2backend
to an appropriate value. 
The command
agda2measureloadtime
no longer “touches” the file, and the optional argumentDONTTOUCH
has been removed. 
New command
Cu (Cu) Cc Cs
: Simplify or normalise the solutionCc Cs
producesWhen writing examples, it is nice to have the hole filled in with a normalised version of the solution. Calling
Cc Cs
on_ : reverse (0 ∷ 1 ∷ []) ≡ ? _ = refl
used to yield the non informative
reverse (0 ∷ 1 ∷ [])
when we would have hopped to get1 ∷ 0 ∷ []
instead. We can now control finely the degree to which the solution is simplified. 
Changed feature: Solving the hole at point
Calling
Cc Cs
inside a specific goal does not solve all the goals already instantiated internally anymore: it only solves the one at hand (if possible). 
New bindings: All the blackboard bold letters are now available [Pull Request #2305]
The Agda input method only bound a handful of the blackboard bold letters but programmers were actually using more than these. They are now all available: lowercase and uppercase. Some previous bindings had to be modified for consistency. The naming scheme is as follows:
\bx
for lowercase blackboard bold\bX
for uppercase blackboard bold\bGx
for lowercase greek blackboard bold (similar to\Gx
for greeks)\bGX
for uppercase greek blackboard bold (similar to\GX
for uppercase greeks)

Replaced binding for go back
Use
M,
(instead ofM*
) for go back in Emacs ≥ 25.1 (and continue usingM*
with previous versions of Emacs).
Compiler backends

JS compiler backend
The JavaScript backend has been (partially) rewritten. The JavaScript backend now supports most Agda features, notably copatterns can now be compiled to JavaScript. Furthermore, the existing optimizations from the other backends now apply to the JavaScript backend as well.

GHC, JS and UHC compiler backends
Added new primitives to builtin floats [Issues #2194 and #2200]:
primFloatNegate : Float → Float primCos : Float → Float primTan : Float → Float primASin : Float → Float primACos : Float → Float primATan : Float → Float primATan2 : Float → Float → Float
LaTeX backend

Code blocks are now (by default) surrounded by vertical space. [Issue #2198]
Use
\AgdaNoSpaceAroundCode{}
to avoid this vertical space, and\AgdaSpaceAroundCode{}
to reenable it.Note that, if
\AgdaNoSpaceAroundCode{}
is used, then empty lines before or after a code block will not necessarily lead to empty lines in the generated document. However, empty lines inside the code block do (by default) lead to empty lines in the output.If you prefer the previous behaviour, then you can use the
agda.sty
file that came with the previous version of Agda. 
\AgdaHide{...}
now eats trailing spaces (using\ignorespaces
). 
New environments:
AgdaAlign
,AgdaSuppressSpace
andAgdaMultiCode
.Sometimes one might want to break up a code block into multiple pieces, but keep code in different blocks aligned with respect to each other. Then one can use the
AgdaAlign
environment. Example usage:\begin{AgdaAlign} \begin{code} code code (more code) \end{code} Explanation... \begin{code} aligned with "code" code (aligned with (more code)) \end{code} \end{AgdaAlign}
Note that
AgdaAlign
environments should not be nested.Sometimes one might also want to hide code in the middle of a code block. This can be accomplished in the following way:
\begin{AgdaAlign} \begin{code} visible \end{code} \AgdaHide{ \begin{code} hidden \end{code}} \begin{code} visible \end{code} \end{AgdaAlign}
However, the result may be ugly: extra space is perhaps inserted around the code blocks.
The
AgdaSuppressSpace
environment ensures that extra space is only inserted before the first code block, and after the last one (but not if\AgdaNoSpaceAroundCode{}
is used).The environment takes one argument, the number of wrapped code blocks (excluding hidden ones). Example usage:
\begin{AgdaAlign} \begin{code} code more code \end{code} Explanation... \begin{AgdaSuppressSpace}{2} \begin{code} aligned with "code" aligned with "more code" \end{code} \AgdaHide{ \begin{code} hidden code \end{code}} \begin{code} also aligned with "more code" \end{code} \end{AgdaSuppressSpace} \end{AgdaAlign}
Note that
AgdaSuppressSpace
environments should not be nested.There is also a combined environment,
AgdaMultiCode
, that combines the effects ofAgdaAlign
andAgdaSuppressSpace
.
Tools
agdaghcnames
The agdaghcnames
now has its own repository at
https://github.com/agda/agdaghcnames
and is no longer distributed with Agda.
Release notes for Agda version 2.5.1.2
 Fixed broken type signatures that were incorrectly accepted due to GHC #12784.
Release notes for Agda version 2.5.1.1
Installation and infrastructure

Added support for GHC 8.0.1.

Documentation is now built with Python >=3.3, as done by readthedocs.org.
Bug fixes

Fixed a serious performance problem with instance search

Interactively splitting variable with
Cc Cc
no longer introduces new trailing patterns. This fixes Issue #1950.data Ty : Set where _⇒_ : Ty → Ty → Ty ⟦_⟧ : Ty → Set ⟦ A ⇒ B ⟧ = ⟦ A ⟧ → ⟦ B ⟧ data Term : Ty → Set where K : (A B : Ty) → Term (A ⇒ (B ⇒ A)) test : (A : Ty) (a : Term A) → ⟦ A ⟧ test A a = {!a!}
Before change, case splitting on
a
would givetest .(A ⇒ (B ⇒ A)) (K A B) x x₁ = ?
Now, it yields
test .(A ⇒ (B ⇒ A)) (K A B) = ?

In literate TeX files,
\begin{code}
and\end{code}
can be preceded (resp. followed) by TeX code on the same line. This fixes Issue #2077. 
Other issues fixed (see bug tracker):
#1951 (mixfix binders not working in ‘syntax’)
#1967 (too eager insteance search error)
#1974 (lost constraint dependencies)
#1982 (internal error in unifier)
#2034 (function type instance goals)
Compiler backends

UHC compiler backend
Added support for UHC 1.1.9.4.
Release notes for Agda version 2.5.1
Documentation
 There is now an official Agda User Manual: http://agda.readthedocs.org/en/stable/
Installation and infrastructure

Builtins and primitives are now defined in a new set of modules available to all users, independent of any particular library. The modules are
Agda.Builtin.Bool Agda.Builtin.Char Agda.Builtin.Coinduction Agda.Builtin.Equality Agda.Builtin.Float Agda.Builtin.FromNat Agda.Builtin.FromNeg Agda.Builtin.FromString Agda.Builtin.IO Agda.Builtin.Int Agda.Builtin.List Agda.Builtin.Nat Agda.Builtin.Reflection Agda.Builtin.Size Agda.Builtin.Strict Agda.Builtin.String Agda.Builtin.TrustMe Agda.Builtin.Unit
The standard library reexports the primitives from the new modules.
The
Agda.Builtin
modules are installed in the same way asAgda.Primitive
, but unlikeAgda.Primitive
they are not loaded automatically.
Pragmas and options

Library management
There is a new ‘library’ concept for managing include paths. A library consists of
 a name,
 a set of libraries it depends on, and
 a set of include paths.
A library is defined in a
.agdalib
file using the following format:name: LIBRARYNAME  Comment depend: LIB1 LIB2 LIB3 LIB4 include: PATH1 PATH2 PATH3
Dependencies are library names, not paths to
.agdalib
files, and include paths are relative to the location of the libraryfile.To be useable, a library file has to be listed (with its full path) in
AGDA_DIR/libraries
(orAGDA_DIR/librariesVERSION
, for a given Agda version).AGDA_DIR
defaults to~/.agda
on Unixlike systems andC:/Users/USERNAME/AppData/Roaming/agda
or similar on Windows, and can be overridden by setting theAGDA_DIR
environment variable.Environment variables in the paths (of the form
$VAR
or${VAR}
) are expanded. The location of the libraries file used can be overridden using thelibraryfile=FILE
flag, although this is not expected to be very useful.You can find out the precise location of the ‘libraries’ file by calling
agda l fjdsk Dummy.agda
and looking at the error message (assuming you don’t have a library called fjdsk installed).There are three ways a library gets used:

You supply the
library=LIB
(orl LIB
) option to Agda. This is equivalent to adding aiPATH
for each of the include paths ofLIB
and its (transitive) dependencies. 
No explicit
library
flag is given, and the current project root (of the Agda file that is being loaded) or one of its parent directories contains a.agdalib
file defining a libraryLIB
. This library is used as if alibrarary=LIB
option had been given, except that it is not necessary for the library to be listed in theAGDA_DIR/libraries
file. 
No explicit
library
flag, and no.agdalib
file in the project root. In this case the fileAGDA_DIR/defaults
is read and all libraries listed are added to the path. The defaults file should contain a list of library names, each on a separate line. In this case the current directory is also added to the path.To disable default libraries, you can give the flag
nodefaultlibraries
.
Library names can end with a version number (for instance,
mylib1.2.3
). When resolving a library name (given in alibrary
flag, or listed as a default library or library dependency) the following rules are followed:
If you don’t give a version number, any version will do.

If you give a version number an exact match is required.

When there are multiple matches an exact match is preferred, and otherwise the latest matching version is chosen.
For example, suppose you have the following libraries installed:
mylib
,mylib1.0
,otherlib2.1
, andotherlib2.3
. In this case, aside from the exact matches you can also saylibrary=otherlib
to getotherlib2.3
. 
New Pragma
COMPILED_DECLARE_DATA
for binding recursively defined Haskell data types to recursively defined Agda data types.If you have a Haskell type like
{# LANGUAGE GADTs #} module Issue223 where data A where BA :: B > A data B where AB :: A > B BB :: B
You can now bind it to corresponding mutual Agda inductive data types as follows:
{# IMPORT Issue223 #} data A : Set {# COMPILED_DECLARE_DATA A Issue223.A #} data B : Set {# COMPILED_DECLARE_DATA B Issue223.B #} data A where BA : B → A {# COMPILED_DATA A Issue223.A Issue223.BA #} data B where AB : A → B BB : B {# COMPILED_DATA B Issue223.B Issue223.AB Issue223.BB #}
This fixes Issue #223.

New pragma
HASKELL
for adding inline Haskell code (GHC backend only)Arbitrary Haskell code can be added to a module using the
HASKELL
pragma. For instance,{# HASKELL echo :: IO () echo = getLine >>= putStrLn #} postulate echo : IO ⊤ {# COMPILED echo echo #}

New option
exactsplit
.The
exactsplit
flag causes Agda to raise an error whenever a clause in a definition by pattern matching cannot be made to hold definitionally (i.e. as a reduction rule). Specific clauses can be excluded from this check by means of the{# CATCHALL #}
pragma.For instance, the following definition will be rejected as the second clause cannot be made to hold definitionally:
min : Nat → Nat → Nat min zero y = zero min x zero = zero min (suc x) (suc y) = suc (min x y
Catchall clauses have to be marked as such, for instance:
eq : Nat → Nat → Bool eq zero zero = true eq (suc m) (suc n) = eq m n {# CATCHALL #} eq _ _ = false

New option:
noexactsplit
.This option can be used to override a global
exactsplit
in a file, by adding a pragma{# OPTIONS noexactsplit #}
. 
New options:
sharing
andnosharing
.These options are used to enable/disable sharing and callbyneed evaluation. The default is
nosharing
.Note that they cannot appear in an OPTIONS pragma, but have to be given as command line arguments or added to the Agda Program Args from Emacs with
Mx customizegroup agda2
. 
New pragma
DISPLAY
.{# DISPLAY f e1 .. en = e #}
This causes
f e1 .. en
to be printed in the same way ase
, whereei
can bind variables used ine
. The expressionsei
ande
are scope checked, but not type checked.For example this can be used to print overloaded (instance) functions with the overloaded name:
instance NumNat : Num Nat NumNat = record { ..; _+_ = natPlus } {# DISPLAY natPlus a b = a + b #}
Limitations

Lefthand sides are restricted to variables, constructors, defined functions or types, and literals. In particular, lambdas are not allowed in lefthand sides.

Since
DISPLAY
pragmas are not type checked implicit argument insertion may not work properly if the type off
computes to an implicit function space after pattern matching.


Removed pragma
{# ETA R #}
The pragma
{# ETA R #}
is replaced by theetaequality
directive inside record declarations. 
New option
noetaequality
.The
noetaequality
flag disables eta rules for declared record types. It has the same effect asnoetaequality
inside each declaration of a record typeR
.If used with the OPTIONS pragma it will not affect records defined in other modules.

The semantics of
{# REWRITE r #}
pragmas in parametrized modules has changed (see Issue #1652).Rewrite rules are no longer lifted to the top context. Instead, they now only apply to terms in (extensions of) the module context. If you want the old behaviour, you should put the
{# REWRITE r #}
pragma outside of the module (i.e. unindent it). 
New pragma
{# INLINE f #}
causesf
to be inlined during compilation. 
The
STATIC
pragma is now taken into account during compilation.Calls to a function marked
STATIC
are normalised before compilation. The typical use case for this is to mark the interpreter of an embedded language asSTATIC
. 
Option
typeintype
no longer impliesnouniversepolymorphism
, thus, it can be used with explicit universe levels. [Issue #1764] It simply turns off error reporting for any level mismatch now. Examples:{# OPTIONS typeintype #} Type : Set Type = Set data D {α} (A : Set α) : Set where d : A → D A data E α β : Set β where e : Set α → E α β

New
NO_POSITIVITY_CHECK
pragma to switch off the positivity checker for data/record definitions and mutual blocks.The pragma must precede a data/record definition or a mutual block.
The pragma cannot be used in
safe
mode.Examples (see
Issue1614*.agda
andIssue1760*.agda
intest/Succeed/
):
Skipping a single data definition.
{# NO_POSITIVITY_CHECK #} data D : Set where lam : (D → D) → D

Skipping a single record definition.
{# NO_POSITIVITY_CHECK #} record U : Set where field ap : U → U

Skipping an oldstyle mutual block: Somewhere within a
mutual
block before a data/record definition.mutual data D : Set where lam : (D → D) → D {# NO_POSITIVITY_CHECK #} record U : Set where field ap : U → U

Skipping an oldstyle mutual block: Before the
mutual
keyword.{# NO_POSITIVITY_CHECK #} mutual data D : Set where lam : (D → D) → D record U : Set where field ap : U → U

Skipping a newstyle mutual block: Anywhere before the declaration or the definition of data/record in the block.
record U : Set data D : Set record U where field ap : U → U {# NO_POSITIVITY_CHECK #} data D where lam : (D → D) → D


Removed
nocoveragecheck
option. [Issue #1918]
Language
Operator syntax

The default fixity for syntax declarations has changed from 666 to 20.

Sections.
Operators can be sectioned by replacing arguments with underscores. There must not be any whitespace between these underscores and the adjacent nameparts. Examples:
pred : ℕ → ℕ pred = _∸ 1 T : Bool → Set T = if_then ⊤ else ⊥ if : {A : Set} (b : Bool) → A → A → A if b = if b then_else_
Sections are translated into lambda expressions. Examples:
_∸ 1 ↦ λ section → section ∸ 1 if_then ⊤ else ⊥ ↦ λ section → if section then ⊤ else ⊥ if b then_else_ ↦ λ section section₁ → if b then section else section₁
Operator sections have the same fixity as the underlying operator (except in cases like
if b then_else_
, in which the section is “closed”, but the operator is not).Operator sections are not supported in patterns (with the exception of dot patterns), and notations coming from syntax declarations cannot be sectioned.

A longstanding operator fixity bug has been fixed. As a consequence some programs that used to parse no longer do.
Previously each precedence level was (incorrectly) split up into five separate ones, ordered as follows, with the earlier ones binding less tightly than the later ones:

Nonassociative operators.

Left associative operators.

Right associative operators.

Prefix operators.

Postfix operators.
Now this problem has been addressed. It is no longer possible to mix operators of a given precedence level but different associativity. However, prefix and right associative operators are seen as having the same associativity, and similarly for postfix and left associative operators.
Examples
The following code is no longer accepted:
infixl 6 _+_ infix 6 _∸_ rejected : ℕ rejected = 1 + 0 ∸ 1
However, the following previously rejected code is accepted:
infixr 4 _,_ infix 4 ,_ ,_ : {A : Set} {B : A → Set} {x : A} → B x → Σ A B , y = _ , y accepted : Σ ℕ λ i → Σ ℕ λ j → Σ (i ≡ j) λ _ → Σ ℕ λ k → j ≡ k accepted = 5 , , refl , , refl


The classification of notations with binders into the categories infix, prefix, postfix or closed has changed. [Issue #1450]
The difference is that, when classifying the notation, only regular holes are taken into account, not binding ones.
Example: The notation
syntax m >>= (λ x → f) = x < m , f
was previously treated as infix, but is now treated as prefix.

Notation can now include wildcard binders.
Example:
syntax Σ A (λ _ → B) = A × B

If an overloaded operator is in scope with several distinct precedence levels, then several instances of this operator will be included in the operator grammar, possibly leading to ambiguity. Previously the operator was given the default fixity [Issue #1436].
There is an exception to this rule: If there are multiple precedences, but at most one is explicitly declared, then only one instance will be included in the grammar. If there are no explicitly declared precedences, then this instance will get the default precedence, and otherwise it will get the declared precedence.
If multiple occurrences of an operator are “merged” in the grammar, and they have distinct associativities, then they are treated as being nonassociative.
The three paragraphs above also apply to identical notations (coming from syntax declarations) for a given overloaded name.
Examples:
module A where infixr 5 _∷_ infixr 5 _∙_ infixl 3 _+_ infix 1 bind syntax bind c (λ x → d) = x ← c , d module B where infix 5 _∷_ infixr 4 _∙_  No fixity declaration for _+_. infixl 2 bind syntax bind c d = c ∙ d module C where infixr 2 bind syntax bind c d = c ∙ d open A open B open C  _∷_ is infix 5.  _∙_ has two fixities: infixr 4 and infixr 5.  _+_ is infixl 3.  A.bind's notation is infix 1.  B.bind and C.bind's notations are infix 2.  There is one instance of "_ ∷ _" in the grammar, and one  instance of "_ + _".  There are three instances of "_ ∙ _" in the grammar, one  corresponding to A._∙_, one corresponding to B._∙_, and one  corresponding to both B.bind and C.bind.
Reflection

The reflection framework has received a massive overhaul.
A new type of reflected type checking computations supplants most of the old reflection primitives. The
quoteGoal
,quoteContext
and tactic primitives are deprecated and will be removed in the future, and theunquoteDecl
andunquote
primitives have changed behaviour. Furthermore the following primitive functions have been replaced by builtin type checking computations: primQNameType > AGDATCMGETTYPE  primQNameDefinition > AGDATCMGETDEFINITION  primDataConstructors > subsumed by AGDATCMGETDEFINITION  primDataNumberOfParameters > subsumed by AGDATCMGETDEFINITION
See below for details.

Types are no longer packaged with a sort.
The
AGDATYPE
andAGDATYPEEL
builtins have been removed. Reflected types are now simply terms. 
Reflected definitions have more information.
The type for reflected definitions has changed to
data Definition : Set where fundef : List Clause → Definition datatype : Nat → List Name → Definition  parameters and constructors recordtype : Name → Definition  name of the data/record type datacon : Name → Definition  name of the constructor axiom : Definition primfun : Definition
Correspondingly the builtins for function, data and record definitions (
AGDAFUNDEF
,AGDAFUNDEFCON
,AGDADATADEF
,AGDARECORDDEF
) have been removed. 
Reflected type checking computations.
There is a primitive
TC
monad representing type checking computations. Theunquote
,unquoteDecl
, and the newunquoteDef
all expect computations in this monad (see below). The interface to the monad is the following Error messages can contain embedded names and terms. data ErrorPart : Set where strErr : String → ErrorPart termErr : Term → ErrorPart nameErr : Name → ErrorPart {# BUILTIN AGDAERRORPART ErrorPart #} {# BUILTIN AGDAERRORPARTSTRING strErr #} {# BUILTIN AGDAERRORPARTTERM termErr #} {# BUILTIN AGDAERRORPARTNAME nameErr #} postulate TC : ∀ {a} → Set a → Set a returnTC : ∀ {a} {A : Set a} → A → TC A bindTC : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B  Unify two terms, potentially solving metavariables in the process. unify : Term → Term → TC ⊤  Throw a type error. Can be caught by catchTC. typeError : ∀ {a} {A : Set a} → List ErrorPart → TC A  Block a type checking computation on a metavariable. This will abort  the computation and restart it (from the beginning) when the  metavariable is solved. blockOnMeta : ∀ {a} {A : Set a} → Meta → TC A  Backtrack and try the second argument if the first argument throws a  type error. catchTC : ∀ {a} {A : Set a} → TC A → TC A → TC A  Infer the type of a given term inferType : Term → TC Type  Check a term against a given type. This may resolve implicit arguments  in the term, so a new refined term is returned. Can be used to create  new metavariables: newMeta t = checkType unknown t checkType : Term → Type → TC Term  Compute the normal form of a term. normalise : Term → TC Term  Get the current context. getContext : TC (List (Arg Type))  Extend the current context with a variable of the given type. extendContext : ∀ {a} {A : Set a} → Arg Type → TC A → TC A  Set the current context. inContext : ∀ {a} {A : Set a} → List (Arg Type) → TC A → TC A  Quote a value, returning the corresponding Term. quoteTC : ∀ {a} {A : Set a} → A → TC Term  Unquote a Term, returning the corresponding value. unquoteTC : ∀ {a} {A : Set a} → Term → TC A  Create a fresh name. freshName : String → TC QName  Declare a new function of the given type. The function must be defined  later using 'defineFun'. Takes an Arg Name to allow declaring instances  and irrelevant functions. The Visibility of the Arg must not be hidden. declareDef : Arg QName → Type → TC ⊤  Define a declared function. The function may have been declared using  'declareDef' or with an explicit type signature in the program. defineFun : QName → List Clause → TC ⊤  Get the type of a defined name. Replaces 'primQNameType'. getType : QName → TC Type  Get the definition of a defined name. Replaces 'primQNameDefinition'. getDefinition : QName → TC Definition {# BUILTIN AGDATCM TC #} {# BUILTIN AGDATCMRETURN returnTC #} {# BUILTIN AGDATCMBIND bindTC #} {# BUILTIN AGDATCMUNIFY unify #} {# BUILTIN AGDATCMNEWMETA newMeta #} {# BUILTIN AGDATCMTYPEERROR typeError #} {# BUILTIN AGDATCMBLOCKONMETA blockOnMeta #} {# BUILTIN AGDATCMCATCHERROR catchTC #} {# BUILTIN AGDATCMINFERTYPE inferType #} {# BUILTIN AGDATCMCHECKTYPE checkType #} {# BUILTIN AGDATCMNORMALISE normalise #} {# BUILTIN AGDATCMGETCONTEXT getContext #} {# BUILTIN AGDATCMEXTENDCONTEXT extendContext #} {# BUILTIN AGDATCMINCONTEXT inContext #} {# BUILTIN AGDATCMQUOTETERM quoteTC #} {# BUILTIN AGDATCMUNQUOTETERM unquoteTC #} {# BUILTIN AGDATCMFRESHNAME freshName #} {# BUILTIN AGDATCMDECLAREDEF declareDef #} {# BUILTIN AGDATCMDEFINEFUN defineFun #} {# BUILTIN AGDATCMGETTYPE getType #} {# BUILTIN AGDATCMGETDEFINITION getDefinition #}

Builtin type for metavariables
There is a new builtin type for metavariables used by the new reflection framework. It is declared as follows and comes with primitive equality, ordering and show.
postulate Meta : Set {# BUILTIN AGDAMETA Meta #} primitive primMetaEquality : Meta → Meta → Bool primitive primMetaLess : Meta → Meta → Bool primitive primShowMeta : Meta → String
There are corresponding new constructors in the
Term
andLiteral
data types:data Term : Set where ... meta : Meta → List (Arg Term) → Term {# BUILTIN AGDATERMMETA meta #} data Literal : Set where ... meta : Meta → Literal {# BUILTIN AGDALITMETA meta #}

Builtin unit type
The type checker needs to know about the unit type, which you can allow by
record ⊤ : Set where {# BUILTIN UNIT ⊤ #}

Changed behaviour of
unquote
The
unquote
primitive now expects a type checking computation instead of a pure term. In particularunquote e
requirese : Term → TC ⊤
where the argument is the representation of the hole in which the result should go. The old
unquote
behaviour (whereunquote
expected aTerm
argument) can be recovered byOLD: unquote v NEW: unquote λ hole → unify hole v

Changed behaviour of
unquoteDecl
The
unquoteDecl
primitive now expects a type checking computation instead of a pure function definition. It is possible to define multiple (mutually recursive) functions at the same time. More specificallyunquoteDecl x₁ .. xₙ = m
requires
m : TC ⊤
and thatx₁ .. xₙ
are defined (usingdeclareDef
anddefineFun
) after executingm
. As beforex₁ .. xₙ : QName
inm
, but have their declared types outside theunquoteDecl
. 
New primitive
unquoteDef
There is a new declaration
unquoteDef x₁ .. xₙ = m
This works exactly as
unquoteDecl
(see above) with the exception thatx₁ .. xₙ
are required to already be declared.The main advantage of
unquoteDef
overunquoteDecl
is thatunquoteDef
is allowed in mutual blocks, allowing mutually recursion between generated definitions and handwritten definitions. 
The reflection interface now exposes the name hint (as a string) for variables. As before, the actual binding structure is with de Bruijn indices. The String value is just a hint used as a prefix to help display the variable. The type
Abs
is a new builtin type used for the constructorsTerm.lam
,Term.pi
,Pattern.var
(bultinsAGDATERMLAM
,AGDATERMPI
andAGDAPATVAR
).data Abs (A : Set) : Set where abs : (s : String) (x : A) → Abs A {# BUILTIN ABS Abs #} {# BUILTIN ABSABS abs #}
Updated constructor types:
Term.lam : Hiding → Abs Term → Term Term.pi : Arg Type → Abs Type → Term Pattern.var : String → Pattern

Reflectionbased macros
Macros are functions of type
t1 → t2 → .. → Term → TC ⊤
that are defined in amacro
block. Macro application is guided by the type of the macro, whereTerm
arguments desugar into thequoteTerm
syntax andName
arguments into thequote
syntax. Arguments of any other type are preserved asis. The lastTerm
argument is the hole term given tounquote
computation (see above).For example, the macro application
f u v w
where the macrof
has the typeTerm → Name → Bool → Term → TC ⊤
desugars intounquote (f (quoteTerm u) (quote v) w)
Limitations:
 Macros cannot be recursive. This can be worked around by defining the recursive function outside the macro block and have the macro call the recursive function.
Silly example:
macro plustotimes : Term → Term → TC ⊤ plustotimes (def (quote _+_) (a ∷ b ∷ [])) hole = unify hole (def (quote _*_) (a ∷ b ∷ [])) plustotimes v hole = unify hole v thm : (a b : Nat) → plustotimes (a + b) ≡ a * b thm a b = refl
Macros are most useful when writing tactics, since they let you hide the reflection machinery. For instance, suppose you have a solver
magic : Type → Term
that takes a reflected goal and outputs a proof (when successful). You can then define the following macro
macro bymagic : Term → TC ⊤ bymagic hole = bindTC (inferType hole) λ goal → unify hole (magic goal)
This lets you apply the magic tactic without any syntactic noise at all:
thm : ¬ P ≡ NP thm = bymagic
Literals and builtins

Overloaded number literals.
You can now overload natural number literals using the new builtin
FROMNAT
:{# BUILTIN FROMNAT fromNat #}
The target of the builtin should be a defined name. Typically you would do something like
record Number (A : Set) : Set where field fromNat : Nat → A open Number {{...}} public {# BUILTIN FROMNAT fromNat #}
This will cause number literals
n
to be desugared tofromNat n
before type checking. 
Negative number literals.
Number literals can now be negative. For floating point literals it works as expected. For integer literals there is a new builtin
FROMNEG
that enables negative integer literals:{# BUILTIN FROMNEG fromNeg #}
This causes negative literals
n
to be desugared tofromNeg n
. 
Overloaded string literals.
String literals can be overladed using the
FROMSTRING
builtin:{# BUILTIN FROMSTRING fromString #}
The will cause string literals
s
to be desugared tofromString s
before type checking. 
Change to builtin integers.
The
INTEGER
builtin now needs to be bound to a datatype with two constructors that should be bound to the new builtinsINTEGERPOS
andINTEGERNEGSUC
as follows:data Int : Set where pos : Nat > Int negsuc : Nat > Int {# BUILTIN INTEGER Int #} {# BUILTIN INTEGERPOS pos #} {# BUILTIN INTEGERNEGSUC negsuc #}
where
negsuc n
represents the integern  1
. For instance,5
is represented asnegsuc 4
. All primitive functions on integers exceptprimShowInteger
have been removed, since these can be defined without too much trouble on the above representation using the corresponding functions on natural numbers.The primitives that have been removed are
primIntegerPlus primIntegerMinus primIntegerTimes primIntegerDiv primIntegerMod primIntegerEquality primIntegerLess primIntegerAbs primNatToInteger

New primitives for strict evaluation
primitive primForce : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) → (∀ x → B x) → B x primForceLemma : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) (f : ∀ x → B x) → primForce x f ≡ f x
primForce x f
evaluates tof x
if x is in weak head normal form, andprimForceLemma x f
evaluates torefl
in the same situation. The following values are considered to be in weak head normal form: constructor applications
 literals
 lambda abstractions
 type constructor (data/record types) applications
 function types
 Set a
Modules

Modules in import directives
When you use
using
/hiding
/renaming
on a name it now automatically applies to any module of the same name, unless you explicitly mention the module. For instance,open M using (D)
is equivalent to
open M using (D; module D)
if
M
defines a moduleD
. This is most useful for record and data types where you always get a module of the same name as the type.With this feature there is no longer useful to be able to qualify a constructor (or field) by the name of the data type even when it differs from the name of the corresponding module. The follow (weird) code used to work, but doesn’t work anymore:
module M where data D where c : D open M using (D) renaming (module D to MD) foo : D foo = D.c
If you want to import only the type name and not the module you have to hide it explicitly:
open M using (D) hiding (module D)
See discussion on Issue #836.

Private definitions of a module are no longer in scope at the Emacs mode toplevel.
The reason for this change is that
.agdaifiles
are stripped of unused private definitions (which can yield significant performance improvements for moduleheavy code).To test private definitions you can create a hole at the bottom of the module, in which private definitions will be visible.
Records

New record directives
etaequality
/noetaequality
The keywords
etaequality
/noetaequality
enable/disable eta rules for the (inductive) record type being declared.record Σ (A : Set) (B : A > Set) : Set where noetaequality constructor _,_ field fst : A snd : B fst open Σ  fail : ∀ {A : Set}{B : A > Set} → (x : Σ A B) → x ≡ (fst x , snd x)  fail x = refl   x != fst x , snd x of type Σ .A .B  when checking that the expression refl has type x ≡ (fst x , snd x)

Building records from modules.
The
record { <fields> }
syntax is now extended to accept module names as well. Fields are thus defined using the corresponding definitions from the given module.For instance assuming this record type
R
and moduleM
:record R : Set where field x : X y : Y z : Z module M where x = {! ... !} y = {! ... !} r : R r = record { M; z = {! ... !} }
Previously one had to write
record { x = M.x; y = M.y; z = {! ... !} }
.More precisely this construction now supports any combination of explicit field definitions and applied modules.
If a field is both given explicitly and available in one of the modules, then the explicit one takes precedence.
If a field is available in more than one module then this is ambiguous and therefore rejected. As a consequence the order of assignments does not matter.
The modules can be both applied to arguments and have import directives such as
hiding
,using
, andrenaming
. In particular this construct subsumes the record update construction.Here is an example of record update:
 Record update. Same as: record r { y = {! ... !} } r2 : R r2 = record { R r; y = {! ... !} }
A contrived example showing the use of
hiding
/renaming
:module M2 (a : A) where w = {! ... !} z = {! ... !} r3 : A → R r3 a = record { M hiding (y); M2 a renaming (w to y) }

Record patterns are now accepted.
Examples:
swap : {A B : Set} (p : A × B) → B × A swap record{ proj₁ = a; proj₂ = b } = record{ proj₁ = b; proj₂ = a } thd3 : ... thd3 record{ proj₂ = record { proj₂ = c }} = c

Record modules now properly hide all their parameters [Issue #1759]
Previously parameters to parent modules were not hidden in the record module, resulting in different behaviour between
module M (A : Set) where record R (B : Set) : Set where
and
module M where record R (A B : Set) : Set where
where in the former case,
A
would be an explicit argument to the moduleM.R
, but implicit in the latter case. NowA
is implicit in both cases.
Instance search

Performance has been improved, recursive instance search which was previously exponential in the depth is now only quadratic.

Constructors of records and datatypes are not anymore automatically considered as instances, you have to do so explicitely, for instance:
 only [b] is an instance of D data D : Set where a : D instance b : D c : D  the constructor is now an instance record tt : Set where instance constructor tt

Lambdabound variables are no longer automatically considered instances.
Lambdabound variables need to be bound as instance arguments to be considered for instance search. For example,
_==_ : {A : Set} {{_ : Eq A}} → A → A → Bool fails : {A : Set} → Eq A → A → Bool fails eqA x = x == x works : {A : Set} {{_ : Eq A}} → A → Bool works x = x == x

Letbound variables are no longer automatically considered instances.
To make a letbound variable available as an instance it needs to be declared with the
instance
keyword, just like toplevel instances. For example,mkEq : {A : Set} → (A → A → Bool) → Eq A fails : {A : Set} → (A → A → Bool) → A → Bool fails eq x = let eqA = mkEq eq in x == x works : {A : Set} → (A → A → Bool) → A → Bool works eq x = let instance eqA = mkEq eq in x == x

Record fields can be declared instances.
For example,
record EqSet : Set₁ where field set : Set instance eq : Eq set
This causes the projection function
eq : (E : EqSet) → Eq (set E)
to be considered for instance search. 
Instance search can now find arguments in variable types (but such candidates can only be lambdabound variables, they can’t be declared as instances)
module _ {A : Set} (P : A → Set) where postulate bla : {x : A} {{_ : P x}} → Set → Set  Works, the instance argument is found in the context test : {x : A} {{_ : P x}} → Set → Set test B = bla B  Still forbidden, because [P] could be instantiated later to anything instance postulate forbidden : {x : A} → P x

Instance search now refuses to solve constraints with unconstrained metavariables, since this can lead to nontermination.
See [Issue #1532] for an example.

Toplevel instances are now only considered if they are in scope. [Issue #1913]
Note that lambdabound instances need not be in scope.
Other changes

Unicode ellipsis character is allowed for the ellipsis token
...
inwith
expressions. 
Prop
is no longer a reserved word.
Type checking

Large indices.
Force constructor arguments no longer count towards the size of a datatype. For instance, the definition of equality below is accepted.
data _≡_ {a} {A : Set a} : A → A → Set where refl : ∀ x → x ≡ x
This gets rid of the asymmetry that the version of equality which indexes only on the second argument could be small, but not the version above which indexes on both arguments.

Detection of datatypes that satisfy K (i.e. sets)
Agda will now try to detect datatypes that satisfy K when
withoutK
is enabled. A datatype satisfies K when it follows these three rules:
The types of all nonrecursive constructor arguments should satisfy K.

All recursive constructor arguments should be firstorder.

The types of all indices should satisfy K.
For example, the types
Nat
,List Nat
, andx ≡ x
(wherex : Nat
) are all recognized by Agda as satisfying K. 

New unifier for case splitting
The unifier used by Agda for case splitting has been completely rewritten. The new unifier takes a much more typedirected approach in order to avoid the problems in issues #1406, #1408, #1427, and #1435.
The new unifier also has etaequality for record types builtin. This should avoid unnecessary case splitting on record constructors and improve the performance of Agda on code that contains deeply nested record patterns (see issues #473, #635, #1575, #1603, #1613, and #1645).
In some cases, the locations of the dot patterns computed by the unifier did not correspond to the locations given by the user (see Issue #1608). This has now been fixed by adding an extra step after case splitting that checks whether the userwritten patterns are compatible with the computed ones.
In some rare cases, the new unifier is still too restrictive when
withoutK
is enabled because it cannot generalize over the datatype indices (yet). For example, the following code is rejected:data Bar : Set₁ where bar : Bar baz : (A : Set) → Bar data Foo : Bar → Set where foo : Foo bar test : foo ≡ foo → Set₁ test refl = Set

The aggressive behaviour of
with
introduced in 2.4.2.5 has been rolled back [Issue #1692]. With no longer abstracts in the types of variables appearing in the withexpressions. [Issue #745]This means that the following example no longer works:
fails : (f : (x : A) → a ≡ x) (b : A) → b ≡ a fails f b with a  f b fails f b  .b  refl = f b
The
with
no longer abstracts the type off
overa
, sincef
appears in the second withexpressionf b
. You can use a nestedwith
to make this example work.This example does work again:
test : ∀{A : Set}{a : A}{f : A → A} (p : f a ≡ a) → f (f a) ≡ a test p rewrite p = p
After
rewrite p
the goal has changed tof a ≡ a
, but the type ofp
has not been rewritten, thus, the finalp
solves the goal.The following, which worked in 2.4.2.5, no longer works:
fails : (f : (x : A) → a ≡ x) (b : A) → b ≡ a fails f b rewrite f b = f b
The rewrite with
f b : a ≡ b
is not applied tof
as the latter is part of the rewrite expressionf b
. Thus, the type off
remains untouched, and the changed goalb ≡ b
is not solved byf b
. 
When using
rewrite
on a termeq
of typelhs ≡ rhs
, thelhs
is no longer abstracted inrhs
[Issue #520]. This means thatf pats rewrite eq = body
is more than syntactic sugar for
f pats with lhs  eq f pats  _  refl = body
In particular, the following application of
rewrite
is now possibleid : Bool → Bool id true = true id false = false isid : ∀ x → x ≡ id x isid true = refl isid false = refl postulate P : Bool → Set b : Bool p : P (id b) proof : P b proof rewrite isid b = p
Previously, this was desugared to
proof with b  isid b proof  _  refl = p
which did not type check as
refl
does not have typeb ≡ id b
. Now, Agda gets the task of checkingrefl : _ ≡ id b
leading to instantiation of_
toid b
.
Compiler backends

Major Bug Fixes:
 Function clauses with different arities are now always compiled correctly by the GHC/UHC backends. (Issue #727)

Copatterns

Optimizations
 Builtin naturals are now represented as arbitraryprecision Integers. See the user manual, section “Agda Compilers > Optimizations” for details.

GHC Haskell backend (MAlonzo)

Pragmas
Since builtin naturals are compiled to
Integer
you can no longer give a{# COMPILED_DATA #}
pragma forNat
. The same goes for builtin booleans, integers, floats, characters and strings which are now hardwired to appropriate Haskell types.


UHC compiler backend
A new backend targeting the Utrecht Haskell Compiler (UHC) is available. It targets the UHC Core language, and it’s design is inspired by the Epic backend. See the user manual, section “Agda Compilers > UHC Backend” for installation instructions.

FFI
The UHC backend has a FFI to Haskell similar to MAlonzo’s. The target Haskell code also needs to be compilable using UHC, which does not support the Haskell base library version 4.*.
FFI pragmas for the UHC backend are not checked in any way. If the pragmas are wrong, bad things will happen.

Imports
Additional Haskell modules can be brought into scope with the
IMPORT_UHC
pragma:{# IMPORT_UHC Data.Char #}
The Haskell modules
UHC.Base
andUHC.Agda.Builtins
are always in scope and don’t need to be imported explicitly. 
Datatypes
Agda datatypes can be bound to Haskell datatypes as follows:
Haskell:
data HsData a = HsCon1  HsCon2 (HsData a)
Agda:
data AgdaData (A : Set) : Set where AgdaCon1 : AgdaData A AgdaCon2 : AgdaData A > AgdaData A {# COMPILED_DATA_UHC AgdaData HsData HsCon1 HsCon2 #}
The mapping has to cover all constructors of the used Haskell datatype, else runtime behavior is undefined!
There are special reserved names to bind Agda datatypes to certain Haskell datatypes. For example, this binds an Agda datatype to Haskell’s list datatype:
Agda:
data AgdaList (A : Set) : Set where Nil : AgdaList A Cons : A > AgdaList A > AgdaList A {# COMPILED_DATA_UHC AgdaList __LIST__ __NIL__ __CONS__ #}
The following “magic” datatypes are available:
HS Datatype  Datatype Pragma  HS Constructor  Constructor Pragma () __UNIT__ () __UNIT__ List __LIST__ (:) __CONS__ [] __NIL__ Bool __BOOL__ True __TRUE__ False __FALSE__

Functions
Agda postulates can be bound to Haskell functions. Similar as in MAlonzo, all arguments of type
Set
need to be dropped before calling Haskell functions. An example calling the return function:Agda:
postulate hsreturn : {A : Set} > A > IO A {# COMPILED_UHC hsreturn (\_ > UHC.Agda.Builtins.primReturn) #}

Emacs mode and interaction

Module contents (
Cc Co
) now also works for records. [See Issue #1926 ] If you have an inferable expression of record type in an interaction point, you can invokeCc Co
to see its fields and types. Examplerecord R : Set where field f : A test : R → R test r = {!r!}  Cc Co here

Less aggressive error notification.
Previously Emacs could jump to the position of an error even if the typechecking process was not initiated in the current buffer. Now this no longer happens: If the typechecking process was initiated in another buffer, then the cursor is moved to the position of the error in the buffer visiting the file (if any) and in every window displaying the file, but focus should not change from one file to another.
In the cases where focus does change from one file to another, one can now use the goback functionality to return to the previous position.

Removed the
agdaincludedirs
customization parameter.Use
agdaprogramargs
withiDIR
orlLIB
instead, or add libraries to~/.agda/defaults
(C:/Users/USERNAME/AppData/Roaming/agda/defaults
or similar on Windows). See Library management, above, for more information.
Tools
LaTeXbackend

The default font has been changed to XITS (which is part of TeX Live):
http://www.ctan.org/texarchive/fonts/xits/
This font is more complete with respect to Unicode.
agdaghcnames

New tool: The command
agdaghcnames fixprof <compiledir> <ProgName>.prof
converts
*.prof
files obtained from profiling runs of MAlonzocompiled code to*.agdaIdents.prof
, with the original Agda identifiers replacing the MAlonzogenerated Haskell identifiers.For usage and more details, see
src/agdaghcnames/README.txt
.
Highlighting and textual backends
 Names in import directives are now highlighted and are clickable. [Issue #1714] This leads also to nicer printing in the LaTeX and html backends.
Fixed issues
See bug tracker (milestone 2.5.1)
Release notes for Agda version 2.4.2.5
Installation and infrastructure

Added support for GHC 7.10.3.

Added
cpphs
Cabal flagTurn on/off this flag to choose cpphs/cpp as the C preprocessor.
This flag is turn on by default.
(This flag was added in Agda 2.4.2.1 but it was not documented)
Pragmas and options
 Termination pragmas are no longer allowed inside
where
clauses [Issue #1137].
Type checking

with
abstraction is more aggressive, abstracts also in types of variables that are used in thewith
expressions, unless they are also used in the types of thewith
expressions. [Issue #1692]Example:
test : (f : (x : A) → a ≡ x) (b : A) → b ≡ a test f b with a  f b test f b  .b  refl = f b
Previously,
with
would not abstract in types of variables that appear in thewith
expressions, in this case, bothf
andb
, leaving their types unchanged. Now, it tries to abstract inf
, as onlyb
appears in the types of thewith
expressions which areA
(ofa
) anda ≡ b
(off b
). As a result, the type off
changes to(x : A) → b ≡ x
and the type of the goal tob ≡ b
(as previously).This also affects
rewrite
, which is implemented in terms ofwith
.test : (f : (x : A) → a ≡ x) (b : A) → b ≡ a test f b rewrite f b = f b
As the new
with
is not fully backwardscompatible, some parts of your Agda developments usingwith
orrewrite
might need maintenance.
Fixed issues
See bug tracker
Release notes for Agda version 2.4.2.4
Installation and infrastructure
 Removed support for GHC 7.4.2.
Pragmas and options

Option
copatterns
is now on by default. To switch off parsing of copatterns, use:{# OPTIONS nocopatterns #}

Option
rewriting
is now needed to useREWRITE
pragmas and rewriting during reduction. Rewriting is notsafe
.To use rewriting, first specify a relation symbol
R
that will later be used to add rewrite rules. A canonical candidate would be propositional equality{# BUILTIN REWRITE _≡_ #}
but any symbol
R
of typeΔ → A → A → Set i
for someA
andi
is accepted. Then symbolsq
can be added to rewriting provided their type is of the formΓ → R ds l r
. This will add a rewrite ruleΓ ⊢ l ↦ r : A[ds/Δ]
to the signature, which fires whenever a term is an instance of
l
. For example, ifplus0 : ∀ x → x + 0 ≡ x
(ideally, there is a proof for
plus0
, but it could be a postulate), then{# REWRITE plus0 #}
will prompt Agda to rewrite any welltyped term of the form
t + 0
tot
.Some caveats: Agda accepts and applies rewrite rules naively, it is very easy to break consistency and termination of type checking. Some examples of rewrite rules that should not be added:
refl : ∀ x → x ≡ x  Agda loops plussym : ∀ x y → x + y ≡ y + x  Agda loops absurd : true ≡ false  Breaks consistency
Adding only proven equations should at least preserve consistency, but this is only a conjecture, so know what you are doing! Using rewriting, you are entering into the wilderness, where you are on your own!
Language

forall
/∀
now parses likeλ
, i.e., the following parses now [Issue #1583]:⊤ × ∀ (B : Set) → B → B

The underscore pattern
_
can now also stand for an inaccessible pattern (dot pattern). This alleviates the need for writing._
. [Issue #1605] Instead oftransVOld : ∀{A : Set} (a b c : A) → a ≡ b → b ≡ c → a ≡ c transVOld _ ._ ._ refl refl = refl
one can now write
transVNew : ∀{A : Set} (a b c : A) → a ≡ b → b ≡ c → a ≡ c transVNew _ _ _ refl refl = refl
and let Agda decide where to put the dots. This was always possible by using hidden arguments
transH : ∀{A : Set}{a b c : A} → a ≡ b → b ≡ c → a ≡ c transH refl refl = refl
which is now equivalent to
transHNew : ∀{A : Set}{a b c : A} → a ≡ b → b ≡ c → a ≡ c transHNew {a = _}{b = _}{c = _} refl refl = refl
Before, underscore
_
stood for an unnamed variable that could not be instantiated by an inaccessible pattern. If one no wants to prevent Agda from instantiating, one needs to use a variable name other than underscore (however, in practice this situation seems unlikely).
Type checking

Polarity of phantom arguments to data and record types has changed. [Issue #1596] Polarity of size arguments is Nonvariant (both monotone and antitone). Polarity of other arguments is Covariant (monotone). Both were Invariant before (neither monotone nor antitone).
The following example typechecks now:
open import Common.Size  List should be monotone in both arguments  (even when `cons' is missing). data List (i : Size) (A : Set) : Set where [] : List i A castLL : ∀{i A} → List i (List i A) → List ∞ (List ∞ A) castLL x = x  Stream should be antitone in the first and monotone in the second argument  (even with field `tail' missing). record Stream (i : Size) (A : Set) : Set where coinductive field head : A castSS : ∀{i A} → Stream ∞ (Stream ∞ A) → Stream i (Stream i A) castSS x = x

SIZELT
lambdas must be consistent [Issue #1523, see Abel and Pientka, ICFP 2013]. When lambdaabstracting over type (Size< size
) thensize
must be nonzero, for any valid instantiation of size variables.
The good:
data Nat (i : Size) : Set where zero : ∀ (j : Size< i) → Nat i suc : ∀ (j : Size< i) → Nat j → Nat i {# TERMINATING #}  This definition is fine, the termination checker is too strict at the moment. fix : ∀ {C : Size → Set} → (∀ i → (∀ (j : Size< i) → Nat j > C j) → Nat i → C i) → ∀ i → Nat i → C i fix t i (zero j) = t i (λ (k : Size< i) → fix t k) (zero j) fix t i (suc j n) = t i (λ (k : Size< i) → fix t k) (suc j n)
The
λ (k : Size< i)
is fine in both cases, as contexti : Size, j : Size< i
guarantees that
i
is nonzero. 
The bad:
record Stream {i : Size} (A : Set) : Set where coinductive constructor _∷ˢ_ field head : A tail : ∀ {j : Size< i} → Stream {j} A open Stream public _++ˢ_ : ∀ {i A} → List A → Stream {i} A → Stream {i} A [] ++ˢ s = s (a ∷ as) ++ˢ s = a ∷ˢ (as ++ˢ s)
This fails, maybe unjustified, at
i : Size, s : Stream {i} A ⊢ a ∷ˢ (λ {j : Size< i} → as ++ˢ s)
Fixed by defining the constructor by copattern matching:
record Stream {i : Size} (A : Set) : Set where coinductive field head : A tail : ∀ {j : Size< i} → Stream {j} A open Stream public _∷ˢ_ : ∀ {i A} → A → Stream {i} A → Stream {↑ i} A head (a ∷ˢ as) = a tail (a ∷ˢ as) = as _++ˢ_ : ∀ {i A} → List A → Stream {i} A → Stream {i} A [] ++ˢ s = s (a ∷ as) ++ˢ s = a ∷ˢ (as ++ˢ s)

The ugly:
fix : ∀ {C : Size → Set} → (∀ i → (∀ (j : Size< i) → C j) → C i) → ∀ i → C i fix t i = t i λ (j : Size< i) → fix t j
For
i=0
, there is no suchj
at runtime, leading to looping behavior.

Interaction

Issue #635 has been fixed. Case splitting does not spit out implicit record patterns any more.
record Cont : Set₁ where constructor _◃_ field Sh : Set Pos : Sh → Set open Cont data W (C : Cont) : Set where sup : (s : Sh C) (k : Pos C s → W C) → W C bogus : {C : Cont} → W C → Set bogus w = {!w!}
Case splitting on
w
yielded, since the fix of Issue #473,bogus {Sh ◃ Pos} (sup s k) = ?
Now it gives, as expected,
bogus (sup s k) = ?
Performance
 As one result of the 21st Agda Implementor’s Meeting (AIM XXI), serialization of the standard library is 50% faster (time reduced by a third), without using additional disk space for the interface files.
Bug fixes
Issues fixed (see bug tracker):
#1546 (copattern matching and withclauses)
#1560 (positivity checker inefficiency)
#1584 (let pattern with trailing implicit)
Release notes for Agda version 2.4.2.3
Installation and infrastructure

Added support for GHC 7.10.1.

Removed support for GHC 7.0.4.
Language

_
is no longer a valid name for a definition. The following fails now: [Issue #1465]postulate _ : Set

Typed bindings can now contain hiding information [Issue #1391]. This means you can now write
assoc : (xs {ys zs} : List A) → ((xs ++ ys) ++ zs) ≡ (xs ++ (ys ++ zs))
instead of the longer
assoc : (xs : List A) {ys zs : List A} → ...
It also works with irrelevance
.(xs {ys zs} : List A) → ...
but of course does not make sense if there is hiding information already. Thus, this is (still) a parse error:
{xs {ys zs} : List A} → ...

The builtins for sized types no longer need accompanying postulates. The BUILTIN pragmas for size stuff now also declare the identifiers they bind to.
{# BUILTIN SIZEUNIV SizeUniv #}  SizeUniv : SizeUniv {# BUILTIN SIZE Size #}  Size : SizeUniv {# BUILTIN SIZELT Size<_ #}  Size<_ : ..Size → SizeUniv {# BUILTIN SIZESUC ↑_ #}  ↑_ : Size → Size {# BUILTIN SIZEINF ∞ #}  ∞ : Size
Size
andSize<
now live in the new universeSizeUniv
. It is forbidden to build function spaces in this universe, in order to prevent the malicious assumption of a size predecessorpred : (i : Size) → Size< i
[Issue #1428].

Unambiguous notations (coming from syntax declarations) that resolve to ambiguous names are now parsed unambiguously [Issue #1194].

If only some instances of an overloaded name have a given associated notation (coming from syntax declarations), then this name can only be resolved to the given instances of the name, not to other instances [Issue #1194].
Previously, if different instances of an overloaded name had different associated notations, then none of the notations could be used. Now all of them can be used.
Note that notation identity does not only involve the righthand side of the syntax declaration. For instance, the following notations are not seen as identical, because the implicit argument names are different:
module A where data D : Set where c : {x y : D} → D syntax c {x = a} {y = b} = a ∙ b module B where data D : Set where c : {y x : D} → D syntax c {y = a} {x = b} = a ∙ b

If an overloaded operator is in scope with at least two distinct fixities, then it gets the default fixity [Issue #1436].
Similarly, if two or more identical notations for a given overloaded name are in scope, and these notations do not all have the same fixity, then they get the default fixity.
Type checking

Functions of varying arity can now have withclauses and use rewrite.
Example:
NPred : Nat → Set NPred 0 = Bool NPred (suc n) = Nat → NPred n const : Bool → ∀{n} → NPred n const b {0} = b const b {suc n} m = const b {n} allOdd : ∀ n → NPred n allOdd 0 = true allOdd (suc n) m with even m ...  true = const false ...  false = allOdd n

Function defined by copattern matching can now have
with
clauses and userewrite
.Example:
{# OPTIONS copatterns #} record Stream (A : Set) : Set where coinductive constructor delay field force : A × Stream A open Stream map : ∀{A B} → (A → B) → Stream A → Stream B force (map f s) with force s ...  a , as = f a , map f as record Bisim {A B} (R : A → B → Set) (s : Stream A) (t : Stream B) : Set where coinductive constructor ~delay field ~force : let a , as = force s b , bs = force t in R a b × Bisim R as bs open Bisim SEq : ∀{A} (s t : Stream A) → Set SEq = Bisim (_≡_)  Slightly weird definition of symmetry to demonstrate rewrite. ~sym' : ∀{A} {s t : Stream A} → SEq s t → SEq t s ~force (~sym' {s = s} {t} p) with force s  force t  ~force p ...  a , as  b , bs  r , q rewrite r = refl , ~sym' q

Instances can now be defined by copattern matching. [Issue #1413] The following example extends the one in [Abel, Pientka, Thibodeau, Setzer, POPL 2013, Section 2.2]:
{# OPTIONS copatterns #}  The Monad type class record Monad (M : Set → Set) : Set1 where field return : {A : Set} → A → M A _>>=_ : {A B : Set} → M A → (A → M B) → M B open Monad {{...}}  The State newtype record State (S A : Set) : Set where field runState : S → A × S open State  State is an instance of Monad instance stateMonad : {S : Set} → Monad (State S) runState (return {{stateMonad}} a ) s = a , s  NEW runState (_>>=_ {{stateMonad}} m k) s₀ =  NEW let a , s₁ = runState m s₀ in runState (k a) s₁  stateMonad fulfills the monad laws leftId : {A B S : Set}(a : A)(k : A → State S B) → (return a >>= k) ≡ k a leftId a k = refl rightId : {A B S : Set}(m : State S A) → (m >>= return) ≡ m rightId m = refl assoc : {A B C S : Set}(m : State S A)(k : A → State S B)(l : B → State S C) → ((m >>= k) >>= l) ≡ (m >>= λ a → k a >>= l) assoc m k l = refl
Emacs mode

The new menu option
Switch to another version of Agda
tries to do what it says. 
Changed feature: Interactively split result.
[ This is as before: ] Makecase (
Cc Cc
) with no variables given tries to split on the result to introduce projection patterns. The hole needs to be of record type, of course.test : {A B : Set} (a : A) (b : B) → A × B test a b = ?
Resultsplitting
?
will produce the new clauses:proj₁ (test a b) = ? proj₂ (test a b) = ?
[ This has changed: ] If hole is of function type,
makecase
will introduce only pattern variables (as much as it can).testFun : {A B : Set} (a : A) (b : B) → A × B testFun = ?
Resultsplitting
?
will produce the new clause:testFun a b = ?
A second invocation of
makecase
will then introduce projection patterns.
Error messages

Agda now suggests corrections of misspelled options, e.g.
{# OPTIONS dontterminationcheck withoutk senfgurke #}
Unrecognized options:
dontterminationcheck (did you mean noterminationcheck ?) withoutk (did you mean withoutK ?) senfgurke
Nothing close to
senfgurke
, I am afraid.
Compiler backends
 The Epic backend has been removed [Issue #1481].
Bug fixes

Fixed bug with
unquoteDecl
not working in instance blocks [Issue #1491]. 
Other issues fixed (see bug tracker
Release notes for Agda version 2.4.2.2
Bug fixes
Release notes for Agda version 2.4.2.1
Pragmas and options

New pragma
{# TERMINATING #}
replacing{# NO_TERMINATION_CHECK #}
Complements the existing pragma
{# NON_TERMINATING #}
. Skips termination check for the associated definitions and marks them as terminating. Thus, it is a replacement for{# NO_TERMINATION_CHECK #}
with the same semantics.You can no longer use pragma
{# NO_TERMINATION_CHECK #}
to skip the termination check, but must label your definitions as either{# TERMINATING #}
or{# NON_TERMINATING #}
instead.Note:
{# OPTION noterminationcheck #}
labels all your definitions as{# TERMINATING #}
, putting you in the danger zone of a loop in the type checker.
Language

Referring to a local variable shadowed by module opening is now an error. Previous behavior was preferring the local over the imported definitions. [Issue #1266]
Note that module parameters are locals as well as variables bound by λ, dependent function type, patterns, and let.
Example:
module M where A = Set1 test : (A : Set) → let open M in A
The last
A
produces an error, since it could refer to the local variableA
or to the definition imported from moduleM
. 
with
on a variable bound by a module telescope or a pattern of a parent function is now forbidden. [Issue #1342]data Unit : Set where unit : Unit id : (A : Set) → A → A id A a = a module M (x : Unit) where dx : Unit → Unit dx unit = x g : ∀ u → x ≡ dx u g with x g  unit = id (∀ u → unit ≡ dx u) ?
Even though this code looks right, Agda complains about the type expression
∀ u → unit ≡ dx u
. If you ask Agda what should go there instead, it happily tells you that it wants∀ u → unit ≡ dx u
. In fact what you do not see and Agda will never show you is that the two expressions actually differ in the invisible first argument todx
, which is visible only outside moduleM
. What Agda wants is an invisibleunit
afterdx
, but all you can write is an invisiblex
(which is inserted behind the scenes).To avoid those kinds of paradoxes,
with
is now outlawed on module parameters. This should ensure that the invisible arguments are always exactly the module parameters.Since a
where
block is desugared as module with pattern variables of the parent clause as module parameters, the same strikes you for uses ofwith
on pattern variables of the parent function.f : Unit → Unit f x = unit where dx : Unit → Unit dx unit = x g : ∀ u → x ≡ dx u g with x g  unit = id ((u : Unit) → unit ≡ dx u) ?
The
with
on pattern variablex
of the parent clausef x = unit
is outlawed now.
Type checking

Termination check failure is now a proper error.
We no longer continue type checking after termination check failures. Use pragmas
{# NON_TERMINATING #}
and{# NO_TERMINATION_CHECK #}
near the offending definitions if you want to do so. Or switch off the termination checker altogether with{# OPTIONS noterminationcheck #}
(at your own risk!). 
(Since Agda 2.4.2): Termination checking
withoutK
restricts structural descent to arguments ending in data types orSize
. Likewise, guardedness is only tracked when result type is data or record type.mutual data WOne : Set where wrap : FOne → WOne FOne = ⊥ → WOne noo : (X : Set) → (WOne ≡ X) → X → ⊥ noo .WOne refl (wrap f) = noo FOne iso f
noo
is rejected since at typeX
the structural descentf < wrap f
is discountedwithoutK
.data Pandora : Set where C : ∞ ⊥ → Pandora loop : (A : Set) → A ≡ Pandora → A loop .Pandora refl = C (♯ (loop ⊥ foo))
loop
is rejected since guardedness is not tracked at typeA
withoutK
.
Termination checking

The termination checker can now recognize simple subterms in dot patterns.
data Subst : (d : Nat) → Set where c₁ : ∀ {d} → Subst d → Subst d c₂ : ∀ {d₁ d₂} → Subst d₁ → Subst d₂ → Subst (suc d₁ + d₂) postulate comp : ∀ {d₁ d₂} → Subst d₁ → Subst d₂ → Subst (d₁ + d₂) lookup : ∀ d → Nat → Subst d → Set₁ lookup d zero (c₁ ρ) = Set lookup d (suc v) (c₁ ρ) = lookup d v ρ lookup .(suc d₁ + d₂) v (c₂ {d₁} {d₂} ρ σ) = lookup (d₁ + d₂) v (comp ρ σ)
The dot pattern here is actually normalized, so it is
suc (d₁ + d₂)
and the corresponding recursive call argument is
(d₁ + d₂)
. In such simple cases, Agda can now recognize that the pattern is constructor applied to call argument, which is valid descent.Note however, that Agda only looks for syntactic equality when identifying subterms, since it is not allowed to normalize terms on the rhs during termination checking.
Actually writing the dot pattern has no effect, this works as well, and looks pretty magical… ;)
hidden : ∀{d} → Nat → Subst d → Set₁ hidden zero (c₁ ρ) = Set hidden (suc v) (c₁ ρ) = hidden v ρ hidden v (c₂ ρ σ) = hidden v (comp ρ σ)
Tools
LaTeXbackend
 Fixed the issue of identifiers containing operators being typeset with excessive math spacing.
Bug fixes

Issue #1194

Issue #836: Fields and constructors can be qualified by the record/data type as well as by their record/data module. This now works also for record/data type imported from parametrized modules:
module M (_ : Set₁) where record R : Set₁ where field X : Set open M Set using (R)  rather than using (module R) X : R → Set X = R.X
Release notes for Agda version 2.4.2
Pragmas and options

New option:
withK
This can be used to override a global
withoutK
in a file, by adding a pragma{# OPTIONS withK #}
. 
New pragma
{# NON_TERMINATING #}
This is a safer version of
NO_TERMINATION_CHECK
which doesn’t treat the affected functions as terminating. This means thatNON_TERMINATING
functions do not reduce during type checking. They do reduce at runtime and when invokingCc Cn
at toplevel (but not in a hole).
Language

Instance search is now more efficient and recursive (see Issue #938) (but without termination check yet).
A new keyword
instance
has been introduced (in the style ofabstract
andprivate
) which must now be used for every definition/postulate that has to be taken into account during instance resolution. For example:record RawMonoid (A : Set) : Set where field nil : A _++_ : A > A > A open RawMonoid {{...}} instance rawMonoidList : {A : Set} > RawMonoid (List A) rawMonoidList = record { nil = []; _++_ = List._++_ } rawMonoidMaybe : {A : Set} {{m : RawMonoid A}} > RawMonoid (Maybe A) rawMonoidMaybe {A} = record { nil = nothing ; _++_ = catMaybe } where catMaybe : Maybe A > Maybe A > Maybe A catMaybe nothing mb = mb catMaybe ma nothing = ma catMaybe (just a) (just b) = just (a ++ b)
Moreover, each type of an instance must end in (something that reduces to) a named type (e.g. a record, a datatype or a postulate). This allows us to build a simple index structure
data/record name > possible instances
that speeds up instance search.
Instance search takes into account all local bindings and all global
instance
bindings and the search is recursive. For instance, searching for? : RawMonoid (Maybe (List A))
will consider the candidates {
rawMonoidList
,rawMonoidMaybe
}, fail to unify the first one, succeeding with the second one? = rawMonoidMaybe {A = List A} {{m = ?m}} : RawMonoid (Maybe (List A))
and continue with goal
?m : RawMonoid (List A)
This will then find
?m = rawMonoidList {A = A}
and putting together we have the solution.
Be careful that there is no termination check for now, you can easily make Agda loop by declaring the identity function as an instance. But it shouldn’t be possible to make Agda loop by only declaring structurally recursive instances (whatever that means).
Additionally:

Uniqueness of instances is up to definitional equality (see Issue #899).

Instances of the following form are allowed:
EqSigma : {A : Set} {B : A → Set} {{EqA : Eq A}} {{EqB : {a : A} → Eq (B a)}} → Eq (Σ A B)
When searching recursively for an instance of type
{a : A} → Eq (B a)
, a lambda will automatically be introduced and instance search will search for something of typeEq (B a)
in the context extended bya : A
. When searching for an instance, thea
argument does not have to be implicit, but in the definition ofEqSigma
, instance search will only be able to useEqB
ifa
is implicit. 
There is no longer any attempt to solve irrelevant metas by instance search.

Constructors of records and datatypes are automatically added to the instance table.


You can now use
quote
in patterns.For instance, here is a function that unquotes a (closed) natural number term.
unquoteNat : Term → Maybe Nat unquoteNat (con (quote Nat.zero) []) = just zero unquoteNat (con (quote Nat.suc) (arg _ n ∷ [])) = fmap suc (unquoteNat n) unquoteNat _ = nothing

The builtin constructors
AGDATERMUNSUPPORTED
andAGDASORTUNSUPPORTED
are now translated to meta variables when unquoting. 
New syntactic sugar
tactic e
andtactic e  e1  ..  en
.It desugars as follows and makes it less unwieldy to call reflectionbased tactics.
tactic e > quoteGoal g in unquote (e g) tactic e  e1  ..  en > quoteGoal g in unquote (e g) e1 .. en
Note that in the second form the tactic function should generate a function from a number of new subgoals to the original goal. The type of
e
should beTerm > Term
in both cases. 
New reflection builtins for literals.
The term data type
AGDATERM
now needs an additional constructorAGDATERMLIT
taking a reflected literal defined as follows (with appropriate builtin bindings for the typesNat
,Float
, etc).data Literal : Set where nat : Nat → Literal float : Float → Literal char : Char → Literal string : String → Literal qname : QName → Literal {# BUILTIN AGDALITERAL Literal #} {# BUILTIN AGDALITNAT nat #} {# BUILTIN AGDALITFLOAT float #} {# BUILTIN AGDALITCHAR char #} {# BUILTIN AGDALITSTRING string #} {# BUILTIN AGDALITQNAME qname #}
When quoting (
quoteGoal
orquoteTerm
) literals will be mapped to theAGDATERMLIT
constructor. Previously natural number literals were quoted tosuc
/zero
application and other literals were quoted toAGDATERMUNSUPPORTED
. 
New reflection builtins for function definitions.
AGDAFUNDEF
should now map to a data type defined as follows(with
{# BUILTIN QNAME QName #} {# BUILTIN ARG Arg #} {# BUILTIN AGDATERM Term #} {# BUILTIN AGDATYPE Type #} {# BUILTIN AGDALITERAL Literal #}
).
data Pattern : Set where con : QName → List (Arg Pattern) → Pattern dot : Pattern var : Pattern lit : Literal → Pattern proj : QName → Pattern absurd : Pattern {# BUILTIN AGDAPATTERN Pattern #} {# BUILTIN AGDAPATCON con #} {# BUILTIN AGDAPATDOT dot #} {# BUILTIN AGDAPATVAR var #} {# BUILTIN AGDAPATLIT lit #} {# BUILTIN AGDAPATPROJ proj #} {# BUILTIN AGDAPATABSURD absurd #} data Clause : Set where clause : List (Arg Pattern) → Term → Clause absurdclause : List (Arg Pattern) → Clause {# BUILTIN AGDACLAUSE Clause #} {# BUILTIN AGDACLAUSECLAUSE clause #} {# BUILTIN AGDACLAUSEABSURD absurdclause #} data FunDef : Set where fundef : Type → List Clause → FunDef {# BUILTIN AGDAFUNDEF FunDef #} {# BUILTIN AGDAFUNDEFCON fundef #}

New reflection builtins for extended (patternmatching) lambda.
The
AGDATERM
data type has been augmented with a constructorAGDATERMEXTLAM : List AGDACLAUSE → List (ARG AGDATERM) → AGDATERM
Absurd lambdas (
λ ()
) are quoted to extended lambdas with an absurd clause. 
Unquoting declarations.
You can now define (recursive) functions by reflection using the new
unquoteDecl
declarationunquoteDecl x = e
Here e should have type
AGDAFUNDEF
and evaluate to a closed value. This value is then spliced in as the definition ofx
. In the bodye
,x
has typeQNAME
which lets you splice in recursive definitions.Standard modifiers, such as fixity declarations, can be applied to
x
as expected. 
Quoted levels
Universe levels are now quoted properly instead of being quoted to
AGDASORTUNSUPPORTED
.Setω
still gets an unsupported sort, however. 
Module applicants can now be operator applications.
Example:
postulate [_] : A > B module M (b : B) where module N (a : A) = M [ a ]
[See Issue #1245]

Minor change in module application semantics. [Issue #892]
Previously reexported functions were not redefined when instantiating a module. For instance
module A where f = ... module B (X : Set) where open A public module C = B Nat
In this example
C.f
would be an alias forA.f
, so if bothA
andC
were openedf
would not be ambiguous. However, this behaviour is not correct whenA
andB
share some module parameters (Issue #892). To fix thisC
now defines its own copy off
(which evaluates toA.f
), which means that openingA
andC
results in an ambiguousf
.
Type checking

Recursive records need to be declared as either
inductive
orcoinductive
.inductive
is no longer default for recursive records. Examples:record _×_ (A B : Set) : Set where constructor _,_ field fst : A snd : B record Tree (A : Set) : Set where inductive constructor tree field elem : A subtrees : List (Tree A) record Stream (A : Set) : Set where coinductive constructor _::_ field head : A tail : Stream A
If you are using oldstyle (musical) coinduction, a record may have to be declared as inductive, paradoxically.
record Stream (A : Set) : Set where inductive  YES, THIS IS INTENDED ! constructor _∷_ field head : A tail : ∞ (Stream A)
This is because the “coinduction” happens in the use of
∞
and not in the use ofrecord
.
Tools
Emacs mode
 A new menu option
Display
can be used to display the version of the running Agda process.
LaTeXbackend

New experimental option
references
has been added. When specified, i.e.:\usepackage[references]{agda}
a new command called
\AgdaRef
is provided, which lets you reference previously typeset commands, e.g.:Let us postulate
\AgdaRef{apa}
.\begin{code} postulate apa : Set \end{code}
Above
apa
will be typeset (highlighted) the same in the text as in the code, provided that the LaTeX output is postprocessed usingsrc/data/postprocesslatex.pl
, e.g.:cp $(dirname $(dirname $(agdamode locate)))/postprocesslatex.pl . agda i. latex Example.lagda cd latex/ perl ../postprocesslatex.pl Example.tex > Example.processed mv Example.processed Example.tex xelatex Example.tex
Mixfix and Unicode should work as expected (Unicode requires XeLaTeX/LuaLaTeX), but there are limitations:

Overloading identifiers should be avoided, if multiples exist
\AgdaRef
will typeset according to the first it finds. 
Only the current module is used, should you need to reference identifiers in other modules then you need to specify which other module manually, i.e.
\AgdaRef[module]{identifier}
.

Release notes for Agda 2 version 2.4.0.2

The Agda input mode now supports alphabetical super and subscripts, in addition to the numerical ones that were already present. [Issue #1240]

New feature: Interactively split result.
Make case (
Cc Cc
) with no variables given tries to split on the result to introduce projection patterns. The hole needs to be of record type, of course.test : {A B : Set} (a : A) (b : B) → A × B test a b = ?
Resultsplitting
?
will produce the new clauses:proj₁ (test a b) = ? proj₂ (test a b) = ?
If hole is of function type ending in a record type, the necessary pattern variables will be introduced before the split. Thus, the same result can be obtained by starting from:
test : {A B : Set} (a : A) (b : B) → A × B test = ?

The so far undocumented
ETA
pragma now throws an error if applied to definitions that are not records.ETA
can be used to force etaequality at recursive record types, for which eta is not enabled automatically by Agda. Here is such an example:mutual data Colist (A : Set) : Set where [] : Colist A _∷_ : A → ∞Colist A → Colist A record ∞Colist (A : Set) : Set where coinductive constructor delay field force : Colist A open ∞Colist {# ETA ∞Colist #} test : {A : Set} (x : ∞Colist A) → x ≡ delay (force x) test x = refl
Note: Unsafe use of
ETA
can make Agda loop, e.g. by triggering infinite eta expansion! 
Bugs fixed (see bug tracker):
Release notes for Agda 2 version 2.4.0.1

The option
compilenomain
has been renamed tonomain
. 
COMPILED_DATA
pragmas can now be given for records. 
Various bug fixes.
Release notes for Agda 2 version 2.4.0
Installation and infrastructure

A new module called
Agda.Primitive
has been introduced. This module is available to all users, even if the standard library is not used. Currently the module contains level primitives and their representation in Haskell when compiling with MAlonzo:infixl 6 _⊔_ postulate Level : Set lzero : Level lsuc : (ℓ : Level) → Level _⊔_ : (ℓ₁ ℓ₂ : Level) → Level {# COMPILED_TYPE Level () #} {# COMPILED lzero () #} {# COMPILED lsuc (\_ > ()) #} {# COMPILED _⊔_ (\_ _ > ()) #} {# BUILTIN LEVEL Level #} {# BUILTIN LEVELZERO lzero #} {# BUILTIN LEVELSUC lsuc #} {# BUILTIN LEVELMAX _⊔_ #}
To bring these declarations into scope you can use a declaration like the following one:
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
The standard library reexports these primitives (using the names
zero
andsuc
instead oflzero
andlsuc
) from theLevel
module.Existing developments using universe polymorphism might now trigger the following error message:
Duplicate binding for builtin thing LEVEL, previous binding to .Agda.Primitive.Level
To fix this problem, please remove the duplicate bindings.
Technical details (perhaps relevant to those who build Agda packages):
The include path now always contains a directory
<DATADIR>/lib/prim
, and this directory is supposed to contain a subdirectory Agda containing a filePrimitive.agda
.The standard location of
<DATADIR>
is system and installationspecific. E.g., in a Cabaluser
installation of Agda2.3.4 on a standard singleghc Linux system it would be$HOME/.cabal/share/Agda2.3.4
or something similar.The location of the
<DATADIR>
directory can be configured at compiletime using Cabal flags (datadir
anddatasubdir
). The location can also be set at runtime, using theAgda_datadir
environment variable.
Pragmas and options

Pragma
NO_TERMINATION_CHECK
placed within a mutual block is now applied to the whole mutual block (rather than being discarded silently). Adding to the uses 1.4. outlined in the release notes for 2.3.2 we allow:3a. Skipping an oldstyle mutual block: Somewhere within
mutual
block before a type signature or first function clause.mutual {# NO_TERMINATION_CHECK #} c : A c = d d : A d = c

New option
nopatternmatching
Disables all forms of pattern matching (for the current file). You can still import files that use pattern matching.

New option
v profile:7
Prints some stats on which phases Agda spends how much time. (Number might not be very reliable, due to garbage collection interruptions, and maybe due to laziness of Haskell.)

New option
nosizedtypes
Option
sizedtypes
is now default.nosizedtypes
will turn off an extra (inexpensive) analysis on data types used for subtyping of sized types.
Language

Experimental feature:
quoteContext
There is a new keyword
quoteContext
that gives users access to the list of names in the current local context. For instance:open import Data.Nat open import Data.List open import Reflection foo : ℕ → ℕ → ℕ foo 0 m = 0 foo (suc n) m = quoteContext xs in ?
In the remaining goal, the list
xs
will consist of two names,n
andm
, corresponding to the two local variables. At the moment it is not possible to access let bound variables (this feature may be added in the future). 
Experimental feature: Varying arity. Function clauses may now have different arity, e.g.,
Sum : ℕ → Set Sum 0 = ℕ Sum (suc n) = ℕ → Sum n sum : (n : ℕ) → ℕ → Sum n sum 0 acc = acc sum (suc n) acc m = sum n (m + acc)
or,
T : Bool → Set T true = Bool T false = Bool → Bool f : (b : Bool) → T b f false true = false f false false = true f true = true
This feature is experimental. Yet unsupported:

Varying arity and
with
. 
Compilation of functions with varying arity to Haskell, JS, or Epic.


Experimental feature: copatterns. (Activated with option
copatterns
)We can now define a record by explaining what happens if you project the record. For instance:
{# OPTIONS copatterns #} record _×_ (A B : Set) : Set where constructor _,_ field fst : A snd : B open _×_ pair : {A B : Set} → A → B → A × B fst (pair a b) = a snd (pair a b) = b swap : {A B : Set} → A × B → B × A fst (swap p) = snd p snd (swap p) = fst p swap3 : {A B C : Set} → A × (B × C) → C × (B × A) fst (swap3 t) = snd (snd t) fst (snd (swap3 t)) = fst (snd t) snd (snd (swap3 t)) = fst t
Taking a projection on the left hand side (lhs) is called a projection pattern, applying to a pattern is called an application pattern. (Alternative terms: projection/application copattern.)
In the first example, the symbol
pair
, if applied to variable patternsa
andb
and then projected viafst
, reduces toa
.pair
by itself does not reduce.A typical application are coinductive records such as streams:
record Stream (A : Set) : Set where coinductive field head : A tail : Stream A open Stream repeat : {A : Set} (a : A) > Stream A head (repeat a) = a tail (repeat a) = repeat a
Again,
repeat a
by itself will not reduce, but you can take a projection (head or tail) and then it will reduce to the respective rhs. This way, we get the lazy reduction behavior necessary to avoid looping corecursive programs.Application patterns do not need to be trivial (i.e., variable patterns), if we mix with projection patterns. E.g., we can have
nats : Nat > Stream Nat head (nats zero) = zero tail (nats zero) = nats zero head (nats (suc x)) = x tail (nats (suc x)) = nats x
Here is an example (not involving coinduction) which demostrates records with fields of function type:
 The State monad record State (S A : Set) : Set where constructor state field runState : S → A × S open State  The Monad type class record Monad (M : Set → Set) : Set1 where constructor monad field return : {A : Set} → A → M A _>>=_ : {A B : Set} → M A → (A → M B) → M B  State is an instance of Monad  Demonstrates the interleaving of projection and application patterns stateMonad : {S : Set} → Monad (State S) runState (Monad.return stateMonad a ) s = a , s runState (Monad._>>=_ stateMonad m k) s₀ = let a , s₁ = runState m s₀ in runState (k a) s₁ module MonadLawsForState {S : Set} where open Monad (stateMonad {S}) leftId : {A B : Set}(a : A)(k : A → State S B) → (return a >>= k) ≡ k a leftId a k = refl rightId : {A B : Set}(m : State S A) → (m >>= return) ≡ m rightId m = refl assoc : {A B C : Set}(m : State S A)(k : A → State S B)(l : B → State S C) → ((m >>= k) >>= l) ≡ (m >>= λ a → (k a >>= l)) assoc m k l = refl
Copatterns are yet experimental and the following does not work:

Copatterns and
with
clauses. 
Compilation of copatterns to Haskell, JS, or Epic.

Projections generated by
open R {{...}}
are not handled properly on lhss yet.

Conversion checking is slower in the presence of copatterns, since stuck definitions of record type do no longer count as neutral, since they can become unstuck by applying a projection. Thus, comparing two neutrals currently requires comparing all they projections, which repeats a lot of work.


Toplevel module no longer required.
The toplevel module can be omitted from an Agda file. The module name is then inferred from the file name by dropping the path and the
.agda
extension. So, a module defined in/A/B/C.agda
would get the nameC
.You can also suppress only the module name of the toplevel module by writing
module _ where
This works also for parameterised modules.

Module parameters are now always hidden arguments in projections. For instance:
module M (A : Set) where record Prod (B : Set) : Set where constructor _,_ field fst : A snd : B open Prod public open M
Now, the types of
fst
andsnd
arefst : {A : Set}{B : Set} → Prod A B → A snd : {A : Set}{B : Set} → Prod A B → B
Until 2.3.2, they were
fst : (A : Set){B : Set} → Prod A B → A snd : (A : Set){B : Set} → Prod A B → B
This change is a step towards symmetry of constructors and projections. (Constructors always took the module parameters as hidden arguments).

Telescoping lets: Local bindings are now accepted in telescopes of modules, function types, and lambdaabstractions.
The syntax of telescopes as been extended to support
let
:id : (let ★ = Set) (A : ★) → A → A id A x = x
In particular one can now
open
modules inside telescopes:module Star where ★ : Set₁ ★ = Set module MEndo (let open Star) (A : ★) where Endo : ★ Endo = A → A
Finally a shortcut is provided for opening modules:
module N (open Star) (A : ★) (open MEndo A) (f : Endo) where ...
The semantics of the latter is
module _ where open Star module _ (A : ★) where open MEndo A module N (f : Endo) where ...
The semantics of telescoping lets in function types and lambda abstractions is just expanding them into ordinary lets.

More liberal lefthand sides in lets [Issue #1028]:
You can now write lefthand sides with arguments also for let bindings without a type signature. For instance,
let f x = suc x in f zero
Let bound functions still can’t do pattern matching though.

Ambiguous names in patterns are now optimistically resolved in favor of constructors. [Issue #822] In particular, the following succeeds now:
module M where data D : Set₁ where [_] : Set → D postulate [_] : Set → Set open M Foo : _ → Set Foo [ A ] = A

Anonymous
where
modules are opened public. [Issue #848]<clauses> f args = rhs module _ telescope where body <more clauses>
means the following (not proper Agda code, since you cannot put a module inbetween clauses)
<clauses> module _ {argtelescope} telescope where body f args = rhs <more clauses>
Example:
A : Set1 A = B module _ where B : Set1 B = Set C : Set1 C = B

Builtin
ZERO
andSUC
have been merged withNATURAL
.When binding the
NATURAL
builtin,ZERO
andSUC
are bound to the appropriate constructors automatically. This means that instead of writing{# BUILTIN NATURAL Nat #} {# BUILTIN ZERO zero #} {# BUILTIN SUC suc #}
you just write
{# BUILTIN NATURAL Nat #}

Pattern synonym can now have implicit arguments. [Issue #860]
For example,
pattern tail=_ {x} xs = x ∷ xs len : ∀ {A} → List A → Nat len [] = 0 len (tail= xs) = 1 + len xs

Syntax declarations can now have implicit arguments. [Issue #400]
For example
id : ∀ {a}{A : Set a} > A > A id x = x syntax id {A} x = x ∈ A

Minor syntax changes

}
is now parsed as endcomment even if no comment was begun. As a consequence, the following definition gives a parse errorf : {A : Set} > Set f {A} = A
because Agda now sees
ID(f) LBRACE ID(A) ENDCOMMENT
, and no longerID(f) LBRACE ID(A) RBRACE
.The rational is that the previous lexing was to contextsensitive, attempting to commentout
f
using{
and}
lead to a parse error. 
Fixities (binding strengths) can now be negative numbers as well. [Issue #1109]
infix 1 _myop_

Postulates are now allowed in mutual blocks. [Issue #977]

Empty where blocks are now allowed. [Issue #947]

Pattern synonyms are now allowed in parameterised modules. [Issue #941]

Empty hiding and renaming lists in module directives are now allowed.

Module directives
using
,hiding
,renaming
andpublic
can now appear in arbitrary order. Multipleusing
/hiding
/renaming
directives are allowed, but you still cannot have both using andhiding
(because that doesn’t make sense). [Issue #493]

Goal and error display

The error message
Refuse to construct infinite term
has been removed, instead one gets unsolved meta variables. Reason: the error was thrown overeagerly. [Issue #795] 
If an interactive case split fails with message
Since goal is solved, further case distinction is not supported; try `Solve constraints' instead
then the associated interaction meta is assigned to a solution. Press
Cc C=
(Show constraints) to view the solution andCc Cs
(Solve constraints) to apply it. [Issue #289]
Type checking

[ Issue #376 ] Implemented expansion of bound record variables during meta assignment. Now Agda can solve for metas X that are applied to projected variables, e.g.:
X (fst z) (snd z) = z X (fst z) = fst z
Technically, this is realized by substituting
(x , y)
forz
with fresh bound variablesx
andy
. Here the full code for the examples:record Sigma (A : Set)(B : A > Set) : Set where constructor _,_ field fst : A snd : B fst open Sigma test : (A : Set) (B : A > Set) > let X : (x : A) (y : B x) > Sigma A B X = _ in (z : Sigma A B) > X (fst z) (snd z) ≡ z test A B z = refl test' : (A : Set) (B : A > Set) > let X : A > A X = _ in (z : Sigma A B) > X (fst z) ≡ fst z test' A B z = refl
The fresh bound variables are named
fst(z)
andsnd(z)
and can appear in error messages, e.g.:fail : (A : Set) (B : A > Set) > let X : A > Sigma A B X = _ in (z : Sigma A B) > X (fst z) ≡ z fail A B z = refl
results in error:
Cannot instantiate the metavariable _7 to solution fst(z) , snd(z) since it contains the variable snd(z) which is not in scope of the metavariable or irrelevant in the metavariable but relevant in the solution when checking that the expression refl has type _7 A B (fst z) ≡ z

Dependent record types and definitions by copatterns require reduction with previous function clauses while checking the current clause. [Issue #907]
For a simple example, consider
test : ∀ {A} → Σ Nat λ n → Vec A n proj₁ test = zero proj₂ test = []
For the second clause, the lhs and rhs are typed as
proj₂ test : Vec A (proj₁ test) [] : Vec A zero
In order for these types to match, we have to reduce the lhs type with the first function clause.
Note that termination checking comes after type checking, so be careful to avoid nontermination! Otherwise, the type checker might get into an infinite loop.

The implementation of the primitive
primTrustMe
has changed. It now only reduces toREFL
if the two argumentsx
andy
have the same computational normal form. Before, it reduced whenx
andy
were definitionally equal, which included typedirected equality laws such as etaequality. Yet because reduction is untyped, calling conversion from reduction lead to Agda crashes [Issue #882].The amended description of
primTrustMe
is (cf. release notes for 2.2.6):primTrustMe : {A : Set} {x y : A} → x ≡ y
Here
_≡_
is the builtin equality (see BUILTIN hooks for equality, above).If
x
andy
have the same computational normal form, thenprimTrustMe {x = x} {y = y}
reduces torefl
.A note on
primTrustMe
’s runtime behavior: The MAlonzo compiler replaces all uses ofprimTrustMe
with theREFL
builtin, without any check for definitional equality. Incorrect uses ofprimTrustMe
can potentially lead to segfaults or similar problems of the compiled code. 
Implicit patterns of record type are now only etaexpanded if there is a record constructor. [Issues #473, #635]
data D : Set where d : D data P : D → Set where p : P d record Rc : Set where constructor c field f : D works : {r : Rc} → P (Rc.f r) → Set works p = D
This works since the implicit pattern
r
is etaexpanded toc x
which allows the type ofp
to reduce toP x
andx
to be unified withd
. The corresponding explicit version is:works' : (r : Rc) → P (Rc.f r) → Set works' (c .d) p = D
However, if the record constructor is removed, the same example will fail:
record R : Set where field f : D fails : {r : R} → P (R.f r) → Set fails p = D  d != R.f r of type D  when checking that the pattern p has type P (R.f r)
The error is justified since there is no pattern we could write down for
r
. It would have to look likerecord { f = .d }
but anonymous record patterns are not part of the language.

Absurd lambdas at different source locations are no longer different. [Issue #857] In particular, the following code typechecks now:
absurdequality : _≡_ {A = ⊥ → ⊥} (λ()) λ() absurdequality = refl
Which is a good thing!

Printing of named implicit function types.
When printing terms in a context with bound variables Agda renames new bindings to avoid clashes with the previously bound names. For instance, if
A
is in scope, the type(A : Set) → A
is printed as(A₁ : Set) → A₁
. However, for implicit function types the name of the binding matters, since it can be used when giving implicit arguments.For this situation, the following new syntax has been introduced:
{x = y : A} → B
is an implicit function type whose bound variable (in scope inB
) isy
, but where the name of the argument isx
for the purposes of giving it explicitly. For instance, withA
in scope, the type{A : Set} → A
is now printed as{A = A₁ : Set} → A₁
.This syntax is only used when printing and is currently not being parsed.

Changed the semantics of
withoutK
. [Issue #712, Issue #865, Issue #1025]New specification of
withoutK
:When
withoutK
is enabled, the unification of indices for pattern matching is restricted in two ways:
Reflexive equations of the form
x == x
are no longer solved, instead Agda gives an error when such an equation is encountered. 
When unifying two sameheaded constructor forms
c us
andc vs
of typeD pars ixs
, the datatype indicesixs
(but not the parameters) have to be selfunifiable, i.e. unification ofixs
with itself should succeed positively. This is a nontrivial requirement because of point 1.
Examples:

The J rule is accepted.
J : {A : Set} (P : {x y : A} → x ≡ y → Set) → (∀ x → P (refl x)) → ∀ {x y} (x≡y : x ≡ y) → P x≡y J P p (refl x) = p x ```agda This definition is accepted since unification of `x` with `y` doesn't require deletion or injectivity.

The K rule is rejected.
K : {A : Set} (P : {x : A} → x ≡ x → Set) → (∀ x → P (refl {x = x})) → ∀ {x} (x≡x : x ≡ x) → P x≡x K P p refl = p _
Definition is rejected with the following error:
Cannot eliminate reflexive equation x = x of type A because K has been disabled. when checking that the pattern refl has type x ≡ x

Symmetry of the new criterion.
test₁ : {k l m : ℕ} → k + l ≡ m → ℕ test₁ refl = zero test₂ : {k l m : ℕ} → k ≡ l + m → ℕ test₂ refl = zero
Both versions are now accepted (previously only the first one was).

Handling of parameters.
consinjective : {A : Set} (x y : A) → (x ∷ []) ≡ (y ∷ []) → x ≡ y consinjective x .x refl = refl
Parameters are not unified, so they are ignored by the new criterion.

A larger example: antisymmetry of ≤.
data _≤_ : ℕ → ℕ → Set where lz : (n : ℕ) → zero ≤ n ls : (m n : ℕ) → m ≤ n → suc m ≤ suc n ≤antisym : (m n : ℕ) → m ≤ n → n ≤ m → m ≡ n ≤antisym .zero .zero (lz .zero) (lz .zero) = refl ≤antisym .(suc m) .(suc n) (ls m n p) (ls .n .m q) = cong suc (≤antisym m n p q)

[ Issue #1025 ]
postulate mySpace : Set postulate myPoint : mySpace data Foo : myPoint ≡ myPoint → Set where foo : Foo refl test : (i : foo ≡ foo) → i ≡ refl test refl = {!!}
When applying injectivity to the equation
foo ≡ foo
of typeFoo refl
, it is checked that the indexrefl
of typemyPoint ≡ myPoint
is selfunifiable. The equationrefl ≡ refl
again requires injectivity, so now the indexmyPoint
is checked for selfunifiability, hence the error:Cannot eliminate reflexive equation myPoint = myPoint of type mySpace because K has been disabled. when checking that the pattern refl has type foo ≡ foo

Termination checking

A buggy facility coined “matrixshaped orders” that supported uncurried functions (which take tuples of arguments instead of one argument after another) has been removed from the termination checker. [Issue #787]

Definitions which fail the termination checker are not unfolded any longer to avoid loops or stack overflows in Agda. However, the termination checker for a mutual block is only invoked after typechecking, so there can still be loops if you define a nonterminating function. But termination checking now happens before the other supplementary checks: positivity, polarity, injectivity and projectionlikeness. Note that with the pragma
{# NO_TERMINATION_CHECK #}
you can make Agda treat any function as terminating. 
Termination checking of functions defined by
with
has been improved.Cases which previously required
terminationdepth
to pass the termination checker (due to use ofwith
) no longer need the flag. For examplemerge : List A → List A → List A merge [] ys = ys merge xs [] = xs merge (x ∷ xs) (y ∷ ys) with x ≤ y merge (x ∷ xs) (y ∷ ys)  false = y ∷ merge (x ∷ xs) ys merge (x ∷ xs) (y ∷ ys)  true = x ∷ merge xs (y ∷ ys)
This failed to termination check previously, since the
with
expands to an auxiliary functionmergeaux
:mergeaux x y xs ys false = y ∷ merge (x ∷ xs) ys mergeaux x y xs ys true = x ∷ merge xs (y ∷ ys)
This function makes a call to
merge
in which the size of one of the arguments is increasing. To make this pass the termination checker now inlines the definition ofmergeaux
before checking, thus effectively termination checking the original source program.As a result of this transformation doing
with
on a variable no longer preserves termination. For instance, this does not termination check:bad : Nat → Nat bad n with n ...  zero = zero ...  suc m = bad m

The performance of the termination checker has been improved. For higher
terminationdepth
the improvement is significant. While the defaultterminationdepth
is still 1, checking with higherterminationdepth
should now be feasible.
Compiler backends

The MAlonzo compiler backend now has support for compiling modules that are not full programs (i.e. don’t have a main function). The goal is that you can write part of a program in Agda and the rest in Haskell, and invoke the Agda functions from the Haskell code. The following features were added for this reason:

A new commandline option
compilenomain
: the commandagda compilenomain Test.agda
will compile
Test.agda
and all its dependencies to Haskell and compile the resulting Haskell files withmake
, but (unlikecompile
) not tell GHC to treatTest.hs
as the main module. This type of compilation can be invoked from Emacs by customizing theagda2backend
variable to valueMAlonzoNoMain
and then callingCc Cx Cc
as before. 
A new pragma
COMPILED_EXPORT
was added as part of the MAlonzo FFI. If we have an Agda file containing the following:module A.B where test : SomeType test = someImplementation {# COMPILED_EXPORT test someHaskellId #}
then test will be compiled to a Haskell function called
someHaskellId
in moduleMAlonzo.Code.A.B
that can be invoked from other Haskell code. Its type will be translated according to the normal MAlonzo rules.

Tools
Emacs mode

A new goal command
Helper Function Type
(Cc Ch
) has been added.If you write an application of an undefined function in a goal, the
Helper Function Type
command will print the type that the function needs to have in order for it to fit the goal. The type is also added to the Emacs killring and can be pasted into the buffer usingCy
.The application must be of the form
f args
wheref
is the name of the helper function you want to create. The arguments can use all the normal features like named implicits or instance arguments.Example:
Here’s a start on a naive reverse on vectors:
reverse : ∀ {A n} → Vec A n → Vec A n reverse [] = [] reverse (x ∷ xs) = {!snoc (reverse xs) x!}
Calling
Cc Ch
in the goal printssnoc : ∀ {A} {n} → Vec A n → A → Vec A (suc n)

A new command
Explain why a particular name is in scope
(Cc Cw
) has been added. [Issue #207]This command can be called from a goal or from the toplevel and will as the name suggests explain why a particular name is in scope.
For each definition or module that the given name can refer to a trace is printed of all open statements and module applications leading back to the original definition of the name.
For example, given
module A (X : Set₁) where data Foo : Set where mkFoo : Foo module B (Y : Set₁) where open A Y public module C = B Set open C
Calling
Cc Cw
onmkFoo
at the toplevel printsmkFoo is in scope as * a constructor Issue207.C._.Foo.mkFoo brought into scope by  the opening of C at Issue207.agda:13,67  the application of B at Issue207.agda:11,1213  the application of A at Issue207.agda:9,89  its definition at Issue207.agda:6,510
This command is useful if Agda complains about an ambiguous name and you need to figure out how to hide the undesired interpretations.

Improvements to the
make case
command (Cc Cc
)
One can now also split on hidden variables, using the name (starting with
.
) with which they are printed. UseCc C
, to see all variables in context. 
Concerning the printing of generated clauses:

Uses named implicit arguments to improve readability.

Picks explicit occurrences over implicit ones when there is a choice of binding site for a variable.

Avoids binding variables in implicit positions by replacing dot patterns that uses them by wildcards (
._
).



Key bindings for lots of “mathematical” characters (examples: 𝐴𝑨𝒜𝓐𝔄) have been added to the Agda input method. Example: type
\MiA\MIA\McA\MCA\MfA
to get 𝐴𝑨𝒜𝓐𝔄.Note:
\McB
does not exist in Unicode (as well as others in that style), but the\MC
(bold) alphabet is complete. 
Key bindings for “blackboard bold” B (𝔹) and 09 (𝟘𝟡) have been added to the Agda input method (
\bb
and\b[09]
). 
Key bindings for controlling simplification/normalisation:
Commands like
Goal type and context
(Cc C,
) could previously be invoked in two ways. By default the output was normalised, but if a prefix argument was used (for instance viaCu Cc C,
), then no explicit normalisation was performed. Now there are three options:
By default (
Cc C,
) the output is simplified. 
If
Cu
is used exactly once (Cu Cc C,
), then the result is neither (explicitly) normalised nor simplified. 
If
Cu
is used twice (Cu Cu Cc C,
), then the result is normalised.

LaTeXbackend

Two new color scheme options were added to
agda.sty
:\usepackage[bw]{agda}
, which highlights in black and white;\usepackage[conor]{agda}
, which highlights using Conor’s colors.The default (no options passed) is to use the standard colors.

If
agda.sty
cannot be found by the LateX environment, it is now copied into the LateX output directory (latex
by default) instead of the working directory. This means that the commands needed to produce a PDF now isagda latex i . <file>.lagda cd latex pdflatex <file>.tex

The LaTeXbackend has been made more tool agnostic, in particular XeLaTeX and LuaLaTeX should now work. Here is a small example (
test/LaTeXAndHTML/succeed/UnicodeInput.lagda
):\documentclass{article} \usepackage{agda} \begin{document} \begin{code} data αβγδεζθικλμνξρστυφχψω : Set₁ where postulate →⇒⇛⇉⇄↦⇨↠⇀⇁ : Set \end{code} \[ ∀X [ ∅ ∉ X ⇒ ∃f:X ⟶ ⋃ X\ ∀A ∈ X (f(A) ∈ A) ] \] \end{document}
Compiled as follows, it should produce a nice looking PDF (tested with TeX Live 2012):
agda latex <file>.lagda cd latex xelatex <file>.tex (or lualatex <file>.tex)
If symbols are missing or XeLaTeX/LuaLaTeX complains about the font missing, try setting a different font using:
\setmathfont{<mathfont>}
Use the
fclist
tool to list available fonts. 
Add experimental support for hyperlinks to identifiers
If the
hyperref
LateX package is loaded before the Agda package and the links option is passed to the Agda package, then the Agda package provides a function called\AgdaTarget
. Identifiers which have been declared targets, by the user, will become clickable hyperlinks in the rest of the document. Here is a small example (test/LaTeXAndHTML/succeed/Links.lagda
):\documentclass{article} \usepackage{hyperref} \usepackage[links]{agda} \begin{document} \AgdaTarget{ℕ} \AgdaTarget{zero} \begin{code} data ℕ : Set where zero : ℕ suc : ℕ → ℕ \end{code} See next page for how to define \AgdaFunction{two} (doesn't turn into a link because the target hasn't been defined yet). We could do it manually though; \hyperlink{two}{\AgdaDatatype{two}}. \newpage \AgdaTarget{two} \hypertarget{two}{} \begin{code} two : ℕ two = suc (suc zero) \end{code} \AgdaInductiveConstructor{zero} is of type \AgdaDatatype{ℕ}. \AgdaInductiveConstructor{suc} has not been defined to be a target so it doesn't turn into a link. \newpage Now that the target for \AgdaFunction{two} has been defined the link works automatically. \begin{code} data Bool : Set where true false : Bool \end{code} The AgdaTarget command takes a list as input, enabling several targets to be specified as follows: \AgdaTarget{if, then, else, if\_then\_else\_} \begin{code} if_then_else_ : {A : Set} → Bool → A → A → A if true then t else f = t if false then t else f = f \end{code} \newpage Mixfix identifier need their underscores escaped: \AgdaFunction{if\_then\_else\_}. \end{document}
The boarders around the links can be suppressed using hyperref’s hidelinks option:
\usepackage[hidelinks]{hyperref}
Note that the current approach to links does not keep track of scoping or types, and hence overloaded names might create links which point to the wrong place. Therefore it is recommended to not overload names when using the links option at the moment, this might get fixed in the future.
Release notes for Agda 2 version 2.3.2.2

Fixed a bug that sometimes made it tricky to use the Emacs mode on Windows [Issue #757].

Made Agda build with newer versions of some libraries.

Fixed a bug that caused ambiguous parse error messages [Issue #147].
Release notes for Agda 2 version 2.3.2.1
Installation

Made it possible to compile Agda with more recent versions of hashable, QuickCheck and Win32.

Excluded mtl2.1.
Type checking
 Fixed bug in the termination checker (Issue #754).
Release notes for Agda 2 version 2.3.2
Installation

The Agdaexecutable package has been removed.
The executable is now provided as part of the Agda package.

The Emacs mode no longer depends on haskellmode or GHCi.

Compilation of Emacs mode Lisp files.
You can now compile the Emacs mode Lisp files by running
agdamode compile
. This command is run bymake install
.Compilation can, in some cases, give a noticeable speedup.
WARNING: If you reinstall the Agda mode without recompiling the Emacs Lisp files, then Emacs may continue using the old, compiled files.
Pragmas and options

The
withoutK
check now reconstructs constructor parameters.New specification of
withoutK
:If the flag is activated, then Agda only accepts certain casesplits. If the type of the variable to be split is
D pars ixs
, whereD
is a data (or record) type,pars
stands for the parameters, andixs
the indices, then the following requirements must be satisfied:
The indices
ixs
must be applications of constructors (or literals) to distinct variables. Constructors are usually not applied to parameters, but for the purposes of this check constructor parameters are treated as other arguments. 
These distinct variables must not be free in pars.


Irrelevant arguments are printed as
_
by default now. To turn on printing of irrelevant arguments, use optionshowirrelevant

New: Pragma
NO_TERMINATION_CHECK
to switch off termination checker for individual function definitions and mutual blocks.The pragma must precede a function definition or a mutual block. Examples (see
test/Succeed/NoTerminationCheck.agda
):
Skipping a single definition: before type signature.
{# NO_TERMINATION_CHECK #} a : A a = a

Skipping a single definition: before first clause.
b : A {# NO_TERMINATION_CHECK #} b = b

Skipping an oldstyle mutual block: Before
mutual
keyword.{# NO_TERMINATION_CHECK #} mutual c : A c = d d : A d = c

Skipping a newstyle mutual block: Anywhere before a type signature or first function clause in the block
i : A j : A i = j {# NO_TERMINATION_CHECK #} j = i
The pragma cannot be used in
safe
mode. 
Language

Let binding record patterns
record _×_ (A B : Set) : Set where constructor _,_ field fst : A snd : B open _×_ let (x , (y , z)) = t in u
will now be interpreted as
let x = fst t y = fst (snd t) z = snd (snd t) in u
Note that the type of
t
needs to be inferable. If you need to provide a type signature, you can write the following:let a : ... a = t (x , (y , z)) = a in u

Pattern synonyms
A pattern synonym is a declaration that can be used on the left hand side (when pattern matching) as well as the right hand side (in expressions). For example:
pattern z = zero pattern ss x = suc (suc x) f : ℕ > ℕ f z = z f (suc z) = ss z f (ss n) = n
Pattern synonyms are implemented by substitution on the abstract syntax, so definitions are scopechecked but not typechecked. They are particularly useful for universe constructions.

Qualified mixfix operators
It is now possible to use a qualified mixfix operator by qualifying the first part of the name. For instance
import Data.Nat as Nat import Data.Bool as Bool two = Bool.if true then 1 Nat.+ 1 else 0

Sections [Issue #735]. Agda now parses anonymous modules as sections:
module _ {a} (A : Set a) where data List : Set a where [] : List _∷_ : (x : A) (xs : List) → List module _ {a} {A : Set a} where _++_ : List A → List A → List A [] ++ ys = ys (x ∷ xs) ++ ys = x ∷ (xs ++ ys) test : List Nat test = (5 ∷ []) ++ (3 ∷ [])
In general, now the syntax
module _ parameters where declarations
is accepted and has the same effect as
private module M parameters where declarations open M public
for a fresh name
M
. 
Instantiating a module in an open import statement [Issue #481]. Now accepted:
open import Path.Module args [using/hiding/renaming (...)]
This only brings the imported identifiers from
Path.Module
into scope, not the module itself! Consequently, the following is pointless, and raises an error:import Path.Module args [using/hiding/renaming (...)]
You can give a private name
M
to the instantiated module viaimport Path.Module args as M [using/hiding/renaming (...)] open import Path.Module args as M [using/hiding/renaming (...)]
Try to avoid
as
as part of the arguments.as
is not a keyword; the following can be legal, although slightly obfuscated Agda code:open import as as as as as as

Implicit module parameters can be given by name. E.g.
open M {namedArg = bla}
This feature has been introduced in Agda 2.3.0 already.

Multiple type signatures sharing a same type can now be written as a single type signature.
one two : ℕ one = suc zero two = suc one
Goal and error display

Metavariables that were introduced by hidden argument
arg
are now printed as_arg_number
instead of just_number
. [Issue #526] 
Agda expands identifiers in anonymous modules when printing. Should make some goals nicer to read. [Issue #721]

When a module identifier is ambiguous, Agda tells you if one of them is a data type module. [Issues #318, #705]
Type checking

Improved coverage checker. The coverage checker splits on arguments that have constructor or literal pattern, committing to the leftmost split that makes progress. Consider the lookup function for vectors:
data Fin : Nat → Set where zero : {n : Nat} → Fin (suc n) suc : {n : Nat} → Fin n → Fin (suc n) data Vec (A : Set) : Nat → Set where [] : Vec A zero _∷_ : {n : Nat} → A → Vec A n → Vec A (suc n) _!!_ : {A : Set}{n : Nat} → Vec A n → Fin n → A (x ∷ xs) !! zero = x (x ∷ xs) !! suc i = xs !! i
In Agda up to 2.3.0, this definition is rejected unless we add an absurd clause
[] !! ()
This is because the coverage checker committed on splitting on the vector argument, even though this inevitably lead to failed coverage, because a case for the empty vector
[]
is missing.The improvement to the coverage checker consists on committing only on splits that have a chance of covering, since all possible constructor patterns are present. Thus, Agda will now split first on the
Fin
argument, since cases for bothzero
andsuc
are present. Then, it can split on theVec
argument, since the empty vector is already ruled out by instantiatingn
to asuc _
. 
Instance arguments resolution will now consider candidates which still expect hidden arguments. For example:
record Eq (A : Set) : Set where field eq : A → A → Bool open Eq {{...}} eqFin : {n : ℕ} → Eq (Fin n) eqFin = record { eq = primEqFin } testFin : Bool testFin = eq fin1 fin2
The typechecker will now resolve the instance argument of the
eq
function toeqFin {_}
. This is only done for hidden arguments, not instance arguments, so that the instance search stays nonrecursive. 
Constraint solving: Upgraded Miller patterns to record patterns. [Issue #456]
Agda now solves metavariables that are applied to record patterns. A typical (but here, artificial) case is:
record Sigma (A : Set)(B : A > Set) : Set where constructor _,_ field fst : A snd : B fst test : (A : Set)(B : A > Set) > let X : Sigma A B > Sigma A B X = _ in (x : A)(y : B x) > X (x , y) ≡ (x , y) test A B x y = refl
This yields a constraint of the form
_X A B (x , y) := t[x,y]
(with
t[x,y] = (x, y)
) which is not a Miller pattern. However, Agda now solves this as_X A B z := t[fst z,snd z].

Changed: solving recursive constraints. [Issue #585]
Until 2.3.0, Agda sometimes inferred values that did not pass the termination checker later, or would even make Agda loop. To prevent this, the occurs check now also looks into the definitions of the current mutual block, to avoid constructing recursive solutions. As a consequence, also terminating recursive solutions are no longer found automatically.
This effects a programming pattern where the recursively computed type of a recursive function is left to Agda to solve.
mutual T : D > Set T pattern1 = _ T pattern2 = _ f : (d : D) > T d f pattern1 = rhs1 f pattern2 = rhs2
This might no longer work from now on. See examples
test/Fail/Issue585*.agda
. 
Less eager introduction of implicit parameters. [Issue #679]
Until Agda 2.3.0, trailing hidden parameters were introduced eagerly on the left hand side of a definition. For instance, one could not write
test : {A : Set} > Set test = \ {A} > A
because internally, the hidden argument
{A : Set}
was added to the lefthand side, yieldingtest {_} = \ {A} > A
which raised a type error. Now, Agda only introduces the trailing implicit parameters it has to, in order to maintain uniform function arity. For instance, in
test : Bool > {A B C : Set} > Set test true {A} = A test false {B = B} = B
Agda will introduce parameters
A
andB
in all clauses, but notC
, resulting intest : Bool > {A B C : Set} > Set test true {A} {_} = A test false {_} {B = B} = B
Note that for checking
where
clauses, still all hidden trailing parameters are in scope. For instance:id : {i : Level}{A : Set i} > A > A id = myId where myId : forall {A} > A > A myId x = x
To be able to fill in the meta variable
_1
inmyId : {A : Set _1} > A > A
the hidden parameter
{i : Level}
needs to be in scope.As a result of this more lazy introduction of implicit parameters, the following code now passes.
data Unit : Set where unit : Unit T : Unit → Set T unit = {u : Unit} → Unit test : (u : Unit) → T u test unit with unit ...  _ = λ {v} → v
Before, Agda would eagerly introduce the hidden parameter
{v}
as unnamed lefthand side parameter, leaving no way to refer to it.The related Issue #655 has also been addressed. It is now possible to make `synonym’ definitions
name = expression
even when the type of expression begins with a hidden quantifier. Simple example:
id2 = id
That resulted in unsolved metas until 2.3.0.

Agda detects unused arguments and ignores them during equality checking. [Issue #691, solves also Issue #44]
Agda’s polarity checker now assigns ‘Nonvariant’ to arguments that are not actually used (except for absurd matches). If
f
’s first argument is Nonvariant, thenf x
is definitionally equal tof y
regardless ofx
andy
. It is similar to irrelevance, but does not require user annotation.For instance, unused module parameters do no longer get in the way:
module M (x : Bool) where not : Bool → Bool not true = false not false = true open M true open M false renaming (not to not′) test : (y : Bool) → not y ≡ not′ y test y = refl
Matching against record or absurd patterns does not count as `use’, so we get some form of proof irrelevance:
data ⊥ : Set where record ⊤ : Set where constructor trivial data Bool : Set where true false : Bool True : Bool → Set True true = ⊤ True false = ⊥ fun : (b : Bool) → True b → Bool fun true trivial = true fun false () test : (b : Bool) → (x y : True b) → fun b x ≡ fun b y test b x y = refl
More examples in
test/Succeed/NonvariantPolarity.agda
.Phantom arguments: Parameters of record and data types are considered `used’ even if they are not actually used. Consider:
False : Nat → Set False zero = ⊥ False (suc n) = False n module Invariant where record Bla (n : Nat)(p : False n) : Set where module Nonvariant where Bla : (n : Nat) → False n → Set Bla n p = ⊤
Even though record
Bla
does not use its parametersn
andp
, they are considered as used, allowing “phantom type” techniques.In contrast, the arguments of function
Bla
are recognized as unused. The following code typechecks if we openInvariant
but leaves unsolved metas if we openNonvariant
.dropsuc : {n : Nat}{p : False n} → Bla (suc n) p → Bla n p dropsuc _ = _ bla : (n : Nat) → {p : False n} → Bla n p → ⊥ bla zero {()} b bla (suc n) b = bla n (dropsuc b)
If
Bla
is considered invariant, the hidden argument in the recursive call can be inferred to bep
. If it is considered nonvariant, thenBla n X = Bla n p
does not entailX = p
and the hidden argument remains unsolved. Sincebla
does not actually use its hidden argument, its value is not important and it could be searched for. Unfortunately, polarity analysis ofbla
happens only after type checking, thus, the information thatbla
is nonvariant inp
is not available yet when metavariables are solved. (Seetest/Fail/BrokenInferenceDueToNonvariantPolarity.agda
) 
Agda now expands simple definitions (one clause, terminating) to check whether a function is constructor headed. [Issue #747] For instance, the following now also works:
MyPair : Set > Set > Set MyPair A B = Pair A B Vec : Set > Nat > Set Vec A zero = Unit Vec A (suc n) = MyPair A (Vec A n)
Here,
Unit
andPair
are data or record types.
Compiler backends

Werror
is now overridable.To enable compilation of Haskell modules containing warnings, the
Werror
flag for the MAlonzo backend has been made overridable. If, for example,ghcflag=Wwarn
is passed when compiling, one can get away with things like:data PartialBool : Set where true : PartialBool {# COMPILED_DATA PartialBool Bool True #}
The default behavior remains as it used to be and rejects the above program.
Tools
Emacs mode

Asynchronous Emacs mode.
One can now use Emacs while a buffer is typechecked. If the buffer is edited while the typechecker runs, then syntax highlighting will not be updated when typechecking is complete.

Interactive syntax highlighting.
The syntax highlighting is updated while a buffer is typechecked:

At first the buffer is highlighted in a somewhat crude way (without gotodefinition information for overloaded constructors).

If the highlighting level is “interactive”, then the piece of code that is currently being typechecked is highlighted as such. (The default is “noninteractive”.)

When a mutual block has been typechecked it is highlighted properly (this highlighting includes warnings for potential nontermination).
The highlighting level can be controlled via the new configuration variable
agda2highlightlevel
. 

Multiple casesplits can now be performed in one go.
Consider the following example:
_==_ : Bool → Bool → Bool b₁ == b₂ = {!!}
If you split on
b₁ b₂
, then you get the following code:_==_ : Bool → Bool → Bool true == true = {!!} true == false = {!!} false == true = {!!} false == false = {!!}
The order of the variables matters. Consider the following code:
lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A lookup xs i = {!!}
If you split on
xs i
, then you get the following code:lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A lookup [] () lookup (x ∷ xs) zero = {!!} lookup (x ∷ xs) (suc i) = {!!}
However, if you split on
i xs
, then you get the following code instead:lookup : ∀ {a n} {A : Set a} → Vec A n → Fin n → A lookup (x ∷ xs) zero = ? lookup (x ∷ xs) (suc i) = ?
This code is rejected by Agda 2.3.0, but accepted by 2.3.2 thanks to improved coverage checking (see above).

The Emacs mode now presents information about which module is currently being typechecked.

New global menu entry:
Information about the character at point
.If this entry is selected, then information about the character at point is displayed, including (in many cases) information about how to type the character.

Commenting/uncommenting the rest of the buffer.
One can now comment or uncomment the rest of the buffer by typing
Cc Cx M;
or by selecting the menu entryComment/uncomment
the rest of the buffer”. 
The Emacs mode now uses the Agda executable instead of GHCi.
The
*ghci*
buffer has been renamed to*agda2*
.A new configuration variable has been introduced:
agda2programname
, the name of the Agda executable (by defaultagda
).The variable
agda2ghcioptions
has been replaced byagda2programargs
: extra arguments given to the Agda executable (by defaultnone
).If you want to limit Agda’s memory consumption you can add some arguments to
agda2programargs
, for instance+RTS M1.5G RTS
. 
The Emacs mode no longer depends on haskellmode.
Users who have customised certain haskellmode variables (such as
haskellghciprogramargs
) may want to update their configuration.
LaTeXbackend
An experimental LaTeXbackend which does precise highlighting a la the HTMLbackend and code alignment a la lhs2TeX has been added.
Here is a sample input literate Agda file:
\documentclass{article}
\usepackage{agda}
\begin{document}
The following module declaration will be hidden in the output.
\AgdaHide{
\begin{code}
module M where
\end{code}
}
Two or more spaces can be used to make the backend align stuff.
\begin{code}
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
_+_ : ℕ → ℕ → ℕ
zero + n = n
suc m + n = suc (m + n)
\end{code}
\end{document}
To produce an output PDF issue the following commands:
agda latex i . <file>.lagda
pdflatex latex/<file>.tex
Only the topmost module is processed, like with lhs2tex and unlike
with the HTMLbackend. If you want to process imported modules you
have to call agda latex
manually on each of those modules.
There are still issues related to formatting, see the bug tracker for more information:
https://code.google.com/p/agda/issues/detail?id=697
The default agda.sty
might therefore change in backwardsincompatible
ways, as work proceeds in trying to resolve those problems.
Implemented features:

Two or more spaces can be used to force alignment of things, like with lhs2tex. See example above.

The highlighting information produced by the type checker is used to generate the output. For example, the data declaration in the example above, produces:
\AgdaKeyword{data} \AgdaDatatype{ℕ} \AgdaSymbol{:} \AgdaPrimitiveType{Set} \AgdaKeyword{where}
These LaTeX commands are defined in
agda.sty
(which is imported by\usepackage{agda}
) and cause the highlighting. 
The LaTeXbackend checks if
agda.sty
is found by the LaTeX environment, if it isn’t a defaultagda.sty
is copied from Agda’sdatadir
into the working directory (and thus made available to the LaTeX environment).If the default
agda.sty
isn’t satisfactory (colors, fonts, spacing, etc) then the user can modify it and make put it somewhere where the LaTeX environment can find it. Hopefully most aspects should be modifiable viaagda.sty
rather than having to tweak the implementation. 
latexdir
can be used to change the default output directory.
Release notes for Agda 2 version 2.3.0
Language

New more liberal syntax for mutually recursive definitions.
It is no longer necessary to use the
mutual
keyword to define mutually recursive functions or datatypes. Instead, it is enough to declare things before they are used. Instead ofmutual f : A f = a[f, g] g : B[f] g = b[f, g]
you can now write
f : A g : B[f] f = a[f, g] g = b[f, g].
With the new style you have more freedom in choosing the order in which things are type checked (previously type signatures were always checked before definitions). Furthermore you can mix arbitrary declarations, such as modules and postulates, with mutually recursive definitions.
For data types and records the following new syntax is used to separate the declaration from the definition:
 Declaration. data Vec (A : Set) : Nat → Set  Note the absence of 'where'.  Definition. data Vec A where [] : Vec A zero _::_ : {n : Nat} → A → Vec A n → Vec A (suc n)  Declaration. record Sigma (A : Set) (B : A → Set) : Set  Definition. record Sigma A B where constructor _,_ field fst : A snd : B fst
When making separated declarations/definitions private or abstract you should attach the
private
keyword to the declaration and theabstract
keyword to the definition. For instance, a private, abstract function can be defined asprivate f : A abstract f = e
Finally it may be worth noting that the old style of mutually recursive definitions is still supported (it basically desugars into the new style).

Pattern matching lambdas.
Anonymous pattern matching functions can be defined using the syntax
\ { p11 .. p1n > e1 ; ... ; pm1 .. pmn > em }
(where, as usual,
\
and>
can be replaced byλ
and→
). Internally this is translated into a function definition of the following form:.extlam p11 .. p1n = e1 ... .extlam pm1 .. pmn = em
This means that anonymous pattern matching functions are generative. For instance,
refl
will not be accepted as an inhabitant of the type(λ { true → true ; false → false }) ≡ (λ { true → true ; false → false }),
because this is equivalent to
extlam1 ≡ extlam2
for some distinct fresh namesextlam1
andextlam2
.Currently the
where
andwith
constructions are not allowed in (the toplevel clauses of) anonymous pattern matching functions.Examples:
and : Bool → Bool → Bool and = λ { true x → x ; false _ → false } xor : Bool → Bool → Bool xor = λ { true true → false ; false false → false ; _ _ → true } fst : {A : Set} {B : A → Set} → Σ A B → A fst = λ { (a , b) → a } snd : {A : Set} {B : A → Set} (p : Σ A B) → B (fst p) snd = λ { (a , b) → b }

Record update syntax.
Assume that we have a record type and a corresponding value:
record MyRecord : Set where field a b c : ℕ old : MyRecord old = record { a = 1; b = 2; c = 3 }
Then we can update (some of) the record value’s fields in the following way:
new : MyRecord new = record old { a = 0; c = 5 }
Here new normalises to
record { a = 0; b = 2; c = 5 }
. Any expression yielding a value of typeMyRecord
can be used instead of old.Record updating is not allowed to change types: the resulting value must have the same type as the original one, including the record parameters. Thus, the type of a record update can be inferred if the type of the original record can be inferred.
The record update syntax is expanded before type checking. When the expression
record old { updfields }
is checked against a record type
R
, it is expanded tolet r = old in record { newfields },
where old is required to have type
R
and newfields is defined as follows: for each fieldx
inR
,
if
x = e
is contained inupdfields
thenx = e
is included innewfields
, and otherwise 
if
x
is an explicit field thenx = R.x r
is included innewfields
, and 
if
x
is an implicit or instance field, then it is omitted fromnewfields
.
(Instance arguments are explained below.) The reason for treating implicit and instance fields specially is to allow code like the following:
record R : Set where field {length} : ℕ vec : Vec ℕ length  More fields… xs : R xs = record { vec = 0 ∷ 1 ∷ 2 ∷ [] } ys = record xs { vec = 0 ∷ [] }
Without the special treatment the last expression would need to include a new binding for length (for instance
length = _
). 

Record patterns which do not contain data type patterns, but which do contain dot patterns, are no longer rejected.

When the
withoutK
flag is used literals are now treated as constructors. 
Underapplied functions can now reduce.
Consider the following definition:
id : {A : Set} → A → A id x = x
Previously the expression
id
would not reduce. This has been changed so that it now reduces toλ x → x
. Usually this makes little difference, but it can be important in conjunction withwith
. See Issue #365 for an example. 
Unused AgdaLight legacy syntax
(x y : A; z v : B)
for telescopes has been removed.
Universe polymorphism

Universe polymorphism is now enabled by default. Use
nouniversepolymorphism
to disable it. 
Universe levels are no longer defined as a data type.
The basic level combinators can be introduced in the following way:
postulate Level : Set zero : Level suc : Level → Level max : Level → Level → Level {# BUILTIN LEVEL Level #} {# BUILTIN LEVELZERO zero #} {# BUILTIN LEVELSUC suc #} {# BUILTIN LEVELMAX max #}

The BUILTIN equality is now required to be universepolymorphic.

trustMe
is now universepolymorphic.
Metavariables and unification

Unsolved metavariables are now frozen after every mutual block. This means that they cannot be instantiated by subsequent code. For instance,
one : Nat one = _ bla : one ≡ suc zero bla = refl
leads to an error now, whereas previously it lead to the instantiation of
_
withsuc zero
. If you want to make use of the old behaviour, put the two definitions in a mutual block.All metavariables are unfrozen during interactive editing, so that the user can fill holes interactively. Note that typechecking of interactively given terms is not perfect: Agda sometimes refuses to load a file, even though no complaints were raised during the interactive construction of the file. This is because certain checks (for instance, positivity) are only invoked when a file is loaded.

Record types can now be inferred.
If there is a unique known record type with fields matching the fields in a record expression, then the type of the expression will be inferred to be the record type applied to unknown parameters.
If there is no known record type with the given fields the type checker will give an error instead of producing lots of unsolved metavariables.
Note that “known record type” refers to any record type in any imported module, not just types which are in scope.

The occurrence checker distinguishes rigid and strongly rigid occurrences [Reed, LFMTP 2009; Abel & Pientka, TLCA 2011].
The completeness checker now accepts the following code:
h : (n : Nat) → n ≡ suc n → Nat h n ()
Internally this generates a constraint
_n = suc _n
where the metavariable_n
occurs strongly rigidly, i.e. on a constructor path from the root, in its own defining term tree. This is never solvable.Weakly rigid recursive occurrences may have a solution [Jason Reed’s PhD thesis, page 106]:
test : (k : Nat) → let X : (Nat → Nat) → Nat X = _ in (f : Nat → Nat) → X f ≡ suc (f (X (λ x → k))) test k f = refl
The constraint
_X k f = suc (f (_X k (λ x → k)))
has the solution_X k f = suc (f (suc k))
, despite the recursive occurrence of_X
. Here_X
is not strongly rigid, because it occurs under the bound variablef
. Previously Agda rejected this code; now it instead complains about an unsolved metavariable. 
Equation constraints involving the same metavariable in the head now trigger pruning [Pientka, PhD, Sec. 3.1.2; Abel & Pientka, TLCA 2011]. Example:
same : let X : A → A → A → A × A X = _ in {x y z : A} → X x y y ≡ (x , y) × X x x y ≡ X x y y same = refl , refl
The second equation implies that
X
cannot depend on its second argument. After pruning the first equation is linear and can be solved. 
Instance arguments.
A new type of hidden function arguments has been added: instance arguments. This new feature is based on influences from Scala’s implicits and Agda’s existing implicit arguments.
Plain implicit arguments are marked by single braces:
{…}
. Instance arguments are instead marked by double braces:{{…}}
. Example:postulate A : Set B : A → Set a : A f : {{a : A}} → B a
Instead of the double braces you can use the symbols
⦃
and⦄
, but these symbols must in many cases be surrounded by whitespace. (If you are using Emacs and the Agda input method, then you can conjure up the symbols by typing\{{
and\}}
, respectively.)Instance arguments behave as ordinary implicit arguments, except for one important aspect: resolution of arguments which are not provided explicitly. For instance, consider the following code:
test = f
Here Agda will notice that
f
’s instance argument was not provided explicitly, and try to infer it. All definitions in scope atf
’s call site, as well as all variables in the context, are considered. If exactly one of these names has the required typeA
, then the instance argument will be instantiated to this name.This feature can be used as an alternative to Haskell type classes. If we define
record Eq (A : Set) : Set where field equal : A → A → Bool,
then we can define the following projection:
equal : {A : Set} {{eq : Eq A}} → A → A → Bool equal {{eq}} = Eq.equal eq
Now consider the following expression:
equal false false ∨ equal 3 4
If the following
Eq
“instances” forBool
andℕ
are in scope, and no others, then the expression is accepted:eqBool : Eq Bool eqBool = record { equal = … } eqℕ : Eq ℕ eqℕ = record { equal = … }
A shorthand notation is provided to avoid the need to define projection functions manually:
module Eqwithimplicits = Eq {{...}}
This notation creates a variant of
Eq
’s record module, where the mainEq
argument is an instance argument instead of an explicit one. It is equivalent to the following definition:module Eqwithimplicits {A : Set} {{eq : Eq A}} = Eq eq
Note that the shorthand notation allows you to avoid naming the “withimplicits” module:
open Eq {{...}}
Instance argument resolution is not recursive. As an example, consider the following “parametrised instance”:
eqList : {A : Set} → Eq A → Eq (List A) eqList {A} eq = record { equal = eqListA } where eqListA : List A → List A → Bool eqListA [] [] = true eqListA (a ∷ as) (b ∷ bs) = equal a b ∧ eqListA as bs eqListA _ _ = false
Assume that the only
Eq
instances in scope areeqList
andeqℕ
. Then the following code does not typecheck:test = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ [])
However, we can make the code work by constructing a suitable instance manually:
test′ = equal (1 ∷ 2 ∷ []) (3 ∷ 4 ∷ []) where eqListℕ = eqList eqℕ
By restricting the “instance search” to be nonrecursive we avoid introducing a new, compiletimeonly evaluation model to Agda.
For more information about instance arguments, see Devriese & Piessens [ICFP 2011]. Some examples are also available in the examples/instancearguments subdirectory of the Agda distribution.
Irrelevance

Dependent irrelevant function types.
Some examples illustrating the syntax of dependent irrelevant function types:
.(x y : A) → B .{x y z : A} → B ∀ x .y → B ∀ x .{y} {z} .v → B
The declaration
f : .(x : A) → B[x] f x = t[x]
requires that
x
is irrelevant both int[x]
and inB[x]
. This is possible if, for instance,B[x] = B′ x
, withB′ : .A → Set
.Dependent irrelevance allows us to define the eliminator for the
Squash
type:record Squash (A : Set) : Set where constructor squash field .proof : A elimSquash : {A : Set} (P : Squash A → Set) (ih : .(a : A) → P (squash a)) → (a⁻ : Squash A) → P a⁻ elimSquash P ih (squash a) = ih a
Note that this would not typecheck with
(ih : (a : A) > P (squash a)).

Records with only irrelevant fields.
The following now works:
record IsEquivalence {A : Set} (_≈_ : A → A → Set) : Set where field .refl : Reflexive _≈_ .sym : Symmetric _≈_ .trans : Transitive _≈_ record Setoid : Set₁ where infix 4 _≈_ field Carrier : Set _≈_ : Carrier → Carrier → Set .isEquivalence : IsEquivalence _≈_ open IsEquivalence isEquivalence public
Previously Agda complained about the application
IsEquivalence isEquivalence
, becauseisEquivalence
is irrelevant and theIsEquivalence
module expected a relevant argument. Now, when record modules are generated for records consisting solely of irrelevant arguments, the record parameter is made irrelevant:module IsEquivalence {A : Set} {_≈_ : A → A → Set} .(r : IsEquivalence {A = A} _≈_) where …

Irrelevant things are no longer erased internally. This means that they are printed as ordinary terms, not as
_
as before. 
The new flag
experimentalirrelevance
enables irrelevant universe levels and matching on irrelevant data when only one constructor is available. These features are very experimental and likely to change or disappear.
Reflection

The reflection API has been extended to mirror features like irrelevance, instance arguments and universe polymorphism, and to give (limited) access to definitions. For completeness all the builtins and primitives are listed below:
 Names. postulate Name : Set {# BUILTIN QNAME Name #} primitive  Equality of names. primQNameEquality : Name → Name → Bool  Is the argument visible (explicit), hidden (implicit), or an  instance argument? data Visibility : Set where visible hidden instance : Visibility {# BUILTIN HIDING Visibility #} {# BUILTIN VISIBLE visible #} {# BUILTIN HIDDEN hidden #} {# BUILTIN INSTANCE instance #}  Arguments can be relevant or irrelevant. data Relevance : Set where relevant irrelevant : Relevance {# BUILTIN RELEVANCE Relevance #} {# BUILTIN RELEVANT relevant #} {# BUILTIN IRRELEVANT irrelevant #}  Arguments. data Arg A : Set where arg : (v : Visibility) (r : Relevance) (x : A) → Arg A {# BUILTIN ARG Arg #} {# BUILTIN ARGARG arg #}  Terms. mutual data Term : Set where  Variable applied to arguments. var : (x : ℕ) (args : List (Arg Term)) → Term  Constructor applied to arguments. con : (c : Name) (args : List (Arg Term)) → Term  Identifier applied to arguments. def : (f : Name) (args : List (Arg Term)) → Term  Different kinds of λabstraction. lam : (v : Visibility) (t : Term) → Term  Pitype. pi : (t₁ : Arg Type) (t₂ : Type) → Term  A sort. sort : Sort → Term  Anything else. unknown : Term data Type : Set where el : (s : Sort) (t : Term) → Type data Sort : Set where  A Set of a given (possibly neutral) level. set : (t : Term) → Sort  A Set of a given concrete level. lit : (n : ℕ) → Sort  Anything else. unknown : Sort {# BUILTIN AGDASORT Sort #} {# BUILTIN AGDATYPE Type #} {# BUILTIN AGDATERM Term #} {# BUILTIN AGDATERMVAR var #} {# BUILTIN AGDATERMCON con #} {# BUILTIN AGDATERMDEF def #} {# BUILTIN AGDATERMLAM lam #} {# BUILTIN AGDATERMPI pi #} {# BUILTIN AGDATERMSORT sort #} {# BUILTIN AGDATERMUNSUPPORTED unknown #} {# BUILTIN AGDATYPEEL el #} {# BUILTIN AGDASORTSET set #} {# BUILTIN AGDASORTLIT lit #} {# BUILTIN AGDASORTUNSUPPORTED unknown #} postulate  Function definition. Function : Set  Data type definition. Datatype : Set  Record type definition. Record : Set {# BUILTIN AGDAFUNDEF Function #} {# BUILTIN AGDADATADEF Datatype #} {# BUILTIN AGDARECORDDEF Record #}  Definitions. data Definition : Set where function : Function → Definition datatype : Datatype → Definition record′ : Record → Definition constructor′ : Definition axiom : Definition primitive′ : Definition {# BUILTIN AGDADEFINITION Definition #} {# BUILTIN AGDADEFINITIONFUNDEF function #} {# BUILTIN AGDADEFINITIONDATADEF datatype #} {# BUILTIN AGDADEFINITIONRECORDDEF record′ #} {# BUILTIN AGDADEFINITIONDATACONSTRUCTOR constructor′ #} {# BUILTIN AGDADEFINITIONPOSTULATE axiom #} {# BUILTIN AGDADEFINITIONPRIMITIVE primitive′ #} primitive  The type of the thing with the given name. primQNameType : Name → Type  The definition of the thing with the given name. primQNameDefinition : Name → Definition  The constructors of the given data type. primDataConstructors : Datatype → List Name
As an example the expression
primQNameType (quote zero)
is definitionally equal to
el (lit 0) (def (quote ℕ) [])
(if
zero
is a constructor of the data typeℕ
). 
New keyword:
unquote
.The construction
unquote t
converts a representation of an Agda term to actual Agda code in the following way:
The argument
t
must have typeTerm
(see the reflection API above). 
The argument is normalised.

The entire construction is replaced by the normal form, which is treated as syntax written by the user and typechecked in the usual way.
Examples:
test : unquote (def (quote ℕ) []) ≡ ℕ test = refl id : (A : Set) → A → A id = unquote (lam visible (lam visible (var 0 []))) idok : id ≡ (λ A (x : A) → x) idok = refl


New keyword:
quoteTerm
.The construction
quoteTerm t
is similar toquote n
, but whereasquote
is restricted to namesn
,quoteTerm
accepts termst
. The construction is handled in the following way:
The type of
t
is inferred. The termt
must be typecorrect. 
The term
t
is normalised. 
The construction is replaced by the Term representation (see the reflection API above) of the normal form. Any unsolved metavariables in the term are represented by the
unknown
term constructor.
Examples:
test₁ : quoteTerm (λ {A : Set} (x : A) → x) ≡ lam hidden (lam visible (var 0 [])) test₁ = refl  Local variables are represented as de Bruijn indices. test₂ : (λ {A : Set} (x : A) → quoteTerm x) ≡ (λ x → var 0 []) test₂ = refl  Terms are normalised before being quoted. test₃ : quoteTerm (0 + 0) ≡ con (quote zero) [] test₃ = refl

Compiler backends
MAlonzo

The MAlonzo backend’s FFI now handles universe polymorphism in a better way.
The translation of Agda types and kinds into Haskell now supports universepolymorphic postulates. The core changes are that the translation of function types has been changed from
T[[ Pi (x : A) B ]] = if A has a Haskell kind then forall x. () > T[[ B ]] else if x in fv B then undef else T[[ A ]] > T[[ B ]]
into
T[[ Pi (x : A) B ]] = if x in fv B then forall x. T[[ A ]] > T[[ B ]]  Note: T[[A]] not Unit. else T[[ A ]] > T[[ B ]],
and that the translation of constants (postulates, constructors and literals) has been changed from
T[[ k As ]] = if COMPILED_TYPE k T then T T[[ As ]] else undef
into
T[[ k As ]] = if COMPILED_TYPE k T then T T[[ As ]] else if COMPILED k E then () else undef.
For instance, assuming a Haskell definition
type AgdaIO a b = IO b,
we can set up universepolymorphic
IO
in the following way:postulate IO : ∀ {ℓ} → Set ℓ → Set ℓ return : ∀ {a} {A : Set a} → A → IO A _>>=_ : ∀ {a b} {A : Set a} {B : Set b} → IO A → (A → IO B) → IO B {# COMPILED_TYPE IO AgdaIO #} {# COMPILED return (\_ _ > return) #} {# COMPILED _>>=_ (\_ _ _ _ > (>>=)) #}
This is accepted because (assuming that the universe level type is translated to the Haskell unit type
()
)(\_ _ > return) : forall a. () > forall b. () > b > AgdaIO a b = T [[ ∀ {a} {A : Set a} → A → IO A ]]
and
(\_ _ _ _ > (>>=)) : forall a. () > forall b. () > forall c. () > forall d. () > AgdaIO a c > (c > AgdaIO b d) > AgdaIO b d = T [[ ∀ {a b} {A : Set a} {B : Set b} → IO A → (A → IO B) → IO B ]].
Epic

New Epic backend pragma:
STATIC
.In the Epic backend, functions marked with the
STATIC
pragma will be normalised before compilation. Example usage:{# STATIC power #} power : ℕ → ℕ → ℕ power 0 x = 1 power 1 x = x power (suc n) x = power n x * x
Occurrences of
power 4 x
will be replaced by((x * x) * x) * x
. 
Some new optimisations have been implemented in the Epic backend:
 Removal of unused arguments.
A worker/wrapper transformation is performed so that unused arguments can be removed by Epic’s inliner. For instance, the map function is transformed in the following way:
map_wrap : (A B : Set) → (A → B) → List A → List B map_wrap A B f xs = map_work f xs map_work f [] = [] map_work f (x ∷ xs) = f x ∷ map_work f xs
If
map_wrap
is inlined (which it will be in any saturated call), thenA
andB
disappear in the generated code.Unused arguments are found using abstract interpretation. The bodies of all functions in a module are inspected to decide which variables are used. The behaviour of postulates is approximated based on their types. Consider
return
, for instance:postulate return : {A : Set} → A → IO A
The first argument of
return
can be removed, because it is of type Set and thus cannot affect the outcome of a program at runtime. Injection detection.
At runtime many functions may turn out to be inefficient variants of the identity function. This is especially true after forcing. Injection detection replaces some of these functions with more efficient versions. Example:
inject : {n : ℕ} → Fin n → Fin (1 + n) inject {suc n} zero = zero inject {suc n} (suc i) = suc (inject {n} i)
Forcing removes the
Fin
constructors’ℕ
arguments, so this function is an inefficient identity function that can be replaced by the following one:inject {_} x = x
To actually find this function, we make the induction hypothesis that inject is an identity function in its second argument and look at the branches of the function to decide if this holds.
Injection detection also works over data type barriers. Example:
forget : {A : Set} {n : ℕ} → Vec A n → List A forget [] = [] forget (x ∷ xs) = x ∷ forget xs
Given that the constructor tags (in the compiled Epic code) for
Vec.[]
andList.[]
are the same, and that the tags forVec._∷_
andList._∷_
are also the same, this is also an identity function. We can hence replace the definition with the following one:forget {_} xs = xs
To get this to apply as often as possible, constructor tags are chosen after injection detection has been run, in a way to make as many functions as possible injections.
Constructor tags are chosen once per source file, so it may be advantageous to define conversion functions like forget in the same module as one of the data types. For instance, if
Vec.agda
importsList.agda
, then the forget function should be put inVec.agda
to ensure that vectors and lists get the same tags (unless some other injection function, which puts different constraints on the tags, is prioritised). Smashing.
This optimisation finds types whose values are inferable at runtime:

A data type with only one constructor where all fields are inferable is itself inferable.

Set ℓ
is inferable (as it has no runtime representation).
A function returning an inferable data type can be smashed, which means that it is replaced by a function which simply returns the inferred value.
An important example of an inferable type is the usual propositional equality type (
_≡_
). Any function returning a propositional equality can simply return the reflexivity constructor directly without computing anything.This optimisation makes more arguments unused. It also makes the Epic code size smaller, which in turn speeds up compilation.
JavaScript

ECMAScript compiler backend.
A new compiler backend is being implemented, targetting ECMAScript (also known as JavaScript), with the goal of allowing Agda programs to be run in browsers or other ECMAScript environments.
The backend is still at an experimental stage: the core language is implemented, but many features are still missing.
The ECMAScript compiler can be invoked from the command line using the flag
js
:agda js compiledir=<DIR> <FILE>.agda
Each source
<FILE>.agda
is compiled into an ECMAScript target<DIR>/jAgda.<TOPLEVEL MODULE NAME>.js
. The compiler can also be invoked using the Emacs mode (the variableagda2backend
controls which backend is used).Note that ECMAScript is a strict rather than lazy language. Since Agda programs are total, this should not impact program semantics, but it may impact their space or time usage.
ECMAScript does not support algebraic datatypes or patternmatching. These features are translated to a use of the visitor pattern. For instance, the standard library’s
List
data type andnull
function are translated into the following code:exports["List"] = {}; exports["List"]["[]"] = function (x0) { return x0["[]"](); }; exports["List"]["_∷_"] = function (x0) { return function (x1) { return function (x2) { return x2["_∷_"](x0, x1); }; }; }; exports["null"] = function (x0) { return function (x1) { return function (x2) { return x2({ "[]": function () { return jAgda_Data_Bool["Bool"]["true"]; }, "_∷_": function (x3, x4) { return jAgda_Data_Bool["Bool"]["false"]; } }); }; }; };
Agda records are translated to ECMAScript objects, preserving field names.
Toplevel Agda modules are translated to ECMAScript modules, following the
common.js
module specification. A toplevel Agda moduleFoo.Bar
is translated to an ECMAScript modulejAgda.Foo.Bar
.The ECMAScript compiler does not compile to Haskell, so the pragmas related to the Haskell FFI (
IMPORT
,COMPILED_DATA
andCOMPILED
) are not used by the ECMAScript backend. Instead, there is aCOMPILED_JS
pragma which may be applied to any declaration. For postulates, primitives, functions and values, it gives the ECMAScript code to be emitted by the compiler. For data types, it gives a function which is applied to a value of that type, and a visitor object. For instance, a binding of natural numbers to ECMAScript integers (ignoring overflow errors) is:data ℕ : Set where zero : ℕ suc : ℕ → ℕ {# COMPILED_JS ℕ function (x,v) { if (x < 1) { return v.zero(); } else { return v.suc(x1); } } #} {# COMPILED_JS zero 0 #} {# COMPILED_JS suc function (x) { return x+1; } #} _+_ : ℕ → ℕ → ℕ zero + n = n suc m + n = suc (m + n) {# COMPILED_JS _+_ function (x) { return function (y) { return x+y; }; } #}
To allow FFI code to be optimised, the ECMAScript in a
COMPILED_JS
declaration is parsed, using a simple parser that recognises a pure functional subset of ECMAScript, consisting of functions, function applications, return, ifstatements, ifexpressions, sideeffectfree binary operators (no precedence, left associative), sideeffectfree prefix operators, objects (where all member names are quoted), field accesses, and string and integer literals. Modules may be imported using the require (<moduleid>
) syntax: any impure code, or code outside the supported fragment, can be placed in a module and imported.
Tools

New flag
safe
, which can be used to typecheck untrusted code.This flag disables postulates,
primTrustMe
, and “unsafe” OPTION pragmas, some of which are known to make Agda inconsistent.Rejected pragmas:
allowunsolvedmetas experimentalirrelevance guardednesspreservingtypeconstrutors injectivetypeconstructors nocoveragecheck nopositivitycheck noterminationcheck sizedtypes typeintype
Note that, at the moment, it is not possible to define the universe level or coinduction primitives when
safe
is used (because they must be introduced as postulates). This can be worked around by typechecking trusted files in a first pass, without usingsafe
, and then usingsaf
e in a second pass. Modules which have already been typechecked are not retypechecked just becausesafe
is used. 
Dependency graphs.
The new flag
dependencygraph=FILE
can be used to generate a DOT file containing a module dependency graph. The generated file (FILE) can be rendered using a tool like dot. 
The
nounreachablecheck
flag has been removed. 
Projection functions are highlighted as functions instead of as fields. Field names (in record definitions and record values) are still highlighted as fields.

Support for jumping to positions mentioned in the information buffer has been added.

The
make install
command no longer installs Agda globally (by default).
Release notes for Agda 2 version 2.2.10
Language

New flag:
withoutK
.This flag makes pattern matching more restricted. If the flag is activated, then Agda only accepts certain casesplits. If the type of the variable to be split is
D pars ixs
, whereD
is a data (or record) type, pars stands for the parameters, andixs
the indices, then the following requirements must be satisfied:
The indices
ixs
must be applications of constructors to distinct variables. 
These variables must not be free in pars.
The intended purpose of
withoutK
is to enable experiments with a propositional equality without the K rule. Let us define propositional equality as follows:data _≡_ {A : Set} : A → A → Set where refl : ∀ x → x ≡ x
Then the obvious implementation of the J rule is accepted:
J : {A : Set} (P : {x y : A} → x ≡ y → Set) → (∀ x → P (refl x)) → ∀ {x y} (x≡y : x ≡ y) → P x≡y J P p (refl x) = p x
The same applies to Christine PaulinMohring’s version of the J rule:
J′ : {A : Set} {x : A} (P : {y : A} → x ≡ y → Set) → P (refl x) → ∀ {y} (x≡y : x ≡ y) → P x≡y J′ P p (refl x) = p
On the other hand, the obvious implementation of the K rule is not accepted:
K : {A : Set} (P : {x : A} → x ≡ x → Set) → (∀ x → P (refl x)) → ∀ {x} (x≡x : x ≡ x) → P x≡x K P p (refl x) = p x
However, we have not proved that activation of
withoutK
ensures that the K rule cannot be proved in some other way. 

Irrelevant declarations.
Postulates and functions can be marked as irrelevant by prefixing the name with a dot when the name is declared. Example:
postulate .irrelevant : {A : Set} → .A → A
Irrelevant names may only be used in irrelevant positions or in definitions of things which have been declared irrelevant.
The axiom irrelevant above can be used to define a projection from an irrelevant record field:
data Subset (A : Set) (P : A → Set) : Set where _#_ : (a : A) → .(P a) → Subset A P elem : ∀ {A P} → Subset A P → A elem (a # p) = a .certificate : ∀ {A P} (x : Subset A P) → P (elem x) certificate (a # p) = irrelevant p
The righthand side of certificate is relevant, so we cannot define
certificate (a # p) = p
(because
p
is irrelevant). However, certificate is declared to be irrelevant, so it can use the axiom irrelevant. Furthermore the first argument of the axiom is irrelevant, which means that irrelevantp
is wellformed.As shown above the axiom irrelevant justifies irrelevant projections. Previously no projections were generated for irrelevant record fields, such as the field certificate in the following record type:
record Subset (A : Set) (P : A → Set) : Set where constructor _#_ field elem : A .certificate : P elem
Now projections are generated automatically for irrelevant fields (unless the flag
noirrelevantprojections
is used). Note that irrelevant projections are highly experimental. 
Termination checker recognises projections.
Projections now preserve sizes, both in patterns and expressions. Example:
record Wrap (A : Set) : Set where constructor wrap field unwrap : A open Wrap public data WNat : Set where zero : WNat suc : Wrap WNat → WNat id : WNat → WNat id zero = zero id (suc w) = suc (wrap (id (unwrap w)))
In the structural ordering
unwrap w
≤w
. This means thatunwrap w ≤ w < suc w,
and hence the recursive call to id is accepted.
Projections also preserve guardedness.
Tools

Hyperlinks for toplevel module names now point to the start of the module rather than to the declaration of the module name. This applies both to the Emacs mode and to the output of
agda html
. 
Most occurrences of record field names are now highlighted as “fields”. Previously many occurrences were highlighted as “functions”.

Emacs mode: It is no longer possible to change the behaviour of the
TAB
key by customisingagda2indentation
. 
Epic compiler backend.
A new compiler backend is being implemented. This backend makes use of Edwin Brady’s language Epic (http://www.cs.standrews.ac.uk/~eb/epic.php) and its compiler. The backend should handle most Agda code, but is still at an experimental stage: more testing is needed, and some things written below may not be entirely true.
The Epic compiler can be invoked from the command line using the flag
epic
:agda epic epicflag=<EPICFLAG> compiledir=<DIR> <FILE>.agda
The
epicflag
flag can be given multiple times; each flag is given verbatim to the Epic compiler (in the given order). The resulting executable is named after the main module and placed in the directory specified by thecompiledir
flag (default: the project root). Intermediate files are placed in a subdirectory calledEpic
.The backend requires that there is a definition named main. This definition should be a value of type
IO Unit
, but at the moment this is not checked (so it is easy to produce a program which segfaults). Currently the backend represents actions of typeIO A
as functions fromUnit
toA
, and main is applied to the unit value.The Epic compiler compiles via C, not Haskell, so the pragmas related to the Haskell FFI (
IMPORT
,COMPILED_DATA
andCOMPILED
) are not used by the Epic backend. Instead there is a new pragmaCOMPILED_EPIC
. This pragma is used to give Epic code for postulated definitions (Epic code can in turn call C code). The form of the pragma is{# COMPILED_EPIC def code #}
, wheredef
is the name of an Agda postulate andcode
is some Epic code which should include the function arguments, return type and function body. As an example theIO
monad can be defined as follows:postulate IO : Set → Set return : ∀ {A} → A → IO A _>>=_ : ∀ {A B} → IO A → (A → IO B) → IO B {# COMPILED_EPIC return (u : Unit, a : Any) > Any = ioreturn(a) #} {# COMPILED_EPIC _>>=_ (u1 : Unit, u2 : Unit, x : Any, f : Any) > Any = iobind(x,f) #}
Here
ioreturn
andiobind
are Epic functions which are defined in the fileAgdaPrelude.e
which is always included.By default the backend will remove socalled forced constructor arguments (and casesplitting on forced variables will be rewritten). This optimisation can be disabled by using the flag
noforcing
.All data types which look like unary natural numbers after forced constructor arguments have been removed (i.e. types with two constructors, one nullary and one with a single recursive argument) will be represented as “BigInts”. This applies to the standard
Fin
type, for instance.The backend supports Agda’s primitive functions and the BUILTIN pragmas. If the BUILTIN pragmas for unary natural numbers are used, then some operations, like addition and multiplication, will use more efficient “BigInt” operations.
If you want to make use of the Epic backend you need to install some dependencies, see the README.

The Emacs mode can compile using either the MAlonzo or the Epic backend. The variable
agda2backend
controls which backend is used.
Release notes for Agda 2 version 2.2.8
Language

Record pattern matching.
It is now possible to pattern match on named record constructors. Example:
record Σ (A : Set) (B : A → Set) : Set where constructor _,_ field proj₁ : A proj₂ : B proj₁ map : {A B : Set} {P : A → Set} {Q : B → Set} (f : A → B) → (∀ {x} → P x → Q (f x)) → Σ A P → Σ B Q map f g (x , y) = (f x , g y)
The clause above is internally translated into the following one:
map f g p = (f (Σ.proj₁ p) , g (Σ.proj₂ p))
Record patterns containing data type patterns are not translated. Example:
add : ℕ × ℕ → ℕ add (zero , n) = n add (suc m , n) = suc (add (m , n))
Record patterns which do not contain data type patterns, but which do contain dot patterns, are currently rejected. Example:
Foo : {A : Set} (p₁ p₂ : A × A) → proj₁ p₁ ≡ proj₁ p₂ → Set₁ Foo (x , y) (.x , y′) refl = Set

Proof irrelevant function types.
Agda now supports irrelevant nondependent function types:
f : .A → B
This type implies that
f
does not depend computationally on its argument. One intended use case is data structures with embedded proofs, like sorted lists:postulate _≤_ : ℕ → ℕ → Set p₁ : 0 ≤ 1 p₂ : 0 ≤ 1 data SList (bound : ℕ) : Set where [] : SList bound scons : (head : ℕ) → .(head ≤ bound) → (tail : SList head) → SList bound
The effect of the irrelevant type in the signature of
scons
is thatscons
’s second argument is never inspected after Agda has ensured that it has the right type. It is even thrown away, leading to smaller term sizes and hopefully some gain in efficiency. The typechecker ignores irrelevant arguments when checking equality, so two lists can be equal even if they contain different proofs:l₁ : SList 1 l₁ = scons 0 p₁ [] l₂ : SList 1 l₂ = scons 0 p₂ [] l₁≡l₂ : l₁ ≡ l₂ l₁≡l₂ = refl
Irrelevant arguments can only be used in irrelevant contexts. Consider the following subset type:
data Subset (A : Set) (P : A → Set) : Set where _#_ : (elem : A) → .(P elem) → Subset A P
The following two uses are fine:
elimSubset : ∀ {A C : Set} {P} → Subset A P → ((a : A) → .(P a) → C) → C elimSubset (a # p) k = k a p elem : {A : Set} {P : A → Set} → Subset A P → A elem (x # p) = x
However, if we try to project out the proof component, then Agda complains that
variable p is declared irrelevant, so it cannot be used here
:prjProof : ∀ {A P} (x : Subset A P) → P (elem x) prjProof (a # p) = p
Matching against irrelevant arguments is also forbidden, except in the case of irrefutable matches (record constructor patterns which have been translated away). For instance, the match against the pattern
(p , q)
here is accepted:elim₂ : ∀ {A C : Set} {P Q : A → Set} → Subset A (λ x → Σ (P x) (λ _ → Q x)) → ((a : A) → .(P a) → .(Q a) → C) → C elim₂ (a # (p , q)) k = k a p q
Absurd matches
()
are also allowed.Note that record fields can also be irrelevant. Example:
record Subset (A : Set) (P : A → Set) : Set where constructor _#_ field elem : A .proof : P elem
Irrelevant fields are never in scope, neither inside nor outside the record. This means that no record field can depend on an irrelevant field, and furthermore projections are not defined for such fields. Irrelevant fields can only be accessed using pattern matching, as in
elimSubset
above.Irrelevant function types were added very recently, and have not been subjected to much experimentation yet, so do not be surprised if something is changed before the next release. For instance, dependent irrelevant function spaces (
.(x : A) → B
) might be added in the future. 
Mixfix binders.
It is now possible to declare userdefined syntax that binds identifiers. Example:
postulate State : Set → Set → Set put : ∀ {S} → S → State S ⊤ get : ∀ {S} → State S S return : ∀ {A S} → A → State S A bind : ∀ {A B S} → State S B → (B → State S A) → State S A syntax bind e₁ (λ x → e₂) = x ← e₁ , e₂ increment : State ℕ ⊤ increment = x ← get , put (1 + x)
The syntax declaration for
bind
implies thatx
is in scope ine₂
, but not ine₁
.You can give fixity declarations along with syntax declarations:
infixr 40 bind syntax bind e₁ (λ x → e₂) = x ← e₁ , e₂
The fixity applies to the syntax, not the name; syntax declarations are also restricted to ordinary, nonoperator names. The following declaration is disallowed:
syntax _==_ x y = x === y ```agda Syntax declarations must also be linear; the following declaration is disallowed: ```agda syntax wrong x = x + x
Syntax declarations were added very recently, and have not been subjected to much experimentation yet, so do not be surprised if something is changed before the next release.

Prop
has been removed from the language.The experimental sort
Prop
has been disabled. Any program usingProp
should typecheck ifProp
is replaced bySet₀
. Note thatProp
is still a keyword. 
Injective type constructors off by default.
Automatic injectivity of type constructors has been disabled (by default). To enable it, use the flag
injectivetypeconstructors
, either on the command line or in an OPTIONS pragma. Note that this flag makes Agda anticlassical and possibly inconsistent:Agda with excluded middle is inconsistent http://thread.gmane.org/gmane.comp.lang.agda/1367
See
test/Succeed/InjectiveTypeConstructors.agda
for an example. 
Termination checker can count.
There is a new flag
terminationdepth=N
accepting valuesN >= 1
(withN = 1
being the default) which influences the behavior of the termination checker. So far, the termination checker has only distinguished three cases when comparing the argument of a recursive call with the formal parameter of the callee.<
: the argument is structurally smaller than the parameter=
: they are equal?
: the argument is bigger or unrelated to the parameterThis behavior, which is still the default (
N = 1
), will not recognise the following functions as terminating.mutual f : ℕ → ℕ f zero = zero f (suc zero) = zero f (suc (suc n)) = aux n aux : ℕ → ℕ aux m = f (suc m)
The call graph
f (<)> aux (?)> f
yields a recursive call from
f
tof
viaaux
where the relation of call argument to callee parameter is computed as “unrelated” (composition of<
and?
).Setting
N >= 2
allows a finer analysis:n
has two constructors less thansuc (suc n)
, andsuc m
has one more thanm
, so we get the call graph:f (2)> aux (+1)> f
The indirect call
f > f
is now labeled with(1)
, and the termination checker can recognise that the call argument is decreasing on this path.Setting the termination depth to
N
means that the termination checker counts decrease up toN
and increase up toN1
. The default,N=1
, means that no increase is counted, every increase turns to “unrelated”.In practice, examples like the one above sometimes arise when
with
is used. As an example, the programf : ℕ → ℕ f zero = zero f (suc zero) = zero f (suc (suc n)) with zero ...  _ = f (suc n)
is internally represented as
mutual f : ℕ → ℕ f zero = zero f (suc zero) = zero f (suc (suc n)) = aux n zero aux : ℕ → ℕ → ℕ aux m k = f (suc m)
Thus, by default, the definition of
f
usingwith
is not accepted by the termination checker, even though it looks structural (suc n
is a subterm ofsuc suc n
). Now, the termination checker is satisfied if the optionterminationdepth=2
is used.Caveats:

This is an experimental feature, hopefully being replaced by something smarter in the near future.

Increasing the termination depth will quickly lead to very long termination checking times. So, use with care. Setting termination depth to
100
by habit, just to be on the safe side, is not a good idea! 
Increasing termination depth only makes sense for linear data types such as
ℕ
andSize
. For other types, increase cannot be recognised. For instance, consider a similar example with lists.data List : Set where nil : List cons : ℕ → List → List mutual f : List → List f nil = nil f (cons x nil) = nil f (cons x (cons y ys)) = aux y ys aux : ℕ → List → List aux z zs = f (cons z zs)
Here the termination checker compares
cons z zs
toz
and also tozs
. In both cases, the result will be “unrelated”, no matter how high we set the termination depth. This is because when comparingcons z zs
tozs
, for instance,z
is unrelated tozs
, thus,cons z zs
is also unrelated tozs
. We cannot say it is just “one larger” sincez
could be a very large term. Note that this points to a weakness of untyped termination checking.To regain the benefit of increased termination depth, we need to index our lists by a linear type such as
ℕ
orSize
. With termination depth2
, the above example is accepted for vectors instead of lists.


The
codata
keyword has been removed. To use coinduction, use the following new builtins:INFINITY
,SHARP
andFLAT
. Example:{# OPTIONS universepolymorphism #} module Coinduction where open import Level infix 1000 ♯_ postulate ∞ : ∀ {a} (A : Set a) → Set a ♯_ : ∀ {a} {A : Set a} → A → ∞ A ♭ : ∀ {a} {A : Set a} → ∞ A → A {# BUILTIN INFINITY ∞ #} {# BUILTIN SHARP ♯_ #} {# BUILTIN FLAT ♭ #}
Note that (nondependent) pattern matching on
SHARP
is no longer allowed.Note also that strange things might happen if you try to combine the pragmas above with
COMPILED_TYPE
,COMPILED_DATA
orCOMPILED
pragmas, or if the pragmas do not occur right after the postulates.The compiler compiles the
INFINITY
builtin to nothing (more or less), so that the use of coinduction does not get in the way of FFI declarations:data Colist (A : Set) : Set where [] : Colist A _∷_ : (x : A) (xs : ∞ (Colist A)) → Colist A {# COMPILED_DATA Colist [] [] (:) #}

Infinite types.
If the new flag
guardednesspreservingtypeconstructors
is used, then type constructors are treated as inductive constructors when we check productivity (but only in parameters, and only if they are used strictly positively or not at all). This makes examples such as the following possible:data Rec (A : ∞ Set) : Set where fold : ♭ A → Rec A  Σ cannot be a record type below. data Σ (A : Set) (B : A → Set) : Set where _,_ : (x : A) → B x → Σ A B syntax Σ A (λ x → B) = Σ[ x ∶ A ] B  Corecursive definition of the Wtype. W : (A : Set) → (A → Set) → Set W A B = Rec (♯ (Σ[ x ∶ A ] (B x → W A B))) syntax W A (λ x → B) = W[ x ∶ A ] B sup : {A : Set} {B : A → Set} (x : A) (f : B x → W A B) → W A B sup x f = fold (x , f) Wrec : {A : Set} {B : A → Set} (P : W A B → Set) → (∀ {x} {f : B x → W A B} → (∀ y → P (f y)) → P (sup x f)) → ∀ x → P x Wrec P h (fold (x , f)) = h (λ y → Wrec P h (f y))  Inductionrecursion encoded as corecursionrecursion. data Label : Set where ′0 ′1 ′2 ′σ ′π ′w : Label mutual U : Set U = Σ Label U′ U′ : Label → Set U′ ′0 = ⊤ U′ ′1 = ⊤ U′ ′2 = ⊤ U′ ′σ = Rec (♯ (Σ[ a ∶ U ] (El a → U))) U′ ′π = Rec (♯ (Σ[ a ∶ U ] (El a → U))) U′ ′w = Rec (♯ (Σ[ a ∶ U ] (El a → U))) El : U → Set El (′0 , _) = ⊥ El (′1 , _) = ⊤ El (′2 , _) = Bool El (′σ , fold (a , b)) = Σ[ x ∶ El a ] El (b x) El (′π , fold (a , b)) = (x : El a) → El (b x) El (′w , fold (a , b)) = W[ x ∶ El a ] El (b x) Urec : (P : ∀ u → El u → Set) → P (′1 , _) tt → P (′2 , _) true → P (′2 , _) false → (∀ {a b x y} → P a x → P (b x) y → P (′σ , fold (a , b)) (x , y)) → (∀ {a b f} → (∀ x → P (b x) (f x)) → P (′π , fold (a , b)) f) → (∀ {a b x f} → (∀ y → P (′w , fold (a , b)) (f y)) → P (′w , fold (a , b)) (sup x f)) → ∀ u (x : El u) → P u x Urec P P1 P2t P2f Pσ Pπ Pw = rec where rec : ∀ u (x : El u) → P u x rec (′0 , _) () rec (′1 , _) _ = P1 rec (′2 , _) true = P2t rec (′2 , _) false = P2f rec (′σ , fold (a , b)) (x , y) = Pσ (rec _ x) (rec _ y) rec (′π , fold (a , b)) f = Pπ (λ x → rec _ (f x)) rec (′w , fold (a , b)) (fold (x , f)) = Pw (λ y → rec _ (f y))
The
guardednesspreservingtypeconstructors
extension is based on a rather operational understanding of∞
/♯_
; it’s not yet clear if this extension is consistent. 
Qualified constructors.
Constructors can now be referred to qualified by their data type. For instance, given
data Nat : Set where zero : Nat suc : Nat → Nat data Fin : Nat → Set where zero : ∀ {n} → Fin (suc n) suc : ∀ {n} → Fin n → Fin (suc n)
you can refer to the constructors unambiguously as
Nat.zero
,Nat.suc
,Fin.zero
, andFin.suc
(Nat
andFin
are modules containing the respective constructors). Example:inj : (n m : Nat) → Nat.suc n ≡ suc m → n ≡ m inj .m m refl = refl
Previously you had to write something like
inj : (n m : Nat) → _≡_ {Nat} (suc n) (suc m) → n ≡ m
to make the type checker able to figure out that you wanted the natural number suc in this case.

Reflection.
There are two new constructs for reflection:

quoteGoal x in e
In
e
the value ofx
will be a representation of the goal type (the type expected of the whole expression) as an element in a datatype of Agda terms (see below). For instance,example : ℕ example = quoteGoal x in {! at this point x = def (quote ℕ) [] !}

quote x : Name
If
x
is the name of a definition (function, datatype, record, or a constructor),quote x
gives you the representation ofx
as a value in the primitive typeName
(see below).
Quoted terms use the following BUILTINs and primitives (available from the standard library module
Reflection
): The type of Agda names. postulate Name : Set {# BUILTIN QNAME Name #} primitive primQNameEquality : Name → Name → Bool  Arguments. Explicit? = Bool data Arg A : Set where arg : Explicit? → A → Arg A {# BUILTIN ARG Arg #} {# BUILTIN ARGARG arg #}  The type of Agda terms. data Term : Set where var : ℕ → List (Arg Term) → Term con : Name → List (Arg Term) → Term def : Name → List (Arg Term) → Term lam : Explicit? → Term → Term pi : Arg Term → Term → Term sort : Term unknown : Term {# BUILTIN AGDATERM Term #} {# BUILTIN AGDATERMVAR var #} {# BUILTIN AGDATERMCON con #} {# BUILTIN AGDATERMDEF def #} {# BUILTIN AGDATERMLAM lam #} {# BUILTIN AGDATERMPI pi #} {# BUILTIN AGDATERMSORT sort #} {# BUILTIN AGDATERMUNSUPPORTED unknown #}
Reflection may be useful when working with internal decision procedures, such as the standard library’s ring solver.


Minor record definition improvement.
The definition of a record type is now available when type checking record module definitions. This means that you can define things like the following:
record Cat : Set₁ where field Obj : Set _=>_ : Obj → Obj → Set  ...  not possible before: op : Cat op = record { Obj = Obj; _=>_ = λ A B → B => A }
Tools

The
Goal type and context
command now shows the goal type before the context, and the context is shown in reverse order. TheGoal type, context and inferred type
command has been modified in a similar way. 
Show module contents command.
Given a module name
M
the Emacs mode can now display all the toplevel modules and names insideM
, along with types for the names. The command is activated usingCc Co
or the menus. 
Auto command.
A command which searches for type inhabitants has been added. The command is invoked by pressing
CC Ca
(or using the goal menu). There are several flags and parameters, e.g.c
which enables casesplitting in the search. For further information, see the Agda wiki: 
HTML generation is now possible for a module with unsolved metavariables, provided that the
allowunsolvedmetas
flag is used.
Release notes for Agda 2 version 2.2.6
Language

Universe polymorphism (experimental extension).
To enable universe polymorphism give the flag
universepolymorphism
on the command line or (recommended) as an OPTIONS pragma.When universe polymorphism is enabled
Set
takes an argument which is the universe level. For instance, the type of universe polymorphic identity isid : {a : Level} {A : Set a} → A → A.
The type Level is isomorphic to the unary natural numbers and should be specified using the BUILTINs
LEVEL
,LEVELZERO
, andLEVELSUC
:data Level : Set where zero : Level suc : Level → Level {# BUILTIN LEVEL Level #} {# BUILTIN LEVELZERO zero #} {# BUILTIN LEVELSUC suc #}
There is an additional BUILTIN
LEVELMAX
for taking the maximum of two levels:max : Level → Level → Level max zero m = m max (suc n) zero = suc n max (suc n) (suc m) = suc (max n m) {# BUILTIN LEVELMAX max #}
The nonpolymorphic universe levels
Set
,Set₁
and so on are sugar forSet zero
,Set (suc zero)
, etc.At present there is no automatic lifting of types from one level to another. It can still be done (rather clumsily) by defining types like the following one:
data Lifted {a} (A : Set a) : Set (suc a) where lift : A → Lifted A
However, it is likely that automatic lifting is introduced at some point in the future.

Multiple constructors, record fields, postulates or primitives can be declared using a single type signature:
data Bool : Set where false true : Bool postulate A B : Set

Record fields can be implicit:
record R : Set₁ where field {A} : Set f : A → A {B C} D {E} : Set g : B → C → E
By default implicit fields are not printed.

Record constructors can be defined:
record Σ (A : Set) (B : A → Set) : Set where constructor _,_ field proj₁ : A proj₂ : B proj₁
In this example
_,_
gets the type(proj₁ : A) → B proj₁ → Σ A B.
For implicit fields the corresponding constructor arguments become implicit.
Note that the constructor is defined in the outer scope, so any fixity declaration has to be given outside the record definition. The constructor is not in scope inside the record module.
Note also that pattern matching for records has not been implemented yet.

BUILTIN hooks for equality.
The data type
data _≡_ {A : Set} (x : A) : A → Set where refl : x ≡ x
can be specified as the builtin equality type using the following pragmas:
{# BUILTIN EQUALITY _≡_ #} {# BUILTIN REFL refl #}
The builtin equality is used for the new rewrite construct and the
primTrustMe
primitive described below. 
New
rewrite
construct.If
eqn : a ≡ b
, where_≡_
is the builtin equality (see above) you can now writef ps rewrite eqn = rhs
instead of
f ps with a  eqn ...  ._  refl = rhs
The
rewrite
construct has the effect of rewriting the goal and the context by the given equation (left to right).You can rewrite using several equations (in sequence) by separating them with vertical bars ():
f ps rewrite eqn₁  eqn₂  … = rhs
It is also possible to add
with
clauses after rewriting:f ps rewrite eqns with e ...  p = rhs
Note that pattern matching happens before rewriting—if you want to rewrite and then do pattern matching you can use a with after the rewrite.
See
test/Succeed/Rewrite.agda
for some examples. 
A new primitive,
primTrustMe
, has been added:primTrustMe : {A : Set} {x y : A} → x ≡ y
Here
_≡_
is the builtin equality (see BUILTIN hooks for equality, above).If
x
andy
are definitionally equal, thenprimTrustMe {x = x} {y = y}
reduces torefl
.Note that the compiler replaces all uses of
primTrustMe
with theREFL
builtin, without any check for definitional equality. Incorrect uses ofprimTrustMe
can potentially lead to segfaults or similar problems.For an example of the use of
primTrustMe
, seeData.String
in version 0.3 of the standard library, where it is used to implement decidable equality on strings using the primitive boolean equality. 
Changes to the syntax and semantics of IMPORT pragmas, which are used by the Haskell FFI. Such pragmas must now have the following form:
{# IMPORT <module name> #}
These pragmas are interpreted as qualified imports, so Haskell names need to be given qualified (unless they come from the Haskell prelude).

The horizontal tab character (U+0009) is no longer treated as white space.

Line pragmas are no longer supported.

The
includepath
flag can no longer be used as a pragma. 
The experimental and incomplete support for proof irrelevance has been disabled.
Tools

New
intro
command in the Emacs mode. When there is a canonical way of building something of the goal type (for instance, if the goal type is a pair), the goal can be refined in this way. The command works for the following goal types:
A data type where only one of its constructors can be used to construct an element of the goal type. (For instance, if the goal is a nonempty vector, a
cons
will be introduced.) 
A record type. A record value will be introduced. Implicit fields will not be included unless showing of implicit arguments is switched on.

A function type. A lambda binding as many variables as possible will be introduced. The variable names will be chosen from the goal type if its normal form is a dependent function type, otherwise they will be variations on
x
. Implicit lambdas will only be inserted if showing of implicit arguments is switched on.
This command can be invoked by using the
refine
command (Cc Cr
) when the goal is empty. (The old behaviour of the refine command in this situation was to ask for an expression using the minibuffer.) 

The Emacs mode displays
Checked
in the mode line if the current file type checked successfully without any warnings. 
If a file
F
is loaded, and this file defines the moduleM
, it is an error ifF
is not the file which definesM
according to the include path.Note that the commandline tool and the Emacs mode define the meaning of relative include paths differently: the commandline tool interprets them relative to the current working directory, whereas the Emacs mode interprets them relative to the root directory of the current project. (As an example, if the module
A.B.C
is loaded from the file<somepath>/A/B/C.agda
, then the root directory is<somepath>
.) 
It is an error if there are several files on the include path which match a given module name.

Interface files are relocatable. You can move around source trees as long as the include path is updated in a corresponding way. Note that a module
M
may be retypechecked if its time stamp is strictly newer than that of the corresponding interface file (M.agdai
). 
Typechecking is no longer done when an uptodate interface exists. (Previously the initial module was always typechecked.)

Syntax highlighting files for Emacs (
.agda.el
) are no longer used. Theemacs
flag has been removed. (Syntax highlighting information is cached in the interface files.) 
The Agate and Alonzo compilers have been retired. The options
agate
,alonzo
andmalonzo
have been removed. 
The default directory for MAlonzo output is the project’s root directory. The
malonzodir
flag has been renamed tocompiledir
. 
Emacs mode:
Cc Cx Cd
no longer resets the type checking state.Cc Cx Cr
can be used for a more complete reset.Cc Cx Cs
(which used to reload the syntax highlighting information) has been removed.Cc Cl
can be used instead. 
The Emacs mode used to define some “abbrevs”, unless the user explicitly turned this feature off. The new default is not to add any abbrevs. The old default can be obtained by customising
agda2modeabbrevsusedefaults
(a customisation buffer can be obtained by typingMx customizegroup agda2 RET
after an Agda file has been loaded).
Release notes for Agda 2 version 2.2.4
Important changes since 2.2.2:

Change to the semantics of
open import
andopen module
. The declarationopen import M <using/hiding/renaming>
now translates to
import A open A <using/hiding/renaming>
instead of
import A <using/hiding/renaming> open A
The same translation is used for
open module M = E …
. Declarations involving the keywords as or public are changed in a corresponding way (as
always goes with import, andpublic
always with open).This change means that import directives do not affect the qualified names when open import/module is used. To get the old behaviour you can use the expanded version above.

Names opened publicly in parameterised modules no longer inherit the module parameters. Example:
module A where postulate X : Set module B (Y : Set) where open A public
In Agda 2.2.2
B.X
has type(Y : Set) → Set
, whereas in Agda 2.2.4B.X
has type Set. 
Previously it was not possible to export a given constructor name through two different
open public
statements in the same module. This is now possible. 
Unicode subscript digits are now allowed for the hierarchy of universes (
Set₀
,Set₁
, …):Set₁
is equivalent toSet1
.
Release notes for Agda 2 version 2.2.2
Tools

The
malonzodir
option has been renamed tomalonzodir
. 
The output of
agda html
is by default placed in a directory calledhtml
.
Infrastructure

The Emacs mode is included in the Agda Cabal package, and installed by
cabal install
. The recommended way to enable the Emacs mode is to include the following code in.emacs
:(loadfile (let ((codingsystemforread 'utf8)) (shellcommandtostring "agdamode locate")))
Release notes for Agda 2 version 2.2.0
Important changes since 2.1.2 (which was released 20070816):
Language

Exhaustive pattern checking. Agda complains if there are missing clauses in a function definition.

Coinductive types are supported. This feature is under development/evaluation, and may change.
http://wiki.portal.chalmers.se/agda/agda.php?n=ReferenceManual.Codatatypes

Another experimental feature: Sized types, which can make it easier to explain why your code is terminating.

Improved constraint solving for functions with constructor headed right hand sides.
http://wiki.portal.chalmers.se/agda/agda.php?n=ReferenceManual.FindingTheValuesOfImplicitArguments

A simple, welltyped foreign function interface, which allows use of Haskell functions in Agda code.

The tokens
forall
,>
and\
can be written as∀
,→
andλ
. 
Absurd lambdas:
λ ()
andλ {}
. 
Record fields whose values can be inferred can be omitted.

Agda complains if it spots an unreachable clause, or if a pattern variable “shadows” a hidden constructor of matching type.
Tools

Casesplit: The user interface can replace a pattern variable with the corresponding constructor patterns. You get one new lefthand side for every possible constructor.

The MAlonzo compiler.
http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Docs.MAlonzo

A new Emacs input method, which contains bindings for many Unicode symbols, is by default activated in the Emacs mode.
http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Docs.UnicodeInput

Highlighted, hyperlinked HTML can be generated from Agda source code.
http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.HowToGenerateWebPagesFromSourceCode

The commandline interactive mode (
agda I
) is no longer supported, but should still work. 
Reload times when working on large projects are now considerably better.
Libraries

A standard library is under development.
http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Libraries.StandardLibrary
Documentation

The Agda wiki is better organised. It should be easier for a newcomer to find relevant information now.
Infrastructure

Easytoinstall packages for Windows and Debian/Ubuntu have been prepared.
http://wiki.portal.chalmers.se/agda/pmwiki.php?n=Main.Download

Agda 2.2.0 is available from Hackage.