unboundgenerics
Support for programming with names and binders using GHC Generics.
Summary
Specify the binding structure of your data type with an expressive set of type combinators, and unboundgenerics
handles the rest! Automatically derives alphaequivalence, free variable calculation, captureavoiding substitution, and more. See Unbound.Generics.LocallyNameless
to get started.
This is a reimplementation of (parts of) unbound but using GHC generics instead of RepLib.
Example
Here is how you would implement call by value evaluation for the untyped lambda calculus:
{# LANGUAGE DeriveDataTypeable, DeriveGeneric, MultiParamTypeClasses #}
module UntypedLambdaCalc where
import Unbound.Generics.LocallyNameless
import GHC.Generics (Generic)
import Data.Typeable (Typeable)
  Variables stand for expressions
type Var = Name Expr
  Expressions
data Expr = V Var  ^ variables
 Lam (Bind Var Expr)  ^ lambdas bind a variable within a body expression
 App Expr Expr  ^ application
deriving (Show, Generic, Typeable)
 Automatically construct alpha equivalence, free variable computation and binding operations.
instance Alpha Expr
 semiautomatically implement capture avoiding substitution of expressions for expressions
instance Subst Expr Expr where
 `isvar` identifies the variable case in your AST.
isvar (V x) = Just (SubstName x)
isvar _ = Nothing
 evaluation takes an expression and returns a value while using a source of fresh names
eval :: Expr > FreshM Expr
eval (V x) = fail $ "unbound variable " ++ show x
eval e@(Lam {}) = return e
eval (App e1 e2) = do
v1 < eval e1
v2 < eval e2
case v1 of
(Lam bnd) > do
 open the lambda by picking a fresh name for the bound variable x in body
(x, body) < unbind bnd
let body' = subst x v2 body
eval body'
_ > fail "application of nonlambda"
example :: Expr
example =
let x = s2n "x"
y = s2n "y"
e = Lam $ bind x (Lam $ bind y (App (V y) (V x)))
in runFreshM $ eval (App (App e e) e)
 >>> example
 Lam (<y> App (V 0@0) (Lam (<x> Lam (<y> App (V 0@0) (V 1@0)))))
Differences from unbound
For the most part, I tried to keep the same methods with the same signatures. However there are a few differences.

fv :: Alpha t => Fold t (Name n)
The fv
method returns a Fold
(in the sense of the lens library),
rather than an Unbound.Util.Collection
instance. That means you will generally have to write toListOf fv t
or some other summary operation.

Utility methods in the Alpha
class have different types.
You should only notice this if you’re implementing an instance of Alpha
by hand (rather than by using the default
generic instance).
isPat :: Alpha t => t > DisjointSet AnyName
The original unbound
returned a Maybe [AnyName]
here with the same interpretation as DisjointSet
: Nothing
means an inconsistency was encountered, or Just
the free variables of the pattern.
isTerm :: Alpha t => t > All
open :: Alpha t => AlphaCtx > NthPatFind > t > t
, close :: Alpha t => AlphaCtx > NamePatFind > t > t
where NthPatFind
and NamePatFind
are newtypes

embed :: IsEmbed e => Embedded e > e
and unembed :: IsEmbed e => e > Embedded e
The typeclass IsEmbed
has an Iso
(again in the sense of the lens
library) as a method instead of the above pair of methods.
Again, you should only notice this if you’re implementing your own types that are instances of IsEmbed
. The easiest thing to do is to use implement embedded = iso yourEmbed yourUnembed
where iso
comes from lens
. (Although you can also implement it in terms of dimap
if you don’t want to depend on lens)