ersatz
A monad for expressing SAT or QSAT problems using observable sharing.
http://github.com/ekmett/ersatz
Version on this page: | 0.4.4 |
LTS Haskell 22.41: | 0.5@rev:2 |
Stackage Nightly 2024-11-11: | 0.5@rev:2 |
Latest on Hackage: | 0.5@rev:2 |
ersatz-0.4.4@sha256:95222c37b2b01db5ebad7141e1808cc4cf5017522caf5250faa5e5eed359b7d2,9613
Module documentation for 0.4.4
Ersatz
Ersatz is a library for generating QSAT (CNF/QBF) problems using a monad. It takes care of generating the normal form, encoding your problem, marshaling the data to an external solver, and parsing and interpreting the result into Haskell types.
What differentiates Ersatz is the use of observable sharing in the API.
For instance to define a full adder:
full_adder :: Bit -> Bit -> Bit -> (Bit, Bit)
full_adder a b cin = (s2, c1 || c2)
where (s1,c1) = half_adder a b
(s2,c2) = half_adder s1 cin
half_adder :: Bit -> Bit -> (Bit, Bit)
half_adder a b = (a `xor` b, a && b)
as opposed to the following code in satchmo:
full_adder :: Boolean -> Boolean -> Boolean
-> SAT ( Boolean, Boolean )
full_adder a b c = do
let s x y z = sum $ map fromEnum [x,y,z]
r <- fun3 ( \ x y z -> odd $ s x y z ) a b c
d <- fun3 ( \ x y z -> 1 < s x y z ) a b c
return ( r, d )
half_adder :: Boolean -> Boolean
-> SAT ( Boolean, Boolean )
half_adder a b = do
let s x y = sum $ map fromEnum [x,y]
r <- fun2 ( \ x y -> odd $ s x y ) a b
d <- fun2 ( \ x y -> 1 < s x y ) a b
return ( r, d )
This enables you to use the a much richer subset of Haskell than the purely monadic meta-language, and it becomes much easier to see that the resulting encoding is correct.
To allocate fresh existentially or universally quantified variables or to assert that a Bit is true and add the attendant circuit with sharing to the current problem you use the SAT monad.
verify_currying :: (MonadState s m, HasQSAT s) => m ()
verify_currying = do
(x::Bit, y::Bit, z::Bit) <- forall
assert $ ((x && y) ==> z) === (x ==> y ==> z)
We can then hand that off to a SAT solver, and get back an answer:
main = solveWith depqbf verify_currying >>= print
Support is offered for decoding various Haskell datatypes from the solution provided by the SAT solver.
Examples
Included are a couple of examples included with the distribution.
Neither are as fast as a dedicated solver for their respective
domains, but they showcase how you can solve real world problems
involving 10s or 100s of thousands of variables and constraints
with ersatz
.
sudoku
% time ersatz-sudoku
Problem:
┌───────┬───────┬───────┐
│ 5 3 │ 7 │ │
│ 6 │ 1 9 5 │ │
│ 9 8 │ │ 6 │
├───────┼───────┼───────┤
│ 8 │ 6 │ 3 │
│ 4 │ 8 3 │ 1 │
│ 7 │ 2 │ 6 │
├───────┼───────┼───────┤
│ 6 │ │ 2 8 │
│ │ 4 1 9 │ 5 │
│ │ 8 │ 7 9 │
└───────┴───────┴───────┘
Solution:
┌───────┬───────┬───────┐
│ 5 3 4 │ 6 7 8 │ 9 1 2 │
│ 6 7 2 │ 1 9 5 │ 3 4 8 │
│ 1 9 8 │ 3 4 2 │ 5 6 7 │
├───────┼───────┼───────┤
│ 8 5 9 │ 7 6 1 │ 4 2 3 │
│ 4 2 6 │ 8 5 3 │ 7 9 1 │
│ 7 1 3 │ 9 2 4 │ 8 5 6 │
├───────┼───────┼───────┤
│ 9 6 1 │ 5 3 7 │ 2 8 4 │
│ 2 8 7 │ 4 1 9 │ 6 3 5 │
│ 3 4 5 │ 2 8 6 │ 1 7 9 │
└───────┴───────┴───────┘
ersatz-sudoku 1,13s user 0,04s system 99% cpu 1,179 total
regexp-grid
This solves the regular crossword puzzle from the MIT mystery hunt.
% time ersatz-regexp-grid
ersatz-regexp-grid 2,45s user 0,05s system 99% cpu 2,502 total
Contact Information
Contributions and bug reports are welcome!
Please feel free to contact me through github or on the #haskell IRC channel on irc.freenode.net.
-Edward Kmett
Changes
0.4.4 [2018.08.13]
- Avoid the use of failable pattern matches in
do
-notation to support building with GHC 8.6, which enablesMonadFailDesugaring
.
0.4.3 [2018.07.03]
- Make the test suite compile on GHC 8.6.
- Allow building with
containers-0.6
.
0.4.2
- Add
Semigroup
instances forClause
andFormula
. - Generalize
regular
,regular_in_degree
,regular_out_degree
,max_in_degree
,min_in_degree
,max_out_degree
, andmin_out_degree
to work over heterogeneous relations. - Add
buildFrom
toErsatz.Relation.Data
. - Add
difference
,reflexive_closure
, andsymmetric_closure
toErsatz.Relation.Op
. - Add
anti_symmetric
andtotal
toErsatz.Relation.Prop
.
0.4.1
- Add a library dependency on the
doctests
test suite
0.4
- Performance improvements for CNF printing and parsing
- Add the
Ersatz.Counting
,Ersatz.Relation
,Ersatz.Relation.Data
,Ersatz.Relation.Prop
, andErsatz.Relation.Op
modules - Eliminate the
Or
constructor fromBit
towards using AIG - Fix error in the SAT encoding of the
choose
function - Revamp
Setup.hs
to usecabal-doctest
. This makes it build withCabal-2.0
, and makes thedoctest
s work withcabal new-build
and sandboxes.
0.3.1
- Removed the explicit
Safe
annotations. They can’t be maintained by mere mortals. Patches to mark packages upstream asTrustworthy
will be accepted as needed.
0.3
- Unified
Encoding
andDecoding
intoCodec
- Unified the
forall
andexists
implementations into a singleliterally
method inVariable
class. - Added
Orderable
type class and instances - Added
Ersatz.Bits.Bits
for variable-sized bit arithmetic. - Renamed
Ersatz.Bits.half_adder
tohalfAdder
- Renamed
Ersatz.Bits.full_adder
tofullAdder
- Added new examples
- Dropped
blaze
package dependency in favor of newerbytestring
- Significantly shrank the number of “Trustworthy” modules
- Added various generic
V1
instances - Added
Equatable
instances forMap
andIntMap
- Added
Ersatz.BitChar
module for computing withChar
andString
- Wider version bounds for
transformers
andmtl
.
0.2.6.1
- Exported
Ersatz.Variable.GVariable
0.2.6
temporary 1.2
support
0.2.5.1
- Slightly faster builds due to dropping the need for
template-haskell
.
0.2.5
- Support for GHC 7.8 and
lens
4.x
0.2.3
- SafeHaskell support
0.2.2
- Added examples to the documentation.
- Made the examples build as
ersatz-sudoku
andersatz-regexp-grid
.
0.2.1
- Added
examples/sudoku
, a sudoku solver.
0.2.0.1
- Fixed an overly conservative bound on
containers
.
0.2
- Converted to
Control.Lens
internally. - Added
Ersatz.Solver.DepQBF
- Added a bunch of example dimacs files
- The types now prevent one from applying a solver that does not support QSAT to a problem that requires it
- Added
examples/regexp-grid
, a program that solves the regular expression crossword - Made some optimizations to the formula generation.
regexp-grid
went from 71737 literals and 427725 clauses to 8618 literals and 172100 clauses and got much faster - Based
and
andor
inBoolean
onFoldable
; addedall
andany
0.1.0.2
- Added correct links to the source repository and issue tracker to the cabal project
0.1
- Repository Initialized