bruderj15 / Hasmtlib

A monad for interfacing with external SMT solvers
GNU General Public License v3.0
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smt smt-lib2 smt2 smtlib smtlib2

Hackage Static Badge Haskell-CI License: GPL v3

Hasmtlib - Haskell SMTLib MTL Library

Hasmtlib is a library with high-level-abstraction for generating SMTLib2-problems using a monad. It takes care of encoding your problem, marshaling the data to an external solver and parsing and interpreting the result into Haskell types. It is highly inspired by ekmett/ersatz which does the same for QSAT. Communication with external solvers is handled by tweag/smtlib-backends.

Building expressions with type-level representations of the SMTLib2-Sorts guarantees type-safety when communicating with external solvers.

While formula construction is entirely pure, Hasmtlib - just like ersatz - makes use of observable sharing for expressions.

This allows you to use the much richer subset of Haskell than a purely monadic meta-language would, which ultimately results in extremely compact code.

For instance, to define the addition of two V3 containing Real-SMT-Expressions:

v3Add :: V3 (Expr RealSort) -> V3 (Expr RealSort) -> V3 (Expr RealSort)
v3Add = liftA2 (+)

Even better, the Expr-GADT allows a polymorph definition:

v3Add :: Num (Expr t) => V3 (Expr t) -> V3 (Expr t) -> V3 (Expr t)
v3Add = liftA2 (+)

This looks a lot like the definition of Num for V3 a:

instance Num a => Num (V3 a) where
  (+) :: V3 a -> V3 a -> V3 a
  (+) = liftA2 (+)

Hence, no extra definition is needed at all. We can use the existing instances:

{-# LANGUAGE DataKinds #-}

import Language.Hasmtlib
import Linear

-- instances with default impl
instance Codec a => Codec (V3 a)
instance Variable a => Variable (V3 a)

main :: IO ()
main = do
  res <- solveWith @SMT (solver cvc5) $ do
    setLogic "QF_NRA"

    u :: V3 (Expr RealSort) <- variable
    v <- variable

    assert $ dot u v === 5

    return (u,v)

  print res

May print: (Sat,Just (V3 (-2.0) (-1.0) 0.0,V3 (-2.0) (-1.0) 0.0))

Features

Related work

If you want highly specific implementations for different solvers, all their individual configurations and swallow the awkward typing, then use hgoes/smtlib2.

If you want to express properties about Haskell programs and automatically prove them using SMT, then use LevantErkok/sbv.

If you want to encode SMT-problems as lightweight and close to Haskell as possible, then use this library. I personally use it for scheduling/resource-allocation-problems.

Examples

There are some examples in here.

Contact information

Contributions, critics and bug reports are welcome!

Please feel free to contact me through GitHub.