sbv-9.0: Data/SBV/Provers/Prover.hs
-----------------------------------------------------------------------------
-- |
-- Module : Data.SBV.Provers.Prover
-- Copyright : (c) Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Provable abstraction and the connection to SMT solvers
-----------------------------------------------------------------------------
{-# LANGUAGE CPP #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE NamedFieldPuns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TupleSections #-}
{-# OPTIONS_GHC -Wall -Werror #-}
module Data.SBV.Provers.Prover (
SMTSolver(..), SMTConfig(..), Predicate
, MProvable(..), Provable, proveWithAll, proveWithAny , satWithAll, satWithAny
, satConcurrentWithAny, satConcurrentWithAll, proveConcurrentWithAny, proveConcurrentWithAll
, generateSMTBenchmark
, Goal
, ThmResult(..), SatResult(..), AllSatResult(..), SafeResult(..), OptimizeResult(..), SMTResult(..)
, SExecutable(..), isSafe
, runSMT, runSMTWith
, SatModel(..), Modelable(..), displayModels, extractModels
, getModelDictionaries, getModelValues, getModelUninterpretedValues
, abc, boolector, bitwuzla, cvc4, cvc5, dReal, mathSAT, yices, z3, defaultSMTCfg, defaultDeltaSMTCfg
) where
import Control.Monad (when, unless)
import Control.Monad.IO.Class (MonadIO, liftIO)
import Control.DeepSeq (rnf, NFData(..))
import Control.Concurrent.Async (async, waitAny, asyncThreadId, Async, mapConcurrently)
import Control.Exception (finally, throwTo)
import System.Exit (ExitCode(ExitSuccess))
import System.IO.Unsafe (unsafeInterleaveIO) -- only used safely!
import System.Directory (getCurrentDirectory)
import Data.Time (getZonedTime, NominalDiffTime, UTCTime, getCurrentTime, diffUTCTime)
import Data.List (intercalate, isPrefixOf, nub)
import Data.Maybe (mapMaybe, listToMaybe)
import qualified Data.Map.Strict as M
import qualified Data.Foldable as S (toList)
import qualified Data.Text as T
import Data.SBV.Core.Data
import Data.SBV.Core.Symbolic
import Data.SBV.SMT.SMT
import Data.SBV.SMT.Utils (debug, alignPlain)
import Data.SBV.Utils.ExtractIO
import Data.SBV.Utils.TDiff
import qualified Data.SBV.Trans.Control as Control
import qualified Data.SBV.Control.Query as Control
import qualified Data.SBV.Control.Utils as Control
import GHC.Stack
import qualified Data.SBV.Provers.ABC as ABC
import qualified Data.SBV.Provers.Boolector as Boolector
import qualified Data.SBV.Provers.Bitwuzla as Bitwuzla
import qualified Data.SBV.Provers.CVC4 as CVC4
import qualified Data.SBV.Provers.CVC5 as CVC5
import qualified Data.SBV.Provers.DReal as DReal
import qualified Data.SBV.Provers.MathSAT as MathSAT
import qualified Data.SBV.Provers.Yices as Yices
import qualified Data.SBV.Provers.Z3 as Z3
mkConfig :: SMTSolver -> SMTLibVersion -> [Control.SMTOption] -> SMTConfig
mkConfig s smtVersion startOpts = SMTConfig { verbose = False
, timing = NoTiming
, printBase = 10
, printRealPrec = 16
, crackNum = False
, transcript = Nothing
, solver = s
, smtLibVersion = smtVersion
, dsatPrecision = Nothing
, extraArgs = []
, satCmd = "(check-sat)"
, satTrackUFs = True -- i.e., yes, do extract UI function values
, allSatMaxModelCount = Nothing -- i.e., return all satisfying models
, allSatPrintAlong = False -- i.e., do not print models as they are found
, isNonModelVar = const False -- i.e., everything is a model-variable by default
, validateModel = False
, optimizeValidateConstraints = False
, allowQuantifiedQueries = False
, roundingMode = RoundNearestTiesToEven
, solverSetOptions = startOpts
, ignoreExitCode = False
, redirectVerbose = Nothing
}
-- | If supported, this makes all output go to stdout, which works better with SBV
-- Alas, not all solvers support it..
allOnStdOut :: Control.SMTOption
allOnStdOut = Control.DiagnosticOutputChannel "stdout"
-- | Default configuration for the ABC synthesis and verification tool.
abc :: SMTConfig
abc = mkConfig ABC.abc SMTLib2 [allOnStdOut]
-- | Default configuration for the Boolector SMT solver
boolector :: SMTConfig
boolector = mkConfig Boolector.boolector SMTLib2 []
-- | Default configuration for the Bitwuzla SMT solver
bitwuzla :: SMTConfig
bitwuzla = mkConfig Bitwuzla.bitwuzla SMTLib2 []
-- | Default configuration for the CVC4 SMT Solver.
cvc4 :: SMTConfig
cvc4 = mkConfig CVC4.cvc4 SMTLib2 [allOnStdOut]
-- | Default configuration for the CVC5 SMT Solver.
cvc5 :: SMTConfig
cvc5 = mkConfig CVC5.cvc5 SMTLib2 [allOnStdOut]
-- | Default configuration for the Yices SMT Solver.
dReal :: SMTConfig
dReal = mkConfig DReal.dReal SMTLib2 [ Control.OptionKeyword ":smtlib2_compliant" ["true"]
]
-- | Default configuration for the MathSAT SMT solver
mathSAT :: SMTConfig
mathSAT = mkConfig MathSAT.mathSAT SMTLib2 [allOnStdOut]
-- | Default configuration for the Yices SMT Solver.
yices :: SMTConfig
yices = mkConfig Yices.yices SMTLib2 []
-- | Default configuration for the Z3 SMT solver
z3 :: SMTConfig
z3 = mkConfig Z3.z3 SMTLib2 [ Control.OptionKeyword ":smtlib2_compliant" ["true"]
, allOnStdOut
]
-- | The default solver used by SBV. This is currently set to z3.
defaultSMTCfg :: SMTConfig
defaultSMTCfg = z3
-- | The default solver used by SBV for delta-satisfiability problems. This is currently set to dReal,
-- which is also the only solver that supports delta-satisfiability.
defaultDeltaSMTCfg :: SMTConfig
defaultDeltaSMTCfg = dReal
-- | A predicate is a symbolic program that returns a (symbolic) boolean value. For all intents and
-- purposes, it can be treated as an n-ary function from symbolic-values to a boolean. The 'Symbolic'
-- monad captures the underlying representation, and can/should be ignored by the users of the library,
-- unless you are building further utilities on top of SBV itself. Instead, simply use the 'Predicate'
-- type when necessary.
type Predicate = Symbolic SBool
-- | A goal is a symbolic program that returns no values. The idea is that the constraints/min-max
-- goals will serve as appropriate directives for sat/prove calls.
type Goal = Symbolic ()
-- | A type @a@ is provable if we can turn it into a predicate.
-- Note that a predicate can be made from a curried function of arbitrary arity, where
-- each element is either a symbolic type or up-to a 7-tuple of symbolic-types. So
-- predicates can be constructed from almost arbitrary Haskell functions that have arbitrary
-- shapes. (See the instance declarations below.)
class ExtractIO m => MProvable m a where
-- | Generalization of 'Data.SBV.universal_'
universal_ :: a -> SymbolicT m SBool
-- | Generalization of 'Data.SBV.universal'
universal :: [String] -> a -> SymbolicT m SBool
-- | Generalization of 'Data.SBV.existential_'
existential_ :: a -> SymbolicT m SBool
-- | Generalization of 'Data.SBV.existential'
existential :: [String] -> a -> SymbolicT m SBool
-- | Generalization of 'Data.SBV.prove'
prove :: a -> m ThmResult
prove = proveWith defaultSMTCfg
-- | Generalization of 'Data.SBV.proveWith'
proveWith :: SMTConfig -> a -> m ThmResult
proveWith cfg a = do r <- runWithQuery False (checkNoOptimizations >> Control.getSMTResult) cfg a
ThmResult <$> if validationRequested cfg
then validate False cfg a r
else return r
-- | Generalization of 'Data.SBV.dprove'
dprove :: a -> m ThmResult
dprove = dproveWith defaultDeltaSMTCfg
-- | Generalization of 'Data.SBV.dproveWith'
dproveWith :: SMTConfig -> a -> m ThmResult
dproveWith cfg a = do r <- runWithQuery False (checkNoOptimizations >> Control.getSMTResult) cfg a
ThmResult <$> if validationRequested cfg
then validate False cfg a r
else return r
-- | Generalization of 'Data.SBV.sat'
sat :: a -> m SatResult
sat = satWith defaultSMTCfg
-- | Generalization of 'Data.SBV.satWith'
satWith :: SMTConfig -> a -> m SatResult
satWith cfg a = do r <- runWithQuery True (checkNoOptimizations >> Control.getSMTResult) cfg a
SatResult <$> if validationRequested cfg
then validate True cfg a r
else return r
-- | Generalization of 'Data.SBV.sat'
dsat :: a -> m SatResult
dsat = dsatWith defaultDeltaSMTCfg
-- | Generalization of 'Data.SBV.satWith'
dsatWith :: SMTConfig -> a -> m SatResult
dsatWith cfg a = do r <- runWithQuery True (checkNoOptimizations >> Control.getSMTResult) cfg a
SatResult <$> if validationRequested cfg
then validate True cfg a r
else return r
-- | Generalization of 'Data.SBV.allSat'
allSat :: a -> m AllSatResult
allSat = allSatWith defaultSMTCfg
-- | Generalization of 'Data.SBV.allSatWith'
allSatWith :: SMTConfig -> a -> m AllSatResult
allSatWith cfg a = do asr <- runWithQuery True (checkNoOptimizations >> Control.getAllSatResult) cfg a
if validationRequested cfg
then do rs' <- mapM (validate True cfg a) (allSatResults asr)
return asr{allSatResults = rs'}
else return asr
-- | Generalization of 'Data.SBV.optimize'
optimize :: OptimizeStyle -> a -> m OptimizeResult
optimize = optimizeWith defaultSMTCfg
-- | Generalization of 'Data.SBV.optimizeWith'
optimizeWith :: SMTConfig -> OptimizeStyle -> a -> m OptimizeResult
optimizeWith config style optGoal = do
res <- runWithQuery True opt config optGoal
if not (optimizeValidateConstraints config)
then return res
else let v :: SMTResult -> m SMTResult
v = validate True config optGoal
in case res of
LexicographicResult m -> LexicographicResult <$> v m
IndependentResult xs -> let w [] sofar = return (reverse sofar)
w ((n, m):rest) sofar = v m >>= \m' -> w rest ((n, m') : sofar)
in IndependentResult <$> w xs []
ParetoResult (b, rs) -> ParetoResult . (b, ) <$> mapM v rs
where opt = do objectives <- Control.getObjectives
qinps <- Control.getQuantifiedInputs
spgm <- Control.getSBVPgm
when (null objectives) $
error $ unlines [ ""
, "*** Data.SBV: Unsupported call to optimize when no objectives are present."
, "*** Use \"sat\" for plain satisfaction"
]
unless (supportsOptimization (capabilities (solver config))) $
error $ unlines [ ""
, "*** Data.SBV: The backend solver " ++ show (name (solver config)) ++ "does not support optimization goals."
, "*** Please use a solver that has support, such as z3"
]
when (validateModel config && not (optimizeValidateConstraints config)) $
error $ unlines [ ""
, "*** Data.SBV: Model validation is not supported in optimization calls."
, "***"
, "*** Instead, use `cfg{optimizeValidateConstraints = True}`"
, "***"
, "*** which checks that the results satisfy the constraints but does"
, "*** NOT ensure that they are optimal."
]
let universals = S.toList $ getUniversals qinps
firstUniversal
| null universals = error "Data.SBV: Impossible happened! Universal optimization with no universals!"
| True = minimum $ fmap (swNodeId . getSV) universals
mappings :: M.Map SV SBVExpr
mappings = M.fromList (S.toList (pgmAssignments spgm))
chaseUniversal entry = go entry []
where go x sofar
| nx >= firstUniversal
= nub $ [unm | unm <- universals, nx >= swNodeId (getSV unm)] ++ sofar
| True
= let oVars (LkUp _ a b) = [a, b]
oVars (IEEEFP (FP_Cast _ _ o)) = [o]
oVars _ = []
vars = case x `M.lookup` mappings of
Nothing -> []
Just (SBVApp o ss) -> nub (oVars o ++ ss)
in foldr go sofar vars
where nx = swNodeId x
let needsUniversalOpt = let tag _ [] = Nothing
tag nm xs = Just (nm, xs)
needsUniversal (Maximize nm (x, _)) = tag nm (chaseUniversal x)
needsUniversal (Minimize nm (x, _)) = tag nm (chaseUniversal x)
needsUniversal (AssertWithPenalty nm (x, _) _) = tag nm (chaseUniversal x)
in mapMaybe needsUniversal objectives
unless (null universals || null needsUniversalOpt) $
let len = maximum $ 0 : [length nm | (nm, _) <- needsUniversalOpt]
pad n = n ++ replicate (len - length n) ' '
in error $ unlines $ [ ""
, "*** Data.SBV: Problem needs optimization of metric in the scope of universally quantified variable(s):"
, "***"
]
++ [ "*** " ++ pad s ++ " [Depends on: " ++ intercalate ", " (getUserName' <$> xs) ++ "]" | (s, xs) <- needsUniversalOpt ]
++ [ "***"
, "*** Optimization is only meaningful with existentially quantified metrics."
]
let optimizerDirectives = concatMap minmax objectives ++ priority style
where mkEq (x, y) = "(assert (= " ++ show x ++ " " ++ show y ++ "))"
minmax (Minimize _ xy@(_, v)) = [mkEq xy, "(minimize " ++ show v ++ ")"]
minmax (Maximize _ xy@(_, v)) = [mkEq xy, "(maximize " ++ show v ++ ")"]
minmax (AssertWithPenalty nm xy@(_, v) mbp) = [mkEq xy, "(assert-soft " ++ show v ++ penalize mbp ++ ")"]
where penalize DefaultPenalty = ""
penalize (Penalty w mbGrp)
| w <= 0 = error $ unlines [ "SBV.AssertWithPenalty: Goal " ++ show nm ++ " is assigned a non-positive penalty: " ++ shw
, "All soft goals must have > 0 penalties associated."
]
| True = " :weight " ++ shw ++ maybe "" group mbGrp
where shw = show (fromRational w :: Double)
group g = " :id " ++ g
priority Lexicographic = [] -- default, no option needed
priority Independent = ["(set-option :opt.priority box)"]
priority (Pareto _) = ["(set-option :opt.priority pareto)"]
mapM_ (Control.send True) optimizerDirectives
case style of
Lexicographic -> LexicographicResult <$> Control.getLexicographicOptResults
Independent -> IndependentResult <$> Control.getIndependentOptResults (map objectiveName objectives)
Pareto mbN -> ParetoResult <$> Control.getParetoOptResults mbN
-- | Generalization of 'Data.SBV.isVacuous'
isVacuous :: a -> m Bool
isVacuous = isVacuousWith defaultSMTCfg
-- | Generalization of 'Data.SBV.isVacuousWith'
isVacuousWith :: SMTConfig -> a -> m Bool
isVacuousWith cfg a = -- NB. Can't call runWithQuery since last constraint would become the implication!
fst <$> runSymbolic (SMTMode QueryInternal ISetup True cfg) (existential_ a >> Control.executeQuery QueryInternal check)
where
check :: QueryT m Bool
check = do cs <- Control.checkSat
case cs of
Control.Unsat -> return True
Control.Sat -> return False
Control.DSat{} -> return False
Control.Unk -> error "SBV: isVacuous: Solver returned unknown!"
-- | Generalization of 'Data.SBV.isTheorem'
isTheorem :: a -> m Bool
isTheorem = isTheoremWith defaultSMTCfg
-- | Generalization of 'Data.SBV.isTheoremWith'
isTheoremWith :: SMTConfig -> a -> m Bool
isTheoremWith cfg p = do r <- proveWith cfg p
let bad = error $ "SBV.isTheorem: Received:\n" ++ show r
case r of
ThmResult Unsatisfiable{} -> return True
ThmResult Satisfiable{} -> return False
ThmResult DeltaSat{} -> return False
ThmResult SatExtField{} -> return False
ThmResult Unknown{} -> bad
ThmResult ProofError{} -> bad
-- | Generalization of 'Data.SBV.isSatisfiable'
isSatisfiable :: a -> m Bool
isSatisfiable = isSatisfiableWith defaultSMTCfg
-- | Generalization of 'Data.SBV.isSatisfiableWith'
isSatisfiableWith :: SMTConfig -> a -> m Bool
isSatisfiableWith cfg p = do r <- satWith cfg p
case r of
SatResult Satisfiable{} -> return True
SatResult Unsatisfiable{} -> return False
_ -> error $ "SBV.isSatisfiable: Received: " ++ show r
-- | Validate a model obtained from the solver
validate :: Bool -> SMTConfig -> a -> SMTResult -> m SMTResult
validate isSAT cfg p res = case res of
Unsatisfiable{} -> return res
Satisfiable _ m -> case modelBindings m of
Nothing -> error "Data.SBV.validate: Impossible happened; no bindings generated during model validation."
Just env -> check env
DeltaSat {} -> cant [ "The model is delta-satisfiable."
, "Cannot validate delta-satisfiable models."
]
SatExtField{} -> cant [ "The model requires an extension field value."
, "Cannot validate models with infinities/epsilons produced during optimization."
, ""
, "To turn validation off, use `cfg{optimizeValidateConstraints = False}`"
]
Unknown{} -> return res
ProofError{} -> return res
where cant msg = return $ ProofError cfg (msg ++ [ ""
, "Unable to validate the produced model."
]) (Just res)
check env = do let univs = [T.unpack n | ((ALL, NamedSymVar _ n), _) <- env]
envShown = showModelDictionary True True cfg modelBinds
where modelBinds = [(T.unpack n, fake q s v) | ((q, NamedSymVar s n), v) <- env]
fake q s Nothing
| q == ALL
= RegularCV $ CV (kindOf s) $ CUserSort (Nothing, "<universally quantified>")
| True
= RegularCV $ CV (kindOf s) $ CUserSort (Nothing, "<no binding found>")
fake _ _ (Just v) = RegularCV v
notify s
| not (verbose cfg) = return ()
| True = debug cfg ["[VALIDATE] " `alignPlain` s]
notify $ "Validating the model. " ++ if null env then "There are no assignments." else "Assignment:"
mapM_ notify [" " ++ l | l <- lines envShown]
unless (null univs) $ do
notify $ "NB. The following variable(s) are universally quantified: " ++ intercalate ", " univs
notify " We will assume that they are essentially zero for the purposes of validation."
notify " Note that this is a gross simplification of the model validation with universals!"
result <- snd <$> runSymbolic (Concrete (Just (isSAT, env))) ((if isSAT then existential_ p else universal_ p) >>= output)
let explain = [ ""
, "Assignment:" ++ if null env then " <none>" else ""
]
++ [ "" | not (null env)]
++ [ " " ++ l | l <- lines envShown]
++ [ "" ]
wrap tag extras = return $ ProofError cfg (tag : explain ++ extras) (Just res)
giveUp s = wrap ("Data.SBV: Cannot validate the model: " ++ s)
[ "SBV's model validator is incomplete, and cannot handle this particular case."
, "Please report this as a feature request or possibly a bug!"
]
badModel s = wrap ("Data.SBV: Model validation failure: " ++ s)
[ "Backend solver returned a model that does not satisfy the constraints."
, "This could indicate a bug in the backend solver, or SBV itself. Please report."
]
notConcrete sv = wrap ("Data.SBV: Cannot validate the model, since " ++ show sv ++ " is not concretely computable.")
( perhaps (why sv)
++ [ "SBV's model validator is incomplete, and cannot handle this particular case."
, "Please report this as a feature request or possibly a bug!"
]
)
where perhaps Nothing = []
perhaps (Just x) = [x, ""]
-- This is incomplete, but should capture the most common cases
why s = case s `lookup` S.toList (pgmAssignments (resAsgns result)) of
Nothing -> Nothing
Just (SBVApp o as) -> case o of
Uninterpreted v -> Just $ "The value depends on the uninterpreted constant " ++ show v ++ "."
IEEEFP FP_FMA -> Just "Floating point FMA operation is not supported concretely."
IEEEFP _ -> Just "Not all floating point operations are supported concretely."
OverflowOp _ -> Just "Overflow-checking is not done concretely."
_ -> listToMaybe $ mapMaybe why as
cstrs = S.toList $ resConstraints result
walkConstraints [] cont = do
unless (null cstrs) $ notify "Validated all constraints."
cont
walkConstraints ((isSoft, attrs, sv) : rest) cont
| kindOf sv /= KBool
= giveUp $ "Constraint tied to " ++ show sv ++ " is non-boolean."
| isSoft || sv == trueSV
= walkConstraints rest cont
| sv == falseSV
= case mbName of
Just nm -> badModel $ "Named constraint " ++ show nm ++ " evaluated to False."
Nothing -> badModel "A constraint was violated."
| True
= notConcrete sv
where mbName = listToMaybe [n | (":named", n) <- attrs]
-- SAT: All outputs must be true
satLoop []
= do notify "All outputs are satisfied. Validation complete."
return res
satLoop (sv:svs)
| kindOf sv /= KBool
= giveUp $ "Output tied to " ++ show sv ++ " is non-boolean."
| sv == trueSV
= satLoop svs
| sv == falseSV
= badModel "Final output evaluated to False."
| True
= notConcrete sv
-- Proof: At least one output must be false
proveLoop [] somethingFailed
| somethingFailed = do notify "Counterexample is validated."
return res
| True = do notify "Counterexample violates none of the outputs."
badModel "Counter-example violates no constraints."
proveLoop (sv:svs) somethingFailed
| kindOf sv /= KBool
= giveUp $ "Output tied to " ++ show sv ++ " is non-boolean."
| sv == trueSV
= proveLoop svs somethingFailed
| sv == falseSV
= proveLoop svs True
| True
= notConcrete sv
-- Output checking is tricky, since we behave differently for different modes
checkOutputs []
| null cstrs
= giveUp "Impossible happened: There are no outputs nor any constraints to check."
checkOutputs os
= do notify "Validating outputs."
if isSAT then satLoop os
else proveLoop os False
notify $ if null cstrs
then "There are no constraints to check."
else "Validating " ++ show (length cstrs) ++ " constraint(s)."
walkConstraints cstrs (checkOutputs (resOutputs result))
-- | `Provable` is specialization of `MProvable` to the `IO` monad. Unless you are using
-- transformers explicitly, this is the type you should prefer.
type Provable = MProvable IO
-- | Prove a property with multiple solvers, running them in separate threads. The
-- results will be returned in the order produced.
proveWithAll :: Provable a => [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, ThmResult)]
proveWithAll = (`sbvWithAll` proveWith)
-- | Prove a property with multiple solvers, running them in separate threads. Only
-- the result of the first one to finish will be returned, remaining threads will be killed.
-- Note that we send an exception to the losing processes, but we do *not* actually wait for them
-- to finish. In rare cases this can lead to zombie processes. In previous experiments, we found
-- that some processes take their time to terminate. So, this solution favors quick turnaround.
proveWithAny :: Provable a => [SMTConfig] -> a -> IO (Solver, NominalDiffTime, ThmResult)
proveWithAny = (`sbvWithAny` proveWith)
-- | Find a satisfying assignment to a property with multiple solvers, running them in separate threads. The
-- results will be returned in the order produced.
satWithAll :: Provable a => [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, SatResult)]
satWithAll = (`sbvWithAll` satWith)
-- | Find a satisfying assignment to a property with multiple solvers, running them in separate threads. Only
-- the result of the first one to finish will be returned, remaining threads will be killed.
-- Note that we send an exception to the losing processes, but we do *not* actually wait for them
-- to finish. In rare cases this can lead to zombie processes. In previous experiments, we found
-- that some processes take their time to terminate. So, this solution favors quick turnaround.
satWithAny :: Provable a => [SMTConfig] -> a -> IO (Solver, NominalDiffTime, SatResult)
satWithAny = (`sbvWithAny` satWith)
-- | Find a satisfying assignment to a property using a single solver, but
-- providing several query problems of interest, with each query running in a
-- separate thread and return the first one that returns. This can be useful to
-- use symbolic mode to drive to a location in the search space of the solver
-- and then refine the problem in query mode. If the computation is very hard to
-- solve for the solver than running in concurrent mode may provide a large
-- performance benefit.
satConcurrentWithAny :: Provable a => SMTConfig -> [Query b] -> a -> IO (Solver, NominalDiffTime, SatResult)
satConcurrentWithAny solver qs a = do (slvr,time,result) <- sbvConcurrentWithAny solver go qs a
return (slvr, time, SatResult result)
where go cfg a' q = runWithQuery True (do _ <- q; checkNoOptimizations >> Control.getSMTResult) cfg a'
-- | Prove a property by running many queries each isolated to their own thread
-- concurrently and return the first that finishes, killing the others
proveConcurrentWithAny :: Provable a => SMTConfig -> [Query b] -> a -> IO (Solver, NominalDiffTime, ThmResult)
proveConcurrentWithAny solver qs a = do (slvr,time,result) <- sbvConcurrentWithAny solver go qs a
return (slvr, time, ThmResult result)
where go cfg a' q = runWithQuery False (do _ <- q; checkNoOptimizations >> Control.getSMTResult) cfg a'
-- | Find a satisfying assignment to a property using a single solver, but run
-- each query problem in a separate isolated thread and wait for each thread to
-- finish. See 'satConcurrentWithAny' for more details.
satConcurrentWithAll :: Provable a => SMTConfig -> [Query b] -> a -> IO [(Solver, NominalDiffTime, SatResult)]
satConcurrentWithAll solver qs a = do results <- sbvConcurrentWithAll solver go qs a
return $ (\(a',b,c) -> (a',b,SatResult c)) <$> results
where go cfg a' q = runWithQuery True (do _ <- q; checkNoOptimizations >> Control.getSMTResult) cfg a'
-- | Prove a property by running many queries each isolated to their own thread
-- concurrently and wait for each to finish returning all results
proveConcurrentWithAll :: Provable a => SMTConfig -> [Query b] -> a -> IO [(Solver, NominalDiffTime, ThmResult)]
proveConcurrentWithAll solver qs a = do results <- sbvConcurrentWithAll solver go qs a
return $ (\(a',b,c) -> (a',b,ThmResult c)) <$> results
where go cfg a' q = runWithQuery False (do _ <- q; checkNoOptimizations >> Control.getSMTResult) cfg a'
-- | Create an SMT-Lib2 benchmark. The 'Bool' argument controls whether this is a SAT instance, i.e.,
-- translate the query directly, or a PROVE instance, i.e., translate the negated query.
generateSMTBenchmark :: (MonadIO m, MProvable m a) => Bool -> a -> m String
generateSMTBenchmark isSat a = do
t <- liftIO getZonedTime
let comments = ["Automatically created by SBV on " ++ show t]
cfg = defaultSMTCfg { smtLibVersion = SMTLib2 }
(_, res) <- runSymbolic (SMTMode QueryInternal ISetup isSat cfg) $ (if isSat then existential_ else universal_) a >>= output
let SMTProblem{smtLibPgm} = Control.runProofOn (SMTMode QueryInternal IRun isSat cfg) QueryInternal comments res
out = show (smtLibPgm cfg)
return $ out ++ "\n(check-sat)\n"
checkNoOptimizations :: MonadIO m => QueryT m ()
checkNoOptimizations = do objectives <- Control.getObjectives
unless (null objectives) $
error $ unlines [ ""
, "*** Data.SBV: Unsupported call sat/prove when optimization objectives are present."
, "*** Use \"optimize\"/\"optimizeWith\" to calculate optimal satisfaction!"
]
-- If we get a program producing nothing (i.e., Symbolic ()), pretend it simply returns True.
-- This is useful since min/max calls and constraints will provide the context
instance ExtractIO m => MProvable m (SymbolicT m ()) where
universal_ a = universal_ ((a >> return sTrue) :: SymbolicT m SBool)
universal ns a = universal ns ((a >> return sTrue) :: SymbolicT m SBool)
existential_ a = existential_ ((a >> return sTrue) :: SymbolicT m SBool)
existential ns a = existential ns ((a >> return sTrue) :: SymbolicT m SBool)
instance ExtractIO m => MProvable m (SymbolicT m SBool) where
universal_ = id
universal [] = id
universal xs = error $ "SBV.universal: Extra unmapped name(s) in predicate construction: " ++ intercalate ", " xs
existential_ = id
existential [] = id
existential xs = error $ "SBV.existential: Extra unmapped name(s) in predicate construction: " ++ intercalate ", " xs
instance ExtractIO m => MProvable m SBool where
universal_ = return
universal _ = return
existential_ = return
existential _ = return
{-
-- The following works, but it lets us write properties that
-- are not useful.. Such as: prove $ \x y -> (x::SInt8) == y
-- Running that will throw an exception since Haskell's equality
-- is not be supported by symbolic things. (Needs .==).
instance Provable Bool where
universal_ x = universal_ (if x then true else false :: SBool)
universal s x = universal s (if x then true else false :: SBool)
existential_ x = existential_ (if x then true else false :: SBool)
existential s x = existential s (if x then true else false :: SBool)
-}
-- Functions
instance (SymVal a, MProvable m p) => MProvable m (SBV a -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ k a
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ k a
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ k a
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ k a
existential [] k = existential_ k
-- Arrays
instance (HasKind a, HasKind b, MProvable m p) => MProvable m (SArray a b -> p) where
universal_ k = newArray_ Nothing >>= \a -> universal_ $ k a
universal (s:ss) k = newArray s Nothing >>= \a -> universal ss $ k a
universal [] k = universal_ k
existential_ k = newArray_ Nothing >>= \a -> existential_ $ k a
existential (s:ss) k = newArray s Nothing >>= \a -> existential ss $ k a
existential [] k = existential_ k
-- 2 Tuple
instance (SymVal a, SymVal b, MProvable m p) => MProvable m ((SBV a, SBV b) -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ \b -> k (a, b)
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ \b -> k (a, b)
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ \b -> k (a, b)
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ \b -> k (a, b)
existential [] k = existential_ k
-- 3 Tuple
instance (SymVal a, SymVal b, SymVal c, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c) -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ \b c -> k (a, b, c)
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ \b c -> k (a, b, c)
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ \b c -> k (a, b, c)
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ \b c -> k (a, b, c)
existential [] k = existential_ k
-- 4 Tuple
instance (SymVal a, SymVal b, SymVal c, SymVal d, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d) -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ \b c d -> k (a, b, c, d)
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ \b c d -> k (a, b, c, d)
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ \b c d -> k (a, b, c, d)
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ \b c d -> k (a, b, c, d)
existential [] k = existential_ k
-- 5 Tuple
instance (SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ \b c d e -> k (a, b, c, d, e)
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ \b c d e -> k (a, b, c, d, e)
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ \b c d e -> k (a, b, c, d, e)
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ \b c d e -> k (a, b, c, d, e)
existential [] k = existential_ k
-- 6 Tuple
instance (SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ \b c d e f -> k (a, b, c, d, e, f)
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ \b c d e f -> k (a, b, c, d, e, f)
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ \b c d e f -> k (a, b, c, d, e, f)
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ \b c d e f -> k (a, b, c, d, e, f)
existential [] k = existential_ k
-- 7 Tuple
instance (SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) where
universal_ k = sbvForall_ >>= \a -> universal_ $ \b c d e f g -> k (a, b, c, d, e, f, g)
universal (s:ss) k = sbvForall s >>= \a -> universal ss $ \b c d e f g -> k (a, b, c, d, e, f, g)
universal [] k = universal_ k
existential_ k = sbvExists_ >>= \a -> existential_ $ \b c d e f g -> k (a, b, c, d, e, f, g)
existential (s:ss) k = sbvExists s >>= \a -> existential ss $ \b c d e f g -> k (a, b, c, d, e, f, g)
existential [] k = existential_ k
-- | Generalization of 'Data.SBV.runSMT'
runSMT :: MonadIO m => SymbolicT m a -> m a
runSMT = runSMTWith defaultSMTCfg
-- | Generalization of 'Data.SBV.runSMTWith'
runSMTWith :: MonadIO m => SMTConfig -> SymbolicT m a -> m a
runSMTWith cfg a = fst <$> runSymbolic (SMTMode QueryExternal ISetup True cfg) a
-- | Runs with a query.
runWithQuery :: MProvable m a => Bool -> QueryT m b -> SMTConfig -> a -> m b
runWithQuery isSAT q cfg a = fst <$> runSymbolic (SMTMode QueryInternal ISetup isSAT cfg) comp
where comp = do _ <- (if isSAT then existential_ else universal_) a >>= output
Control.executeQuery QueryInternal q
-- | Check if a safe-call was safe or not, turning a 'SafeResult' to a Bool.
isSafe :: SafeResult -> Bool
isSafe (SafeResult (_, _, result)) = case result of
Unsatisfiable{} -> True
Satisfiable{} -> False
DeltaSat{} -> False -- conservative
SatExtField{} -> False -- conservative
Unknown{} -> False -- conservative
ProofError{} -> False -- conservative
-- | Perform an action asynchronously, returning results together with diff-time.
runInThread :: NFData b => UTCTime -> (SMTConfig -> IO b) -> SMTConfig -> IO (Async (Solver, NominalDiffTime, b))
runInThread beginTime action config = async $ do
result <- action config
endTime <- rnf result `seq` getCurrentTime
return (name (solver config), endTime `diffUTCTime` beginTime, result)
-- | Perform action for all given configs, return the first one that wins. Note that we do
-- not wait for the other asyncs to terminate; hopefully they'll do so quickly.
sbvWithAny :: NFData b => [SMTConfig] -> (SMTConfig -> a -> IO b) -> a -> IO (Solver, NominalDiffTime, b)
sbvWithAny [] _ _ = error "SBV.withAny: No solvers given!"
sbvWithAny solvers what a = do beginTime <- getCurrentTime
snd `fmap` (mapM (runInThread beginTime (`what` a)) solvers >>= waitAnyFastCancel)
where -- Async's `waitAnyCancel` nicely blocks; so we use this variant to ignore the
-- wait part for killed threads.
waitAnyFastCancel asyncs = waitAny asyncs `finally` mapM_ cancelFast asyncs
cancelFast other = throwTo (asyncThreadId other) ExitSuccess
sbvConcurrentWithAny :: NFData c => SMTConfig -> (SMTConfig -> a -> QueryT m b -> IO c) -> [QueryT m b] -> a -> IO (Solver, NominalDiffTime, c)
sbvConcurrentWithAny solver what queries a = snd `fmap` (mapM runQueryInThread queries >>= waitAnyFastCancel)
where -- Async's `waitAnyCancel` nicely blocks; so we use this variant to ignore the
-- wait part for killed threads.
waitAnyFastCancel asyncs = waitAny asyncs `finally` mapM_ cancelFast asyncs
cancelFast other = throwTo (asyncThreadId other) ExitSuccess
runQueryInThread q = do beginTime <- getCurrentTime
runInThread beginTime (\cfg -> what cfg a q) solver
sbvConcurrentWithAll :: NFData c => SMTConfig -> (SMTConfig -> a -> QueryT m b -> IO c) -> [QueryT m b] -> a -> IO [(Solver, NominalDiffTime, c)]
sbvConcurrentWithAll solver what queries a = mapConcurrently runQueryInThread queries >>= unsafeInterleaveIO . go
where runQueryInThread q = do beginTime <- getCurrentTime
runInThread beginTime (\cfg -> what cfg a q) solver
go [] = return []
go as = do (d, r) <- waitAny as
-- The following filter works because the Eq instance on Async
-- checks the thread-id; so we know that we're removing the
-- correct solver from the list. This also allows for
-- running the same-solver (with different options), since
-- they will get different thread-ids.
rs <- unsafeInterleaveIO $ go (filter (/= d) as)
return (r : rs)
-- | Perform action for all given configs, return all the results.
sbvWithAll :: NFData b => [SMTConfig] -> (SMTConfig -> a -> IO b) -> a -> IO [(Solver, NominalDiffTime, b)]
sbvWithAll solvers what a = do beginTime <- getCurrentTime
mapM (runInThread beginTime (`what` a)) solvers >>= (unsafeInterleaveIO . go)
where go [] = return []
go as = do (d, r) <- waitAny as
-- The following filter works because the Eq instance on Async
-- checks the thread-id; so we know that we're removing the
-- correct solver from the list. This also allows for
-- running the same-solver (with different options), since
-- they will get different thread-ids.
rs <- unsafeInterleaveIO $ go (filter (/= d) as)
return (r : rs)
-- | Symbolically executable program fragments. This class is mainly used for 'safe' calls, and is sufficiently populated internally to cover most use
-- cases. Users can extend it as they wish to allow 'safe' checks for SBV programs that return/take types that are user-defined.
class ExtractIO m => SExecutable m a where
-- | Generalization of 'Data.SBV.sName_'
sName_ :: a -> SymbolicT m ()
-- | Generalization of 'Data.SBV.sName'
sName :: [String] -> a -> SymbolicT m ()
-- | Generalization of 'Data.SBV.safe'
safe :: a -> m [SafeResult]
safe = safeWith defaultSMTCfg
-- | Generalization of 'Data.SBV.safeWith'
safeWith :: SMTConfig -> a -> m [SafeResult]
safeWith cfg a = do cwd <- (++ "/") <$> liftIO getCurrentDirectory
let mkRelative path
| cwd `isPrefixOf` path = drop (length cwd) path
| True = path
fst <$> runSymbolic (SMTMode QueryInternal ISafe True cfg) (sName_ a >> check mkRelative)
where check :: (FilePath -> FilePath) -> SymbolicT m [SafeResult]
check mkRelative = Control.executeQuery QueryInternal $ Control.getSBVAssertions >>= mapM (verify mkRelative)
-- check that the cond is unsatisfiable. If satisfiable, that would
-- indicate the assignment under which the 'Data.SBV.sAssert' would fail
verify :: (FilePath -> FilePath) -> (String, Maybe CallStack, SV) -> QueryT m SafeResult
verify mkRelative (msg, cs, cond) = do
let locInfo ps = let loc (f, sl) = concat [mkRelative (srcLocFile sl), ":", show (srcLocStartLine sl), ":", show (srcLocStartCol sl), ":", f]
in intercalate ",\n " (map loc ps)
location = (locInfo . getCallStack) `fmap` cs
result <- do Control.push 1
Control.send True $ "(assert " ++ show cond ++ ")"
r <- Control.getSMTResult
Control.pop 1
return r
return $ SafeResult (location, msg, result)
instance (ExtractIO m, NFData a) => SExecutable m (SymbolicT m a) where
sName_ a = a >>= \r -> rnf r `seq` return ()
sName [] = sName_
sName xs = error $ "SBV.SExecutable.sName: Extra unmapped name(s): " ++ intercalate ", " xs
instance ExtractIO m => SExecutable m (SBV a) where
sName_ v = sName_ (output v :: SymbolicT m (SBV a))
sName xs v = sName xs (output v :: SymbolicT m (SBV a))
-- Unit output
instance ExtractIO m => SExecutable m () where
sName_ () = sName_ (output () :: SymbolicT m ())
sName xs () = sName xs (output () :: SymbolicT m ())
-- List output
instance ExtractIO m => SExecutable m [SBV a] where
sName_ vs = sName_ (output vs :: SymbolicT m [SBV a])
sName xs vs = sName xs (output vs :: SymbolicT m [SBV a])
-- 2 Tuple output
instance (ExtractIO m, NFData a, SymVal a, NFData b, SymVal b) => SExecutable m (SBV a, SBV b) where
sName_ (a, b) = sName_ (output a >> output b :: SymbolicT m (SBV b))
sName _ = sName_
-- 3 Tuple output
instance (ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c) => SExecutable m (SBV a, SBV b, SBV c) where
sName_ (a, b, c) = sName_ (output a >> output b >> output c :: SymbolicT m (SBV c))
sName _ = sName_
-- 4 Tuple output
instance (ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d) => SExecutable m (SBV a, SBV b, SBV c, SBV d) where
sName_ (a, b, c, d) = sName_ (output a >> output b >> output c >> output c >> output d :: SymbolicT m (SBV d))
sName _ = sName_
-- 5 Tuple output
instance (ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e) where
sName_ (a, b, c, d, e) = sName_ (output a >> output b >> output c >> output d >> output e :: SymbolicT m (SBV e))
sName _ = sName_
-- 6 Tuple output
instance (ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e, NFData f, SymVal f) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) where
sName_ (a, b, c, d, e, f) = sName_ (output a >> output b >> output c >> output d >> output e >> output f :: SymbolicT m (SBV f))
sName _ = sName_
-- 7 Tuple output
instance (ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e, NFData f, SymVal f, NFData g, SymVal g) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) where
sName_ (a, b, c, d, e, f, g) = sName_ (output a >> output b >> output c >> output d >> output e >> output f >> output g :: SymbolicT m (SBV g))
sName _ = sName_
-- Functions
instance (SymVal a, SExecutable m p) => SExecutable m (SBV a -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ k a
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ k a
sName [] k = sName_ k
-- 2 Tuple input
instance (SymVal a, SymVal b, SExecutable m p) => SExecutable m ((SBV a, SBV b) -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ \b -> k (a, b)
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ \b -> k (a, b)
sName [] k = sName_ k
-- 3 Tuple input
instance (SymVal a, SymVal b, SymVal c, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c) -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ \b c -> k (a, b, c)
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ \b c -> k (a, b, c)
sName [] k = sName_ k
-- 4 Tuple input
instance (SymVal a, SymVal b, SymVal c, SymVal d, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d) -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ \b c d -> k (a, b, c, d)
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ \b c d -> k (a, b, c, d)
sName [] k = sName_ k
-- 5 Tuple input
instance (SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ \b c d e -> k (a, b, c, d, e)
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ \b c d e -> k (a, b, c, d, e)
sName [] k = sName_ k
-- 6 Tuple input
instance (SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ \b c d e f -> k (a, b, c, d, e, f)
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ \b c d e f -> k (a, b, c, d, e, f)
sName [] k = sName_ k
-- 7 Tuple input
instance (SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) where
sName_ k = sbvExists_ >>= \a -> sName_ $ \b c d e f g -> k (a, b, c, d, e, f, g)
sName (s:ss) k = sbvExists s >>= \a -> sName ss $ \b c d e f g -> k (a, b, c, d, e, f, g)
sName [] k = sName_ k
{-# ANN module ("HLint: ignore Reduce duplication" :: String) #-}