sbv-6.0: 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 BangPatterns #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE NamedFieldPuns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeSynonymInstances #-}
module Data.SBV.Provers.Prover (
SMTSolver(..), SMTConfig(..), Predicate, Provable(..), Goal
, ThmResult(..), SatResult(..), AllSatResult(..), SafeResult(..), OptimizeResult(..), SMTResult(..)
, isSatisfiable, isSatisfiableWith, isTheorem, isTheoremWith
, prove, proveWith
, sat, satWith
, allSat, allSatWith
, safe, safeWith, isSafe
, optimize, optimizeWith
, isVacuous, isVacuousWith
, SatModel(..), Modelable(..), displayModels, extractModels
, getModelDictionaries, getModelValues, getModelUninterpretedValues
, boolector, cvc4, yices, z3, mathSAT, abc, defaultSMTCfg
, compileToSMTLib, generateSMTBenchmarks
, internalSATCheck
) where
import Data.Char (isSpace)
import Data.List (intercalate, nub)
import Control.Monad (when, unless)
import System.FilePath (addExtension, splitExtension)
import System.Time (getClockTime)
import System.IO (hGetBuffering, hSetBuffering, stdout, hFlush, BufferMode(..))
import System.IO.Unsafe (unsafeInterleaveIO)
import Control.Concurrent.Async (async, wait, cancel, waitAny, Async)
import GHC.Stack.Compat
#if !MIN_VERSION_base(4,9,0)
import GHC.SrcLoc.Compat
#endif
import qualified Data.Set as Set (toList)
import Data.SBV.Core.Data
import Data.SBV.Core.Symbolic
import Data.SBV.SMT.SMT
import Data.SBV.SMT.SMTLib
import Data.SBV.Utils.TDiff
import Control.DeepSeq (rnf)
import Control.Exception (bracket)
import qualified Data.SBV.Provers.Boolector as Boolector
import qualified Data.SBV.Provers.CVC4 as CVC4
import qualified Data.SBV.Provers.Yices as Yices
import qualified Data.SBV.Provers.Z3 as Z3
import qualified Data.SBV.Provers.MathSAT as MathSAT
import qualified Data.SBV.Provers.ABC as ABC
mkConfig :: SMTSolver -> SMTLibVersion -> [String] -> SMTConfig
mkConfig s smtVersion tweaks = SMTConfig { verbose = False
, timing = NoTiming
, sBranchTimeOut = Nothing
, timeOut = Nothing
, printBase = 10
, printRealPrec = 16
, smtFile = Nothing
, solver = s
, solverTweaks = tweaks
, smtLibVersion = smtVersion
, optimizeArgs = []
, satCmd = "(check-sat)"
, isNonModelVar = const False -- i.e., everything is a model-variable by default
, roundingMode = RoundNearestTiesToEven
, useLogic = Nothing
}
-- | Default configuration for the Boolector SMT solver
boolector :: SMTConfig
boolector = mkConfig Boolector.boolector SMTLib2 []
-- | Default configuration for the CVC4 SMT Solver.
cvc4 :: SMTConfig
cvc4 = mkConfig CVC4.cvc4 SMTLib2 []
-- | 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 ["(set-option :smt.mbqi true) ; use model based quantifier instantiation"]
-- | Default configuration for the MathSAT SMT solver
mathSAT :: SMTConfig
mathSAT = mkConfig MathSAT.mathSAT SMTLib2 []
-- | Default configuration for the ABC synthesis and verification tool.
abc :: SMTConfig
abc = mkConfig ABC.abc SMTLib2 []
-- | The default solver used by SBV. This is currently set to z3.
defaultSMTCfg :: SMTConfig
defaultSMTCfg = z3
-- | 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 Provable a where
-- | Turns a value into a universally quantified predicate, internally naming the inputs.
-- In this case the sbv library will use names of the form @s1, s2@, etc. to name these variables
-- Example:
--
-- > forAll_ $ \(x::SWord8) y -> x `shiftL` 2 .== y
--
-- is a predicate with two arguments, captured using an ordinary Haskell function. Internally,
-- @x@ will be named @s0@ and @y@ will be named @s1@.
forAll_ :: a -> Predicate
-- | Turns a value into a predicate, allowing users to provide names for the inputs.
-- If the user does not provide enough number of names for the variables, the remaining ones
-- will be internally generated. Note that the names are only used for printing models and has no
-- other significance; in particular, we do not check that they are unique. Example:
--
-- > forAll ["x", "y"] $ \(x::SWord8) y -> x `shiftL` 2 .== y
--
-- This is the same as above, except the variables will be named @x@ and @y@ respectively,
-- simplifying the counter-examples when they are printed.
forAll :: [String] -> a -> Predicate
-- | Turns a value into an existentially quantified predicate. (Indeed, 'exists' would have been
-- a better choice here for the name, but alas it's already taken.)
forSome_ :: a -> Predicate
-- | Version of 'forSome' that allows user defined names
forSome :: [String] -> a -> Predicate
instance Provable Predicate where
forAll_ = id
forAll [] = id
forAll xs = error $ "SBV.forAll: Extra unmapped name(s) in predicate construction: " ++ intercalate ", " xs
forSome_ = id
forSome [] = id
forSome xs = error $ "SBV.forSome: Extra unmapped name(s) in predicate construction: " ++ intercalate ", " xs
instance Provable SBool where
forAll_ = return
forAll _ = return
forSome_ = return
forSome _ = 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
forAll_ x = forAll_ (if x then true else false :: SBool)
forAll s x = forAll s (if x then true else false :: SBool)
forSome_ x = forSome_ (if x then true else false :: SBool)
forSome s x = forSome s (if x then true else false :: SBool)
-}
-- Functions
instance (SymWord a, Provable p) => Provable (SBV a -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ k a
forAll (s:ss) k = forall s >>= \a -> forAll ss $ k a
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ k a
forSome (s:ss) k = exists s >>= \a -> forSome ss $ k a
forSome [] k = forSome_ k
-- SFunArrays (memory, functional representation), only supported universally for the time being
instance (HasKind a, HasKind b, Provable p) => Provable (SArray a b -> p) where
forAll_ k = declNewSArray (\t -> "array_" ++ show t) Nothing >>= \a -> forAll_ $ k a
forAll (s:ss) k = declNewSArray (const s) Nothing >>= \a -> forAll ss $ k a
forAll [] k = forAll_ k
forSome_ _ = error "SBV.forSome: Existential arrays are not currently supported."
forSome _ _ = error "SBV.forSome: Existential arrays are not currently supported."
-- SArrays (memory, SMT-Lib notion of arrays), only supported universally for the time being
instance (HasKind a, HasKind b, Provable p) => Provable (SFunArray a b -> p) where
forAll_ k = declNewSFunArray Nothing >>= \a -> forAll_ $ k a
forAll (_:ss) k = declNewSFunArray Nothing >>= \a -> forAll ss $ k a
forAll [] k = forAll_ k
forSome_ _ = error "SBV.forSome: Existential arrays are not currently supported."
forSome _ _ = error "SBV.forSome: Existential arrays are not currently supported."
-- 2 Tuple
instance (SymWord a, SymWord b, Provable p) => Provable ((SBV a, SBV b) -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ \b -> k (a, b)
forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b -> k (a, b)
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ \b -> k (a, b)
forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b -> k (a, b)
forSome [] k = forSome_ k
-- 3 Tuple
instance (SymWord a, SymWord b, SymWord c, Provable p) => Provable ((SBV a, SBV b, SBV c) -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ \b c -> k (a, b, c)
forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c -> k (a, b, c)
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ \b c -> k (a, b, c)
forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c -> k (a, b, c)
forSome [] k = forSome_ k
-- 4 Tuple
instance (SymWord a, SymWord b, SymWord c, SymWord d, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d) -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ \b c d -> k (a, b, c, d)
forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d -> k (a, b, c, d)
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ \b c d -> k (a, b, c, d)
forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d -> k (a, b, c, d)
forSome [] k = forSome_ k
-- 5 Tuple
instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ \b c d e -> k (a, b, c, d, e)
forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d e -> k (a, b, c, d, e)
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ \b c d e -> k (a, b, c, d, e)
forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d e -> k (a, b, c, d, e)
forSome [] k = forSome_ k
-- 6 Tuple
instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SymWord f, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ \b c d e f -> k (a, b, c, d, e, f)
forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d e f -> k (a, b, c, d, e, f)
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ \b c d e f -> k (a, b, c, d, e, f)
forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d e f -> k (a, b, c, d, e, f)
forSome [] k = forSome_ k
-- 7 Tuple
instance (SymWord a, SymWord b, SymWord c, SymWord d, SymWord e, SymWord f, SymWord g, Provable p) => Provable ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) where
forAll_ k = forall_ >>= \a -> forAll_ $ \b c d e f g -> k (a, b, c, d, e, f, g)
forAll (s:ss) k = forall s >>= \a -> forAll ss $ \b c d e f g -> k (a, b, c, d, e, f, g)
forAll [] k = forAll_ k
forSome_ k = exists_ >>= \a -> forSome_ $ \b c d e f g -> k (a, b, c, d, e, f, g)
forSome (s:ss) k = exists s >>= \a -> forSome ss $ \b c d e f g -> k (a, b, c, d, e, f, g)
forSome [] k = forSome_ k
-- | Prove a predicate, equivalent to @'proveWith' 'defaultSMTCfg'@
prove :: Provable a => a -> IO ThmResult
prove = proveWith defaultSMTCfg
-- | Find a satisfying assignment for a predicate, equivalent to @'satWith' 'defaultSMTCfg'@
sat :: Provable a => a -> IO SatResult
sat = satWith defaultSMTCfg
-- | Return all satisfying assignments for a predicate, equivalent to @'allSatWith' 'defaultSMTCfg'@.
-- Satisfying assignments are constructed lazily, so they will be available as returned by the solver
-- and on demand.
--
-- NB. Uninterpreted constant/function values and counter-examples for array values are ignored for
-- the purposes of @'allSat'@. That is, only the satisfying assignments modulo uninterpreted functions and
-- array inputs will be returned. This is due to the limitation of not having a robust means of getting a
-- function counter-example back from the SMT solver.
allSat :: Provable a => a -> IO AllSatResult
allSat = allSatWith defaultSMTCfg
-- | Optimize a given collection of `Objective`s
optimize :: Provable a => a -> IO OptimizeResult
optimize = optimizeWith defaultSMTCfg
-- | Check that all the 'sAssert' calls are safe, equivalent to @'safeWith' 'defaultSMTCfg'@
safe :: SExecutable a => a -> IO [SafeResult]
safe = safeWith defaultSMTCfg
-- | Check if the given constraints are satisfiable, equivalent to @'isVacuousWith' 'defaultSMTCfg'@.
-- See the function 'constrain' for an example use of 'isVacuous'. Also see the 'CheckConstrVacuity'
-- tactic.
isVacuous :: Provable a => a -> IO Bool
isVacuous = isVacuousWith defaultSMTCfg
-- Decision procedures (with optional timeout)
-- | Check whether a given property is a theorem, with an optional time out and the given solver.
-- Returns @Nothing@ if times out, or the result wrapped in a @Just@ otherwise.
isTheoremWith :: Provable a => SMTConfig -> Maybe Int -> a -> IO (Maybe Bool)
isTheoremWith cfg mbTo p = do r <- proveWith cfg{timeOut = mbTo} p
case r of
ThmResult (Unsatisfiable _) -> return $ Just True
ThmResult (Satisfiable _ _) -> return $ Just False
ThmResult (TimeOut _) -> return Nothing
_ -> error $ "SBV.isTheorem: Received:\n" ++ show r
-- | Check whether a given property is satisfiable, with an optional time out and the given solver.
-- Returns @Nothing@ if times out, or the result wrapped in a @Just@ otherwise.
isSatisfiableWith :: Provable a => SMTConfig -> Maybe Int -> a -> IO (Maybe Bool)
isSatisfiableWith cfg mbTo p = do r <- satWith cfg{timeOut = mbTo} p
case r of
SatResult (Satisfiable _ _) -> return $ Just True
SatResult (Unsatisfiable _) -> return $ Just False
SatResult (TimeOut _) -> return Nothing
_ -> error $ "SBV.isSatisfiable: Received: " ++ show r
-- | Checks theoremhood within the given optional time limit of @i@ seconds.
-- Returns @Nothing@ if times out, or the result wrapped in a @Just@ otherwise.
isTheorem :: Provable a => Maybe Int -> a -> IO (Maybe Bool)
isTheorem = isTheoremWith defaultSMTCfg
-- | Checks satisfiability within the given optional time limit of @i@ seconds.
-- Returns @Nothing@ if times out, or the result wrapped in a @Just@ otherwise.
isSatisfiable :: Provable a => Maybe Int -> a -> IO (Maybe Bool)
isSatisfiable = isSatisfiableWith defaultSMTCfg
-- | Compiles to SMT-Lib and returns the resulting program as a string. Useful for saving
-- the result to a file for off-line analysis, for instance if you have an SMT solver that's not natively
-- supported out-of-the box by the SBV library. It takes two arguments:
--
-- * version: The SMTLib-version to produce. Note that we currently only support SMTLib2.
--
-- * isSat : If 'True', will translate it as a SAT query, i.e., in the positive. If 'False', will
-- translate as a PROVE query, i.e., it will negate the result. (In this case, the check-sat
-- call to the SMT solver will produce UNSAT if the input is a theorem, as usual.)
compileToSMTLib :: Provable a => SMTLibVersion -- ^ Version of SMTLib to compile to. (Only SMTLib2 supported currently.)
-> Bool -- ^ If True, translate directly, otherwise negate the goal. (Use True for SAT queries, False for PROVE queries.)
-> a
-> IO String
compileToSMTLib version isSat a = do
t <- getClockTime
let comments = ["Created on " ++ show t]
cvt = case version of
SMTLib2 -> toSMTLib2
SMTProblem{smtLibPgm} <- simulate cvt defaultSMTCfg isSat comments a
let out = show (smtLibPgm defaultSMTCfg NoCase)
return $ out ++ "\n(check-sat)\n"
-- | Create SMT-Lib benchmarks, for supported versions of SMTLib. The first argument is the basename of the file.
-- 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. (See the second boolean argument to
-- 'compileToSMTLib' for details.)
generateSMTBenchmarks :: Provable a => Bool -> FilePath -> a -> IO ()
generateSMTBenchmarks isSat f a = mapM_ gen [minBound .. maxBound]
where gen v = do s <- compileToSMTLib v isSat a
let fn = f `addExtension` smtLibVersionExtension v
writeFile fn s
putStrLn $ "Generated " ++ show v ++ " benchmark " ++ show fn ++ "."
-- | Make sure we're line-buffering if there's going to be parallel calls.
bufferSanity :: Bool -> IO a -> IO a
bufferSanity False a = a
bufferSanity True a = bracket before after (const a)
where before = do b <- hGetBuffering stdout
hSetBuffering stdout LineBuffering
return b
after b = do hFlush stdout
hSetBuffering stdout b
hFlush stdout
-- | Make sure sat/prove calls don't have objectives, and optimize does!
objectiveCheck :: Bool -> [Objective a] -> String -> IO ()
objectiveCheck False [] _ = return ()
objectiveCheck False os w = error $ unlines $ ("\n*** Unsupported call to " ++ show w ++ " in the presence of objective(s):")
: [ "***\t" ++ intercalate ", " (map objectiveName os)
, "*** Use \"optimize\" to optimize for these objectives instead of " ++ show w
]
objectiveCheck True [] w = error $ "*** Unsupported call to " ++ w ++ " when no objectives are present. Use \"sat\" for plain satisfaction"
objectiveCheck True _ _ = return ()
-- | Pick the converter, based on the SMTLib version. Note that
-- we no longer support SMTLib1, so the following is more or less a no-op,
-- but it's good to use it since if we add some other target GHC's pattern-match
-- warning will point us to here.
getConverter :: SMTConfig -> SMTLibConverter
getConverter SMTConfig{smtLibVersion} = case smtLibVersion of
SMTLib2 -> toSMTLib2
-- | Proves the predicate using the given SMT-solver
proveWith :: Provable a => SMTConfig -> a -> IO ThmResult
proveWith config a = do simRes@SMTProblem{tactics, objectives} <- simulate (getConverter config) config False [] a
objectiveCheck False objectives "prove"
let hasPar = any isParallelCaseAnywhere tactics
bufferSanity hasPar $ applyTactics config (False, hasPar) (wrap, unwrap) [] tactics objectives $ callSolver False "Checking Theoremhood.." [] mwrap simRes
where wrap = ThmResult
unwrap (ThmResult r) = r
mwrap [r] = wrap r
mwrap xs = error $ "SBV.proveWith: Backend solver returned a non-singleton answer:\n" ++ show (map ThmResult xs)
-- | Find a satisfying assignment using the given SMT-solver
satWith :: Provable a => SMTConfig -> a -> IO SatResult
satWith config a = do simRes@SMTProblem{tactics, objectives} <- simulate (getConverter config) config True [] a
objectiveCheck False objectives "sat"
let hasPar = any isParallelCaseAnywhere tactics
bufferSanity hasPar $ applyTactics config (True, hasPar) (wrap, unwrap) [] tactics objectives $ callSolver True "Checking Satisfiability.." [] mwrap simRes
where wrap = SatResult
unwrap (SatResult r) = r
mwrap [r] = wrap r
mwrap xs = error $ "SBV.satWith: Backend solver returned a non-singleton answer:\n" ++ show (map SatResult xs)
-- | Optimizes the objectives using the given SMT-solver
optimizeWith :: Provable a => SMTConfig -> a -> IO OptimizeResult
optimizeWith config a = do
msg "Optimizing.."
sbvPgm@SMTProblem{objectives, tactics} <- simulate (getConverter config) config True [] a
objectiveCheck True objectives "optimize"
let hasPar = any isParallelCaseAnywhere tactics
style = case nub [s | OptimizePriority s <- tactics] of
[] -> Lexicographic
[s] -> s
ss -> error $ "SBV: Multiple optimization priorities found: " ++ intercalate ", " (map show ss) ++ ". Please use only one."
optimizer = case style of
Lexicographic -> optLexicographic
Independent -> optIndependent
Pareto -> optPareto
optimizer hasPar config sbvPgm
where msg = when (verbose config) . putStrLn . ("** " ++)
-- | Construct a lexicographic optimization result
optLexicographic :: Bool -> SMTConfig -> SMTProblem -> IO OptimizeResult
optLexicographic hasPar config sbvPgm@SMTProblem{objectives, tactics} = do
result <- bufferSanity hasPar $ applyTactics config (True, hasPar) (id, id) [] tactics objectives $ callSolver True "Lexicographically optimizing.." [] mwrap sbvPgm
return $ LexicographicResult result
where mwrap [r] = r
mwrap xs = error $ "SBV.optLexicographic: Backend solver returned a non-singleton answer:\n" ++ show (map SatResult xs)
-- | Construct an independent optimization result
optIndependent :: Bool -> SMTConfig -> SMTProblem -> IO OptimizeResult
optIndependent hasPar config sbvPgm@SMTProblem{objectives, tactics} = do
let ns = map objectiveName objectives
result <- bufferSanity hasPar $ applyTactics config (True, hasPar) (wrap ns, unwrap) [] tactics objectives $ callSolver True "Independently optimizing.." [] mwrap sbvPgm
return $ IndependentResult result
where wrap :: [String] -> SMTResult -> [(String, SMTResult)]
wrap ns r = zip ns (repeat r)
-- the role of unwrap here is to take the result with more info in case a case-split is
-- performed and we need to decide in a SAT context.
unwrap :: [(String, SMTResult)] -> SMTResult
unwrap xs = case [r | (_, r@Satisfiable{}) <- xs] ++ [r | (_, r@SatExtField{}) <- xs] ++ map snd xs of
(r:_) -> r
[] -> error "SBV.optIndependent: Impossible happened: Received no results!"
mwrap xs
| lobs == lxs = zip (map objectiveName objectives) xs
| True = error $ "SBV.optIndependent: Expected " ++ show lobs ++ " objective results, but received: " ++ show lxs ++ ":\n" ++ show (map SatResult xs)
where lxs = length xs
lobs = length objectives
-- | Construct a pareto-front optimization result
optPareto :: Bool -> SMTConfig -> SMTProblem -> IO OptimizeResult
optPareto hasPar config sbvPgm@SMTProblem{objectives, tactics} = do
result <- bufferSanity hasPar $ applyTactics config (True, hasPar) (wrap, unwrap) [] tactics objectives $ callSolver True "Pareto optimizing.." [] id sbvPgm
return $ ParetoResult result
where wrap :: SMTResult -> [SMTResult]
wrap r = [r]
-- the role of unwrap here is to take the result with more info in case a case-split is
-- performed and we need to decide in a SAT context.
unwrap :: [SMTResult] -> SMTResult
unwrap xs = case [r | r@Satisfiable{} <- xs] ++ [r | r@SatExtField{} <- xs] ++ xs of
(r:_) -> r
[] -> error "SBV.optPareto: Impossible happened: Received no results!"
-- | Apply the given tactics to a problem
applyTactics :: SMTConfig -- ^ Solver configuration
-> (Bool, Bool) -- ^ Are we a sat-problem? Do we have anything parallel going on? (Parallel-case split.)
-> (SMTResult -> res, res -> SMTResult) -- ^ Wrapper/unwrapper pair from result to SMT answer
-> [(String, (String, SW))] -- ^ Level at which we are called. (In case of a nested case-split)
-> [Tactic SW] -- ^ Tactics active at this level
-> [Objective (SW, SW)] -- ^ Optimization goals we have
-> (SMTConfig -> Maybe (OptimizeStyle, Int) -> CaseCond -> IO res) -- ^ The actual continuation at this point
-> IO res
applyTactics cfgIn (isSat, hasPar) (wrap, unwrap) levels tactics objectives cont
= do --
-- TODO: The management of tactics here is quite adhoc. We should have a better story
-- Currently, we:
--
-- - Perform optimization (which requires sat and no case-splitting)
-- - Check for vacuity if asked
-- - Do case-splitting
--
-- If we have more interesting tactics, we'll have to come up with a better "proof manager." The current
-- code is sufficient, however, for the use cases we have now.
-- check that if we have objectives, then we must be sat and there must be no case-splits
when (hasObjectives && not isSat) $ error "SBV: Optimization is only available for sat calls."
when (hasObjectives && hasCaseSplits) $ error "SBV: Optimization and case-splits are not supported together."
let mbOptInfo
| not hasObjectives = Nothing
| True = Just (optimizePriority, length objectives)
if hasObjectives
then cont (finalOptConfig objectives) mbOptInfo (Opt objectives)
else do -- Check vacuity if asked. If result is Nothing, it means we're good to go.
mbRes <- if not shouldCheckConstrVacuity
then return Nothing
else constraintVacuityCheck isSat finalConfig mbOptInfo (wrap, unwrap) cont
-- Do case split, if vacuity said continue
case mbRes of
Just r -> return r
Nothing -> if null caseSplits
then cont finalConfig mbOptInfo (CasePath (map (snd . snd) levels))
else caseSplit finalConfig mbOptInfo shouldCheckCaseVacuity (parallelCase, hasPar) isSat (wrap, unwrap) levels chatty cases cont
where (caseSplits, checkCaseVacuity, parallelCases, checkConstrVacuity, timeOuts, checkUsing, useLogics, useSolvers, optimizePriorities)
= foldr (flip classifyTactics) ([], [], [], [], [], [], [], [], []) tactics
classifyTactics (a, b, c, d, e, f, g, h, i) = \case
t@CaseSplit{} -> (t:a, b, c, d, e, f, g, h, i)
t@CheckCaseVacuity{} -> ( a, t:b, c, d, e, f, g, h, i)
t@ParallelCase{} -> ( a, b, t:c, d, e, f, g, h, i)
t@CheckConstrVacuity{} -> ( a, b, c, t:d, e, f, g, h, i)
t@StopAfter{} -> ( a, b, c, d, t:e, f, g, h, i)
t@CheckUsing{} -> ( a, b, c, d, e, t:f, g, h, i)
t@UseLogic{} -> ( a, b, c, d, e, f, t:g, h, i)
t@UseSolver{} -> ( a, b, c, d, e, f, g, t:h, i)
t@OptimizePriority{} -> ( a, b, c, d, e, f, g, h, t:i)
hasObjectives = not $ null objectives
hasCaseSplits = not $ null cases
parallelCase = not $ null parallelCases
optimizePriority = case [s | OptimizePriority s <- optimizePriorities] of
[] -> Lexicographic
[s] -> s
ss -> error $ "SBV.OptimizePriority: Multiple optimization priorities found, at most one is allowed: " ++ intercalate "," (map show ss)
shouldCheckCaseVacuity = case [b | CheckCaseVacuity b <- checkCaseVacuity] of
[] -> True -- default is to check-case-vacuity
bs -> or bs -- otherwise check vacuity if we're asked to do so
-- for constraint vacuity, default is *not* to check; so a simple or suffices
shouldCheckConstrVacuity = or [b | CheckConstrVacuity b <- checkConstrVacuity]
(chatty, cases) = let (vs, css) = unzip [(v, cs) | CaseSplit v cs <- caseSplits] in (or (verbose cfgIn : vs), concat css)
grabStops c = case [i | StopAfter i <- timeOuts] of
[] -> c
xs -> c {timeOut = Just (maximum xs)}
grabCheckUsing c = case [s | CheckUsing s <- checkUsing] of
[] -> c
[s] -> c {satCmd = "(check-sat-using " ++ s ++ ")"}
ss -> c {satCmd = "(check-sat-using (then " ++ unwords ss ++ "))"}
grabUseLogic c = case [l | UseLogic l <- useLogics] of
[] -> c
ss -> c { useLogic = Just (last ss) }
configToUse = case [s | UseSolver s <- useSolvers] of
[] -> cfgIn
[s] -> s
ss -> error $ "SBV.UseSolver: Multiple UseSolver tactics found, at most one is allowed: " ++ intercalate "," (map show ss)
finalConfig = grabUseLogic . grabCheckUsing . grabStops $ configToUse
finalOptConfig goals = finalConfig { optimizeArgs = optimizeArgs finalConfig ++ optimizerDirectives }
where optimizerDirectives
| hasObjectives = map minmax goals ++ style optimizePriority
| True = []
minmax (Minimize _ (_, v)) = "(minimize " ++ show v ++ ")"
minmax (Maximize _ (_, v)) = "(maximize " ++ show v ++ ")"
minmax (AssertSoft nm (_, v) mbp) = "(assert-soft " ++ show v ++ penalize mbp ++ ")"
where penalize DefaultPenalty = ""
penalize (Penalty w mbGrp)
| w <= 0 = error $ unlines [ "SBV.AssertSoft: 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
style Lexicographic = [] -- default, no option needed
style Independent = ["(set-option :opt.priority box)"]
style Pareto = [ "(set-option :opt.priority pareto)"
, "(set-option :opt.print_model true)"
]
-- | Implements the "constraint vacuity check" tactic, making sure the calls to "constrain"
-- describe a satisfiable condition. Returns:
--
-- - Nothing if this is a SAT call, as that would be a weird thing to do (we only would care about constraint-vacuity in a proof context),
-- - Nothing if satisfiable: The world is OK, just keep moving
-- - ProofError if unsatisfiable. In this case we found that the constraints given are just bad!
--
-- NB. We'll do a SAT call even if there are *no* constraints! This is OK, as the call will be cheap; and this is an opt-in call. (i.e.,
-- the user asked us to do it explicitly.)
constraintVacuityCheck :: forall res.
Bool -- ^ isSAT?
-> SMTConfig -- ^ config
-> Maybe (OptimizeStyle, Int) -- ^ optimization info
-> (SMTResult -> res, res -> SMTResult) -- ^ wrappers back and forth from final result
-> (SMTConfig -> Maybe (OptimizeStyle, Int) -> CaseCond -> IO res) -- ^ continuation
-> IO (Maybe res) -- ^ result, wrapped in Maybe if vacuity fails
constraintVacuityCheck True _ _ _ _ = return Nothing -- for a SAT check, vacuity is meaningless (what would be the point)?
constraintVacuityCheck False config d (wrap, unwrap) f = do
res <- f config d CstrVac
case unwrap res of
Satisfiable{} -> return Nothing
_ -> return $ Just $ wrap vacuityFailResult
where vacuityFailResult = ProofError config [ "Constraint vacuity check failed."
, "User given constraints are not satisfiable."
]
-- | Implements the case-split tactic. Works for both Sat and Proof, hence the quantification on @res@
caseSplit :: forall res.
SMTConfig -- ^ Solver config
-> Maybe (OptimizeStyle, Int) -- ^ Are we optimizing?
-> Bool -- ^ Should we check vacuity of cases?
-> (Bool, Bool) -- ^ Should we run the cases in parallel? Second bool: Is anything parallel going on?
-> Bool -- ^ True if we're sat solving
-> (SMTResult -> res, res -> SMTResult) -- ^ wrapper, unwrapper from sat/proof to the actual result
-> [(String, (String, SW))] -- ^ Path condition as we reached here. (In a nested case split, First #, then actual name.)
-> Bool -- ^ Should we be chatty on the case-splits?
-> [(String, SW, [Tactic SW])] -- ^ List of cases. Case name, condition, plus further tactics for nested case-splitting etc.
-> (SMTConfig -> Maybe (OptimizeStyle, Int) -> CaseCond -> IO res) -- ^ The "solver" once we provide it with a problem and a case
-> IO res
caseSplit config mbOptInfo checkVacuity (runParallel, hasPar) isSAT (wrap, unwrap) level chatty cases cont
| runParallel = goParallel tasks
| True = goSerial tasks
where tasks = zip caseNos cases
lids = map fst level
noOfCases = length cases
casePad = length (show noOfCases)
tagLength = maximum $ map length $ "Coverage" : [s | (s, _, _) <- cases]
showTag t = take tagLength (t ++ repeat ' ')
shCaseId i = let si = show i in replicate (casePad - length si) ' ' ++ si
caseNos = map shCaseId [(1::Int) .. ]
tag tagChar = replicate 2 tagChar ++ replicate (2 * length level) tagChar
mkCaseNameBase s i = "Case " ++ intercalate "." (lids ++ [i]) ++ ": " ++ showTag s
mkCovNameBase = "Coverage " ++ replicate (casePad - 1) ' ' ++ "X"
mkCaseName tagChar s i = tag tagChar ++ ' ' : mkCaseNameBase s i
mkCovName tagChar = tag tagChar ++ ' ' : mkCovNameBase
startCase :: Bool -> Maybe (String, String) -> IO ()
startCase multi mbis
| not chatty = return ()
| Just (i, s) <- mbis = printer $ mkCaseName tagChar s i ++ start
| True = printer $ mkCovName tagChar ++ start
where line = multi || hasPar
printer | line = putStrLn
| True = putStr
tagChar | line = '>'
| True = '*'
start = " [Started]"
vacuityMsg :: Maybe Bool -> Bool -> (String, String) -> IO ()
vacuityMsg mbGood multi (i, s)
| not chatty = return ()
| line = putStrLn $ mkCaseName '=' s i ++ msg
| True = printer msg
where line = multi || hasPar
printer
| failed = putStrLn
| True = putStr
(failed, msg) = case mbGood of
Nothing -> (False, " [Vacuity Skipped]")
Just True -> (False, " [Vacuity OK]")
Just False -> (True, " [Vacuity Failed]")
endCase :: Bool -> Maybe (String, String) -> String -> IO ()
endCase multi mbis msg
| not chatty = return ()
| not line = putStrLn $ ' ' : msg
| Just (i, s) <- mbis = putStrLn $ mkCaseName '<' s i ++ ' ' : msg
| True = putStrLn $ mkCovName '<' ++ ' ' : msg
where line = multi || hasPar
-----------------------------------------------------------------------------------------------------------------
-- Serial case analysis
-----------------------------------------------------------------------------------------------------------------
goSerial :: [(String, (String, SW, [Tactic SW]))] -> IO res
goSerial []
-- At the end, we do a coverage call
= do let multi = runParallel
startCase multi Nothing
res <- cont config mbOptInfo (CaseCov (map (snd . snd) level) [c | (_, c, _) <- cases])
decideSerial multi Nothing (unwrap res) (return res)
goSerial ((i, (nm, cond, ts)):cs)
-- Still going down, do a regular call
= do let multi = not . null $ [() | CaseSplit{} <- ts]
mbis = Just (i, nm)
startCase multi mbis
continue <- if isSAT -- for a SAT check, vacuity is meaningless (what would be the point)?
then return True
else if checkVacuity
then do res <- cont config mbOptInfo (CaseVac (map (snd . snd) level) cond)
case unwrap res of
Satisfiable{} -> vacuityMsg (Just True) multi (i, nm) >> return True
_ -> vacuityMsg (Just False) multi (i, nm) >> return False
else vacuityMsg Nothing multi (i, nm) >> return True
if continue
then do res <- applyTactics config (isSAT, hasPar) (wrap, unwrap) (level ++ [(i, (nm, cond))]) ts [] cont
decideSerial multi mbis (unwrap res) (goSerial cs)
else return $ wrap $ vacuityFailResult (i, nm)
vacuityFailResult cur = ProofError config $ [ "Vacuity check failed."
, "Case constraint not satisfiable. Leading path:"
]
++ map (" " ++) (align ([(i, n) | (i, (n, _)) <- level] ++ [cur]))
++ ["HINT: Try \"CheckCaseVacuity False\" tactic to ignore case vacuity checks."]
where align :: [(String, String)] -> [String]
align path = map join cpath
where len = maximum (0 : map (length . fst) cpath)
join (c, n) = reverse (take len (reverse c ++ repeat ' ')) ++ ": " ++ n
cpath = [(intercalate "." (reverse ls), j) | (ls, j) <- cascade [] path]
trim = reverse . dropWhile isSpace . reverse . dropWhile isSpace
cascade _ [] = []
cascade sofar ((i, j) : rest) = let new = trim i : sofar in (new, j) : cascade new rest
decideSerial
| isSAT = decideSerialSAT
| True = decideSerialProof
-- short name
diag Unsatisfiable{} = "[Unsatisfiable]"
diag Satisfiable {} = "[Satisfiable]"
diag SatExtField {} = "[Satisfiable in Field Extension]"
diag Unknown {} = "[Unknown]"
diag ProofError {} = "[ProofError]"
diag TimeOut {} = "[TimeOut]"
-- If we're SAT, we stop at first satisfiable and report back. Otherwise continue.
-- Note that we also stop if we get a ProofError, as that clearly is not OK
decideSerialSAT :: Bool -> Maybe (String, String) -> SMTResult -> IO res -> IO res
decideSerialSAT multi mbis r@Satisfiable{} _ = endCase multi mbis (diag r) >> return (wrap r)
decideSerialSAT multi mbis r@ProofError{} _ = endCase multi mbis (diag r) >> return (wrap r)
decideSerialSAT multi mbis r k = endCase multi mbis (diag r) >> k
-- If we're Prove, we stop at first *not* unsatisfiable and report back. Otherwise continue.
decideSerialProof :: Bool -> Maybe (String, String) -> SMTResult -> IO res -> IO res
decideSerialProof multi mbis Unsatisfiable{} k = endCase multi mbis "[Proved]" >> k
decideSerialProof multi mbis r _ = endCase multi mbis "[Failed]" >> return (wrap r)
-----------------------------------------------------------------------------------------------------------------
-- Parallel case analysis
-----------------------------------------------------------------------------------------------------------------
goParallel :: [(String, (String, SW, [Tactic SW]))] -> IO res
goParallel cs = do
when chatty $ putStrLn $ topName '>' "[Starting]"
-- Create the case claim:
let mkTask (i, (nm, cond, ts)) =
let caseProof = do continue <- if isSAT -- for a SAT check, vacuity is meaningless (what would be the point)?
then return True
else if checkVacuity
then do res <- cont config mbOptInfo (CaseVac (map (snd . snd) level) cond)
case unwrap res of
Satisfiable{} -> return True
_ -> return False
else return True
if continue
then unwrap `fmap` applyTactics config (isSAT, hasPar) (wrap, unwrap) (level ++ [(i, (nm, cond))]) ts [] cont
else return $ vacuityFailResult (i, nm)
in (mkCaseNameBase nm i, caseProof)
-- Create the coverage claim
let cov = unwrap `fmap` cont config mbOptInfo (CaseCov (map (snd . snd) level) [c | (_, c, _) <- cases])
(decidingTag, res) <- decideParallel $ map mkTask cs ++ [(mkCovNameBase, cov)]
let trim = reverse . dropWhile isSpace . reverse . dropWhile isSpace
let caseMsg
| isSAT = satMsg
| True = proofMsg
where addTag x = x ++ " (at " ++ trim decidingTag ++ ")"
(satMsg, proofMsg) = case res of
Unsatisfiable{} -> ("[Unsatisfiable]", "[Proved]")
Satisfiable{} -> (addTag "[Satisfiable]", addTag "[Failed]")
_ -> let d = diag res in (addTag d, addTag d)
when chatty $ putStrLn $ topName '<' caseMsg
return $ wrap res
where topName c w = tag c ++ topTag ++ " Parallel case split: " ++ range ++ ": " ++ w
topTag = " Case" ++ s ++ intercalate "." lids ++ dot ++ "[1-" ++ show (length cs + 1) ++ "]:"
where dot | null lids = ""
| True = "."
s | null cs = " "
| True = "s "
range = case cs of
[] -> "Coverage"
[_] -> "One case and coverage"
xs -> show (length xs) ++ " cases and coverage"
-- Parallel decision:
-- - If SAT: Run all cases in parallel and return a SAT result from any. If none-of-them is SAT, then we return the last finishing
-- - If Prove: Run all cases in parallel and return the last one if all return UNSAT. Otherwise return the first SAT one.
decideParallel :: [(String, IO SMTResult)] -> IO (String, SMTResult)
decideParallel caseTasks = mapM try caseTasks >>= pick
where try (nm, task) = async $ task >>= \r -> return (nm, r)
pick :: [Async (String, SMTResult)] -> IO (String, SMTResult)
pick [] = error "SBV.caseSplit.decideParallel: Impossible happened, ran out of proofs!"
pick [a] = wait a
pick as = do (d, r) <- waitAny as
let others = filter (/= d) as
continue = pick others
stop = mapM_ cancel others >> return r
case snd r of
Unsatisfiable{} -> continue
Satisfiable{} -> stop
SatExtField{} -> stop
ProofError{} -> stop
Unknown{} -> if isSAT then continue else stop
TimeOut{} -> if isSAT then continue else stop
-- | Check if any of the assertions can be violated
safeWith :: SExecutable a => SMTConfig -> a -> IO [SafeResult]
safeWith cfg a = do
res@Result{resAssertions=asserts} <- runSymbolic (True, cfg) $ sName_ a >>= output
mapM (verify res) asserts
where locInfo (Just ps) = Just $ let loc (f, sl) = concat [srcLocFile sl, ":", show (srcLocStartLine sl), ":", show (srcLocStartCol sl), ":", f]
in intercalate ",\n " (map loc ps)
locInfo _ = Nothing
verify res (msg, cs, cond) = do result <- runProofOn (getConverter cfg) cfg True [] pgm >>= \p -> callSolver True msg [] mwrap p cfg Nothing NoCase
return $ SafeResult (locInfo (getCallStack `fmap` cs), msg, result)
where pgm = res { resInputs = [(EX, n) | (_, n) <- resInputs res] -- make everything existential
, resOutputs = [cond]
}
mwrap [r] = r
mwrap xs = error $ "SBV.safeWith: Backend solver returned a non-singleton answer:\n" ++ show (map SatResult xs)
-- | 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
SatExtField{} -> False -- conservative
Unknown{} -> False -- conservative
ProofError{} -> False -- conservative
TimeOut{} -> False -- conservative
-- | Determine if the constraints are vacuous using the given SMT-solver. Also see
-- the 'CheckConstrVacuity' tactic.
isVacuousWith :: Provable a => SMTConfig -> a -> IO Bool
isVacuousWith config a = do
Result ki tr uic is cs ts as uis ax asgn cstr tactics goals asserts _out <- runSymbolic (True, config) $ forAll_ a >>= output
case cstr of
[] -> return False -- no constraints, no need to check
_ -> do let is' = [(EX, i) | (_, i) <- is] -- map all quantifiers to "exists" for the constraint check
res' = Result ki tr uic is' cs ts as uis ax asgn cstr tactics goals asserts [trueSW]
result <- runProofOn (getConverter config) config True [] res' >>= \p -> callSolver True "Checking Vacuity.." [] mwrap p config Nothing NoCase
case result of
Unsatisfiable{} -> return True -- constraints are unsatisfiable!
Satisfiable{} -> return False -- constraints are satisfiable!
SatExtField{} -> error "SBV: isVacuous: Solver returned a model in the extension field!"
Unknown{} -> error "SBV: isVacuous: Solver returned unknown!"
ProofError _ ls -> error $ "SBV: isVacuous: error encountered:\n" ++ unlines ls
TimeOut _ -> error "SBV: isVacuous: time-out."
where mwrap [r] = r
mwrap xs = error $ "SBV.isVacuousWith: Backend solver returned a non-singleton answer:\n" ++ show (map SatResult xs)
-- | Find all satisfying assignments using the given SMT-solver
allSatWith :: Provable a => SMTConfig -> a -> IO AllSatResult
allSatWith config p = do
msg "Checking Satisfiability, all solutions.."
sbvPgm@SMTProblem{smtInputs=qinps, kindsUsed=ki} <- simulate (getConverter config) config True [] p
let usorts = [s | us@(KUserSort s _) <- Set.toList ki, isFree us]
where isFree (KUserSort _ (Left _)) = True
isFree _ = False
unless (null usorts) $ msg $ "SBV.allSat: Uninterpreted sorts present: " ++ unwords usorts
++ "\n SBV will use equivalence classes to generate all-satisfying instances."
results <- unsafeInterleaveIO $ go sbvPgm (1::Int) []
-- See if there are any existentials below any universals
-- If such is the case, then the solutions are unique upto prefix existentials
let w = ALL `elem` map fst qinps
return $ AllSatResult (w, results)
where msg = when (verbose config) . putStrLn . ("** " ++)
go sbvPgm = loop
where hasPar = any isParallelCaseAnywhere (tactics sbvPgm)
loop !n nonEqConsts = do
curResult <- invoke nonEqConsts hasPar n sbvPgm
case curResult of
Nothing -> return []
Just (SatResult r) -> let cont model = do let modelOnlyAssocs = [v | v@(x, _) <- modelAssocs model, not (isNonModelVar config x)]
rest <- unsafeInterleaveIO $ loop (n+1) (modelOnlyAssocs : nonEqConsts)
return (r : rest)
in case r of
-- We are done! This is really how we should always stop.
Unsatisfiable{} -> return []
-- We have a model. If there are bindings, continue; otherwise stop
Satisfiable _ (SMTModel _ []) -> return [r]
Satisfiable _ model -> cont model
-- Satisfied in an extension field. Stop if no new bindings, otherwise continue if all regular.
-- If the model is in the extension, we also stop
SatExtField _ (SMTModel _ []) -> return [r]
SatExtField _ model@(SMTModel [] _) -> cont model
SatExtField{} -> return []
-- Something bad happened, we stop here. Note that we treat Unknown as bad too in this context.
Unknown{} -> return [r]
ProofError{} -> return [r]
TimeOut{} -> return [r]
invoke nonEqConsts hasPar n simRes@SMTProblem{smtInputs, tactics, objectives} = do
objectiveCheck False objectives "allSat"
msg $ "Looking for solution " ++ show n
case addNonEqConstraints (smtLibVersion config) (roundingMode config) smtInputs nonEqConsts of
Nothing -> -- no new constraints refuted models, stop
return Nothing
Just refutedModels -> do
let wrap = SatResult
unwrap (SatResult r) = r
mwrap [r] = wrap r
mwrap xs = error $ "SBV.allSatWith: Backend solver returned a non-singleton answer:\n" ++ show (map SatResult xs)
res <- bufferSanity hasPar $ applyTactics (updateName (n-1) config) (True, hasPar) (wrap, unwrap) [] tactics objectives
$ callSolver True "Checking Satisfiability.." refutedModels mwrap simRes
return $ Just res
updateName i cfg = cfg{smtFile = upd `fmap` smtFile cfg}
where upd nm = let (b, e) = splitExtension nm in b ++ "_allSat_" ++ show i ++ e
callSolver :: Bool -> String -> [String] -> ([SMTResult] -> b) -> SMTProblem -> SMTConfig -> Maybe (OptimizeStyle, Int) -> CaseCond -> IO b
callSolver isSat checkMsg refutedModels wrap SMTProblem{smtInputs, smtSkolemMap, smtLibPgm} config mbOptInfo caseCond = do
let msg = when (verbose config) . putStrLn . ("** " ++)
finalPgm = intercalate "\n" (pgm ++ refutedModels) where SMTLibPgm _ pgm = smtLibPgm config caseCond
msg checkMsg
msg $ "Generated SMTLib program:\n" ++ (finalPgm ++ intercalate "\n" ("" : optimizeArgs config ++ [satCmd config]))
smtAnswer <- engine (solver config) config isSat mbOptInfo smtInputs smtSkolemMap finalPgm
msg "Done.."
return $ wrap smtAnswer
simulate :: Provable a => SMTLibConverter -> SMTConfig -> Bool -> [String] -> a -> IO SMTProblem
simulate converter config isSat comments predicate = do
let msg = when (verbose config) . putStrLn . ("** " ++)
isTiming = timing config
msg "Starting symbolic simulation.."
res <- timeIf isTiming ProblemConstruction $ runSymbolic (isSat, config) $ (if isSat then forSome_ else forAll_) predicate >>= output
msg $ "Generated symbolic trace:\n" ++ show res
msg "Translating to SMT-Lib.."
runProofOn converter config isSat comments res
runProofOn :: SMTLibConverter -> SMTConfig -> Bool -> [String] -> Result -> IO SMTProblem
runProofOn converter config isSat comments res =
let isTiming = timing config
in case res of
Result ki _qcInfo _codeSegs is consts tbls arrs uis axs pgm cstrs tacs goals assertions [o@(SW KBool _)] ->
timeIf isTiming Translation
$ let skolemMap = skolemize (if isSat then is else map flipQ is)
where flipQ (ALL, x) = (EX, x)
flipQ (EX, x) = (ALL, x)
skolemize :: [(Quantifier, NamedSymVar)] -> [Either SW (SW, [SW])]
skolemize qinps = go qinps ([], [])
where go [] (_, sofar) = reverse sofar
go ((ALL, (v, _)):rest) (us, sofar) = go rest (v:us, Left v : sofar)
go ((EX, (v, _)):rest) (us, sofar) = go rest (us, Right (v, reverse us) : sofar)
smtScript = converter ki isSat comments is skolemMap consts tbls arrs uis axs pgm cstrs o
result = SMTProblem {smtInputs=is, smtSkolemMap=skolemMap, kindsUsed=ki, smtAsserts=assertions, tactics=tacs, objectives=goals, smtLibPgm=smtScript}
in rnf smtScript `seq` return result
Result{resOutputs = os} -> case length os of
0 -> error $ "Impossible happened, unexpected non-outputting result\n" ++ show res
1 -> error $ "Impossible happened, non-boolean output in " ++ show os
++ "\nDetected while generating the trace:\n" ++ show res
_ -> error $ "User error: Multiple output values detected: " ++ show os
++ "\nDetected while generating the trace:\n" ++ show res
++ "\n*** Check calls to \"output\", they are typically not needed!"
-- | Run an external proof on the given condition to see if it is satisfiable.
internalSATCheck :: SMTConfig -> SBool -> State -> String -> IO SatResult
internalSATCheck cfg condInPath st msg = do
sw <- sbvToSW st condInPath
() <- forceSWArg sw
Result ki tr uic is cs ts as uis ax asgn cstr tactics goals assertions _ <- extractSymbolicSimulationState st
let -- Construct the corresponding sat-checker for the branch. Note that we need to
-- forget about the quantifiers and just use an "exist", as we're looking for a
-- point-satisfiability check here; whatever the original program was.
pgm = Result ki tr uic [(EX, n) | (_, n) <- is] cs ts as uis ax asgn cstr tactics goals assertions [sw]
mwrap [r] = SatResult r
mwrap xs = error $ "SBV.internalSATCheck: Backend solver returned a non-singleton answer:\n" ++ show (map SatResult xs)
runProofOn (getConverter cfg) cfg True [] pgm >>= \p -> callSolver True msg [] mwrap p cfg Nothing NoCase
{-# ANN module ("HLint: ignore Reduce duplication" :: String) #-}