----------------------------------------------------------------------------- -- | -- Module : Data.SBV.Core.Symbolic -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- -- Symbolic values ----------------------------------------------------------------------------- {-# LANGUAGE CPP #-} {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE DeriveFunctor #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE NamedFieldPuns #-} {-# LANGUAGE PatternGuards #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TupleSections #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE TypeSynonymInstances #-} {-# OPTIONS_GHC -fno-warn-orphans #-} module Data.SBV.Core.Symbolic ( NodeId(..) , SW(..), swKind, trueSW, falseSW , Op(..), PBOp(..), FPOp(..) , Quantifier(..), needsExistentials , RoundingMode(..) , SBVType(..), newUninterpreted, addAxiom , SVal(..) , svMkSymVar , ArrayContext(..), ArrayInfo , svToSW, svToSymSW, forceSWArg , SBVExpr(..), newExpr, isCodeGenMode , Cached, cache, uncache , ArrayIndex, uncacheAI , NamedSymVar , getSValPathCondition, extendSValPathCondition , getTableIndex , SBVPgm(..), Symbolic, runSymbolic, State(..), withNewIncState, IncState(..), incrementInternalCounter , inSMTMode, SBVRunMode(..), IStage(..), Result(..) , registerKind, registerLabel , addAssertion, addNewSMTOption, imposeConstraint, internalConstraint, internalVariable , SMTLibPgm(..), SMTLibVersion(..), smtLibVersionExtension , SolverCapabilities(..) , extractSymbolicSimulationState , OptimizeStyle(..), Objective(..), Penalty(..), objectiveName, addSValOptGoal , Query(..), QueryState(..) , SMTScript(..), Solver(..), SMTSolver(..), SMTResult(..), SMTModel(..), SMTConfig(..), SMTEngine , outputSVal , SArr(..), readSArr, writeSArr, mergeSArr, newSArr, eqSArr ) where import Control.Arrow (first, second, (***)) import Control.DeepSeq (NFData(..)) import Control.Monad (when, unless) import Control.Monad.Reader (MonadReader, ReaderT, ask, runReaderT) import Control.Monad.State.Lazy (MonadState, StateT(..)) import Control.Monad.Trans (MonadIO, liftIO) import Data.Char (isAlpha, isAlphaNum, toLower) import Data.IORef (IORef, newIORef, readIORef) import Data.List (intercalate, sortBy) import Data.Maybe (isJust, fromJust, fromMaybe) import Data.Time (getCurrentTime, UTCTime) import GHC.Stack import qualified Data.IORef as R (modifyIORef') import qualified Data.Generics as G (Data(..)) import qualified Data.IntMap as IMap (IntMap, empty, size, toAscList, lookup, insert, insertWith) import qualified Data.Map as Map (Map, empty, toList, size, insert, lookup) import qualified Data.Set as Set (Set, empty, toList, insert, member) import qualified Data.Foldable as F (toList) import qualified Data.Sequence as S (Seq, empty, (|>)) import System.Mem.StableName import Data.SBV.Core.Kind import Data.SBV.Core.Concrete import Data.SBV.SMT.SMTLibNames import Data.SBV.Utils.TDiff(Timing) import Data.SBV.Control.Types -- | A symbolic node id newtype NodeId = NodeId Int deriving (Eq, Ord) -- | A symbolic word, tracking it's signedness and size. data SW = SW !Kind !NodeId deriving (Eq, Ord) instance HasKind SW where kindOf (SW k _) = k instance Show SW where show (SW _ (NodeId n)) | n < 0 = "s_" ++ show (abs n) | True = 's' : show n -- | Kind of a symbolic word. swKind :: SW -> Kind swKind (SW k _) = k -- | Forcing an argument; this is a necessary evil to make sure all the arguments -- to an uninterpreted function are evaluated before called; the semantics of uinterpreted -- functions is necessarily strict; deviating from Haskell's forceSWArg :: SW -> IO () forceSWArg (SW k n) = k `seq` n `seq` return () -- | Constant False as an SW. Note that this value always occupies slot -2. falseSW :: SW falseSW = SW KBool $ NodeId (-2) -- | Constant True as an SW. Note that this value always occupies slot -1. trueSW :: SW trueSW = SW KBool $ NodeId (-1) -- | Symbolic operations data Op = Plus | Times | Minus | UNeg | Abs | Quot | Rem | Equal | NotEqual | LessThan | GreaterThan | LessEq | GreaterEq | Ite | And | Or | XOr | Not | Shl | Shr | Rol Int | Ror Int | Extract Int Int -- Extract i j: extract bits i to j. Least significant bit is 0 (big-endian) | Join -- Concat two words to form a bigger one, in the order given | LkUp (Int, Kind, Kind, Int) !SW !SW -- (table-index, arg-type, res-type, length of the table) index out-of-bounds-value | ArrEq Int Int -- Array equality | ArrRead Int | KindCast Kind Kind | Uninterpreted String | Label String -- Essentially no-op; useful for code generation to emit comments. | IEEEFP FPOp -- Floating-point ops, categorized separately | PseudoBoolean PBOp -- Pseudo-boolean ops, categorized separately deriving (Eq, Ord) -- | Floating point operations data FPOp = FP_Cast Kind Kind SW -- From-Kind, To-Kind, RoundingMode. This is "value" conversion | FP_Reinterpret Kind Kind -- From-Kind, To-Kind. This is bit-reinterpretation using IEEE-754 interchange format | FP_Abs | FP_Neg | FP_Add | FP_Sub | FP_Mul | FP_Div | FP_FMA | FP_Sqrt | FP_Rem | FP_RoundToIntegral | FP_Min | FP_Max | FP_ObjEqual | FP_IsNormal | FP_IsSubnormal | FP_IsZero | FP_IsInfinite | FP_IsNaN | FP_IsNegative | FP_IsPositive deriving (Eq, Ord) -- Note that the show instance maps to the SMTLib names. We need to make sure -- this mapping stays correct through SMTLib changes. The only exception -- is FP_Cast; where we handle different source/origins explicitly later on. instance Show FPOp where show (FP_Cast f t r) = "(FP_Cast: " ++ show f ++ " -> " ++ show t ++ ", using RM [" ++ show r ++ "])" show (FP_Reinterpret f t) = case (f, t) of (KBounded False 32, KFloat) -> "(_ to_fp 8 24)" (KBounded False 64, KDouble) -> "(_ to_fp 11 53)" _ -> error $ "SBV.FP_Reinterpret: Unexpected conversion: " ++ show f ++ " to " ++ show t show FP_Abs = "fp.abs" show FP_Neg = "fp.neg" show FP_Add = "fp.add" show FP_Sub = "fp.sub" show FP_Mul = "fp.mul" show FP_Div = "fp.div" show FP_FMA = "fp.fma" show FP_Sqrt = "fp.sqrt" show FP_Rem = "fp.rem" show FP_RoundToIntegral = "fp.roundToIntegral" show FP_Min = "fp.min" show FP_Max = "fp.max" show FP_ObjEqual = "=" show FP_IsNormal = "fp.isNormal" show FP_IsSubnormal = "fp.isSubnormal" show FP_IsZero = "fp.isZero" show FP_IsInfinite = "fp.isInfinite" show FP_IsNaN = "fp.isNaN" show FP_IsNegative = "fp.isNegative" show FP_IsPositive = "fp.isPositive" -- | Pseudo-boolean operations data PBOp = PB_AtMost Int -- ^ At most k | PB_AtLeast Int -- ^ At least k | PB_Exactly Int -- ^ Exactly k | PB_Le [Int] Int -- ^ At most k, with coefficients given. Generalizes PB_AtMost | PB_Ge [Int] Int -- ^ At least k, with coefficients given. Generalizes PB_AtLeast | PB_Eq [Int] Int -- ^ Exactly k, with coefficients given. Generalized PB_Exactly deriving (Eq, Ord, Show) -- Show instance for 'Op'. Note that this is largely for debugging purposes, not used -- for being read by any tool. instance Show Op where show Shl = "<<" show Shr = ">>" show (Rol i) = "<<<" ++ show i show (Ror i) = ">>>" ++ show i show (Extract i j) = "choose [" ++ show i ++ ":" ++ show j ++ "]" show (LkUp (ti, at, rt, l) i e) = "lookup(" ++ tinfo ++ ", " ++ show i ++ ", " ++ show e ++ ")" where tinfo = "table" ++ show ti ++ "(" ++ show at ++ " -> " ++ show rt ++ ", " ++ show l ++ ")" show (ArrEq i j) = "array_" ++ show i ++ " == array_" ++ show j show (ArrRead i) = "select array_" ++ show i show (KindCast fr to) = "cast_" ++ show fr ++ "_" ++ show to show (Uninterpreted i) = "[uninterpreted] " ++ i show (Label s) = "[label] " ++ s show (IEEEFP w) = show w show (PseudoBoolean p) = show p show op | Just s <- op `lookup` syms = s | True = error "impossible happened; can't find op!" where syms = [ (Plus, "+"), (Times, "*"), (Minus, "-"), (UNeg, "-"), (Abs, "abs") , (Quot, "quot") , (Rem, "rem") , (Equal, "=="), (NotEqual, "/=") , (LessThan, "<"), (GreaterThan, ">"), (LessEq, "<="), (GreaterEq, ">=") , (Ite, "if_then_else") , (And, "&"), (Or, "|"), (XOr, "^"), (Not, "~") , (Join, "#") ] -- | Quantifiers: forall or exists. Note that we allow -- arbitrary nestings. data Quantifier = ALL | EX deriving Eq -- | Are there any existential quantifiers? needsExistentials :: [Quantifier] -> Bool needsExistentials = (EX `elem`) -- | A simple type for SBV computations, used mainly for uninterpreted constants. -- We keep track of the signedness/size of the arguments. A non-function will -- have just one entry in the list. newtype SBVType = SBVType [Kind] deriving (Eq, Ord) instance Show SBVType where show (SBVType []) = error "SBV: internal error, empty SBVType" show (SBVType xs) = intercalate " -> " $ map show xs -- | A symbolic expression data SBVExpr = SBVApp !Op ![SW] deriving (Eq, Ord) -- | To improve hash-consing, take advantage of commutative operators by -- reordering their arguments. reorder :: SBVExpr -> SBVExpr reorder s = case s of SBVApp op [a, b] | isCommutative op && a > b -> SBVApp op [b, a] _ -> s where isCommutative :: Op -> Bool isCommutative o = o `elem` [Plus, Times, Equal, NotEqual, And, Or, XOr] -- Show instance for 'SBVExpr'. Again, only for debugging purposes. instance Show SBVExpr where show (SBVApp Ite [t, a, b]) = unwords ["if", show t, "then", show a, "else", show b] show (SBVApp Shl [a, i]) = unwords [show a, "<<", show i] show (SBVApp Shr [a, i]) = unwords [show a, ">>", show i] show (SBVApp (Rol i) [a]) = unwords [show a, "<<<", show i] show (SBVApp (Ror i) [a]) = unwords [show a, ">>>", show i] show (SBVApp (PseudoBoolean pb) args) = unwords (show pb : map show args) show (SBVApp op [a, b]) = unwords [show a, show op, show b] show (SBVApp op args) = unwords (show op : map show args) -- | A program is a sequence of assignments newtype SBVPgm = SBVPgm {pgmAssignments :: S.Seq (SW, SBVExpr)} -- | 'NamedSymVar' pairs symbolic words and user given/automatically generated names type NamedSymVar = (SW, String) -- | Style of optimization. Note that in the pareto case the user is allowed -- to specify a max number of fronts to query the solver for, since there might -- potentially be an infinite number of them and there is no way to know exactly -- how many ahead of time. If 'Nothing' is given, SBV will possibly loop forever -- if the number is really infinite. data OptimizeStyle = Lexicographic -- ^ Objectives are optimized in the order given, earlier objectives have higher priority. This is the default. | Independent -- ^ Each objective is optimized independently. | Pareto (Maybe Int) -- ^ Objectives are optimized according to pareto front: That is, no objective can be made better without making some other worse. deriving (Eq, Show) -- | Penalty for a soft-assertion. The default penalty is @1@, with all soft-assertions belonging -- to the same objective goal. A positive weight and an optional group can be provided by using -- the 'Penalty' constructor. data Penalty = DefaultPenalty -- ^ Default: Penalty of @1@ and no group attached | Penalty Rational (Maybe String) -- ^ Penalty with a weight and an optional group deriving Show -- | Objective of optimization. We can minimize, maximize, or give a soft assertion with a penalty -- for not satisfying it. data Objective a = Minimize String a -- ^ Minimize this metric | Maximize String a -- ^ Maximize this metric | AssertSoft String a Penalty -- ^ A soft assertion, with an associated penalty deriving (Show, Functor) -- | The name of the objective objectiveName :: Objective a -> String objectiveName (Minimize s _) = s objectiveName (Maximize s _) = s objectiveName (AssertSoft s _ _) = s -- | The state we keep track of as we interact with the solver data QueryState = QueryState { queryAsk :: Maybe Int -> String -> IO String , querySend :: Maybe Int -> String -> IO () , queryRetrieveResponse :: Maybe Int -> IO String , queryConfig :: SMTConfig , queryTerminate :: IO () , queryTimeOutValue :: Maybe Int , queryAssertionStackDepth :: Int } -- | A query is a user-guided mechanism to directly communicate and extract results from the solver. newtype Query a = Query (StateT State IO a) deriving (Applicative, Functor, Monad, MonadIO, MonadState State) instance NFData OptimizeStyle where rnf x = x `seq` () instance NFData Penalty where rnf DefaultPenalty = () rnf (Penalty p mbs) = rnf p `seq` rnf mbs `seq` () instance NFData a => NFData (Objective a) where rnf (Minimize s a) = rnf s `seq` rnf a `seq` () rnf (Maximize s a) = rnf s `seq` rnf a `seq` () rnf (AssertSoft s a p) = rnf s `seq` rnf a `seq` rnf p `seq` () -- | Result of running a symbolic computation data Result = Result { reskinds :: Set.Set Kind -- ^ kinds used in the program , resTraces :: [(String, CW)] -- ^ quick-check counter-example information (if any) , resUISegs :: [(String, [String])] -- ^ uninterpeted code segments , resInputs :: ([(Quantifier, NamedSymVar)], [NamedSymVar]) -- ^ inputs (possibly existential) + tracker vars , resConsts :: [(SW, CW)] -- ^ constants , resTables :: [((Int, Kind, Kind), [SW])] -- ^ tables (automatically constructed) (tableno, index-type, result-type) elts , resArrays :: [(Int, ArrayInfo)] -- ^ arrays (user specified) , resUIConsts :: [(String, SBVType)] -- ^ uninterpreted constants , resAxioms :: [(String, [String])] -- ^ axioms , resAsgns :: SBVPgm -- ^ assignments , resConstraints :: [(Maybe String, SW)] -- ^ additional constraints (boolean) , resAssertions :: [(String, Maybe CallStack, SW)] -- ^ assertions , resOutputs :: [SW] -- ^ outputs } -- Show instance for 'Result'. Only for debugging purposes. instance Show Result where -- If there's nothing interesting going on, just print the constant. Note that the -- definiton of interesting here is rather subjective; but essentially if we reduced -- the result to a single constant already, without any reference to anything. show Result{resConsts=cs, resOutputs=[r]} | Just c <- r `lookup` cs = show c show (Result kinds _ cgs is cs ts as uis axs xs cstrs asserts os) = intercalate "\n" $ (if null usorts then [] else "SORTS" : map (" " ++) usorts) ++ ["INPUTS"] ++ map shn (fst is) ++ (if null (snd is) then [] else "TRACKER VARS" : map (shn . (EX,)) (snd is)) ++ ["CONSTANTS"] ++ map shc cs ++ ["TABLES"] ++ map sht ts ++ ["ARRAYS"] ++ map sha as ++ ["UNINTERPRETED CONSTANTS"] ++ map shui uis ++ ["USER GIVEN CODE SEGMENTS"] ++ concatMap shcg cgs ++ ["AXIOMS"] ++ map shax axs ++ ["DEFINE"] ++ map (\(s, e) -> " " ++ shs s ++ " = " ++ show e) (F.toList (pgmAssignments xs)) ++ ["CONSTRAINTS"] ++ map ((" " ++) . shCstr) cstrs ++ ["ASSERTIONS"] ++ map ((" "++) . shAssert) asserts ++ ["OUTPUTS"] ++ sh2 os where sh2 :: Show a => [a] -> [String] sh2 = map ((" "++) . show) usorts = [sh s t | KUserSort s t <- Set.toList kinds] where sh s (Left _) = s sh s (Right es) = s ++ " (" ++ intercalate ", " es ++ ")" shs sw = show sw ++ " :: " ++ show (swKind sw) sht ((i, at, rt), es) = " Table " ++ show i ++ " : " ++ show at ++ "->" ++ show rt ++ " = " ++ show es shc (sw, cw) = " " ++ show sw ++ " = " ++ show cw shcg (s, ss) = ("Variable: " ++ s) : map (" " ++) ss shn (q, (sw, nm)) = " " ++ ni ++ " :: " ++ show (swKind sw) ++ ex ++ alias where ni = show sw ex | q == ALL = "" | True = ", existential" alias | ni == nm = "" | True = ", aliasing " ++ show nm sha (i, (nm, (ai, bi), ctx)) = " " ++ ni ++ " :: " ++ show ai ++ " -> " ++ show bi ++ alias ++ "\n Context: " ++ show ctx where ni = "array_" ++ show i alias | ni == nm = "" | True = ", aliasing " ++ show nm shui (nm, t) = " [uninterpreted] " ++ nm ++ " :: " ++ show t shax (nm, ss) = " -- user defined axiom: " ++ nm ++ "\n " ++ intercalate "\n " ss shCstr (Nothing, c) = show c shCstr (Just nm, c) = nm ++ ": " ++ show c shAssert (nm, stk, p) = " -- assertion: " ++ nm ++ " " ++ maybe "[No location]" #if MIN_VERSION_base(4,9,0) prettyCallStack #else showCallStack #endif stk ++ ": " ++ show p -- | The context of a symbolic array as created data ArrayContext = ArrayFree -- ^ A new array, the contents are uninitialized | ArrayMutate Int SW SW -- ^ An array created by mutating another array at a given cell | ArrayMerge SW Int Int -- ^ An array created by symbolically merging two other arrays instance Show ArrayContext where show ArrayFree = " initialized with random elements" show (ArrayMutate i a b) = " cloned from array_" ++ show i ++ " with " ++ show a ++ " :: " ++ show (swKind a) ++ " |-> " ++ show b ++ " :: " ++ show (swKind b) show (ArrayMerge s i j) = " merged arrays " ++ show i ++ " and " ++ show j ++ " on condition " ++ show s -- | Expression map, used for hash-consing type ExprMap = Map.Map SBVExpr SW -- | Constants are stored in a map, for hash-consing. The bool is needed to tell -0 from +0, sigh type CnstMap = Map.Map (Bool, CW) SW -- | Kinds used in the program; used for determining the final SMT-Lib logic to pick type KindSet = Set.Set Kind -- | Tables generated during a symbolic run type TableMap = Map.Map (Kind, Kind, [SW]) Int -- | Representation for symbolic arrays type ArrayInfo = (String, (Kind, Kind), ArrayContext) -- | Arrays generated during a symbolic run type ArrayMap = IMap.IntMap ArrayInfo -- | Uninterpreted-constants generated during a symbolic run type UIMap = Map.Map String SBVType -- | Code-segments for Uninterpreted-constants, as given by the user type CgMap = Map.Map String [String] -- | Cached values, implementing sharing type Cache a = IMap.IntMap [(StableName (State -> IO a), a)] -- | Stage of an interactive run data IStage = ISetup -- Before we initiate contact | IRun -- After the contact is started -- | Different means of running a symbolic piece of code data SBVRunMode = SMTMode IStage Bool SMTConfig -- ^ In regular mode, with a stage. Bool is True if this is SAT. | CodeGen -- ^ Code generation mode. | Concrete -- ^ Concrete simulation mode. -- Show instance for SBVRunMode; debugging purposes only instance Show SBVRunMode where show (SMTMode ISetup True _) = "Satisfiability setup" show (SMTMode IRun True _) = "Satisfiability" show (SMTMode ISetup False _) = "Proof setup" show (SMTMode IRun False _) = "Proof" show CodeGen = "Code generation" show Concrete = "Concrete evaluation" -- | Is this a CodeGen run? (i.e., generating code) isCodeGenMode :: State -> IO Bool isCodeGenMode State{runMode} = do rm <- readIORef runMode return $ case rm of Concrete{} -> False SMTMode{} -> False CodeGen -> True -- | The state in query mode, i.e., additional context data IncState = IncState { rNewInps :: IORef [NamedSymVar] -- always existential! , rNewKinds :: IORef KindSet , rNewConsts :: IORef CnstMap , rNewArrs :: IORef ArrayMap , rNewTbls :: IORef TableMap , rNewAsgns :: IORef SBVPgm } -- | Get a new IncState newIncState :: IO IncState newIncState = do is <- newIORef [] ks <- newIORef Set.empty nc <- newIORef Map.empty am <- newIORef IMap.empty tm <- newIORef Map.empty pgm <- newIORef (SBVPgm S.empty) return IncState { rNewInps = is , rNewKinds = ks , rNewConsts = nc , rNewArrs = am , rNewTbls = tm , rNewAsgns = pgm } -- | Get a new IncState withNewIncState :: State -> (State -> IO a) -> IO (IncState, a) withNewIncState st cont = do is <- newIncState R.modifyIORef' (rIncState st) (const is) r <- cont st finalIncState <- readIORef (rIncState st) return (finalIncState, r) -- | Return and clean and incState -- | The state of the symbolic interpreter data State = State { pathCond :: SVal -- ^ kind KBool , startTime :: UTCTime , runMode :: IORef SBVRunMode , rIncState :: IORef IncState , rCInfo :: IORef [(String, CW)] , rctr :: IORef Int , rUsedKinds :: IORef KindSet , rUsedLbls :: IORef (Set.Set String) , rinps :: IORef ([(Quantifier, NamedSymVar)], [NamedSymVar]) -- User defined, and internal existential , rConstraints :: IORef [(Maybe String, SW)] , routs :: IORef [SW] , rtblMap :: IORef TableMap , spgm :: IORef SBVPgm , rconstMap :: IORef CnstMap , rexprMap :: IORef ExprMap , rArrayMap :: IORef ArrayMap , rUIMap :: IORef UIMap , rCgMap :: IORef CgMap , raxioms :: IORef [(String, [String])] , rSMTOptions :: IORef [SMTOption] , rOptGoals :: IORef [Objective (SW, SW)] , rAsserts :: IORef [(String, Maybe CallStack, SW)] , rSWCache :: IORef (Cache SW) , rAICache :: IORef (Cache Int) , queryState :: IORef (Maybe QueryState) } -- NFData is a bit of a lie, but it's sufficient, most of the content is iorefs that we don't want to touch instance NFData State where rnf State{} = () -- | Get the current path condition getSValPathCondition :: State -> SVal getSValPathCondition = pathCond -- | Extend the path condition with the given test value. extendSValPathCondition :: State -> (SVal -> SVal) -> State extendSValPathCondition st f = st{pathCond = f (pathCond st)} -- | Are we running in proof mode? inSMTMode :: State -> IO Bool inSMTMode State{runMode} = do rm <- readIORef runMode return $ case rm of CodeGen -> False Concrete{} -> False SMTMode{} -> True -- | The "Symbolic" value. Either a constant (@Left@) or a symbolic -- value (@Right Cached@). Note that caching is essential for making -- sure sharing is preserved. data SVal = SVal !Kind !(Either CW (Cached SW)) instance HasKind SVal where kindOf (SVal k _) = k -- Show instance for 'SVal'. Not particularly "desirable", but will do if needed -- NB. We do not show the type info on constant KBool values, since there's no -- implicit "fromBoolean" applied to Booleans in Haskell; and thus a statement -- of the form "True :: SBool" is just meaningless. (There should be a fromBoolean!) instance Show SVal where show (SVal KBool (Left c)) = showCW False c show (SVal k (Left c)) = showCW False c ++ " :: " ++ show k show (SVal k (Right _)) = " :: " ++ show k -- | Equality constraint on SBV values. Not desirable since we can't really compare two -- symbolic values, but will do. instance Eq SVal where SVal _ (Left a) == SVal _ (Left b) = a == b a == b = error $ "Comparing symbolic bit-vectors; Use (.==) instead. Received: " ++ show (a, b) SVal _ (Left a) /= SVal _ (Left b) = a /= b a /= b = error $ "Comparing symbolic bit-vectors; Use (./=) instead. Received: " ++ show (a, b) -- | Things we do not support in interactive mode, at least for now! noInteractive :: [String] -> a noInteractive ss = error $ unlines $ "" : "*** Data.SBV: Unsupported interactive/query mode feature." : map ("*** " ++) ss ++ ["*** Data.SBV: Please report this as a feature request!"] -- | Modification of the state, but carefully handling the interactive tasks. -- Note that the state is always updated regardless of the mode, but we get -- to also perform extra operation in interactive mode. (Typically error out, but also simply -- ignore if it has no impact.) modifyState :: State -> (State -> IORef a) -> (a -> a) -> IO () -> IO () modifyState st@State{runMode} field update interactiveUpdate = do R.modifyIORef' (field st) update rm <- readIORef runMode case rm of SMTMode IRun _ _ -> interactiveUpdate _ -> return () -- | Modify the incremental state modifyIncState :: State -> (IncState -> IORef a) -> (a -> a) -> IO () modifyIncState State{rIncState} field update = do incState <- readIORef rIncState R.modifyIORef' (field incState) update -- | Increment the variable counter incrementInternalCounter :: State -> IO Int incrementInternalCounter st = do ctr <- readIORef (rctr st) modifyState st rctr (+1) (return ()) return ctr -- | Create a new uninterpreted symbol, possibly with user given code newUninterpreted :: State -> String -> SBVType -> Maybe [String] -> IO () newUninterpreted st nm t mbCode | null nm || not enclosed && (not (isAlpha (head nm)) || not (all validChar (tail nm))) = error $ "Bad uninterpreted constant name: " ++ show nm ++ ". Must be a valid identifier." | True = do uiMap <- readIORef (rUIMap st) case nm `Map.lookup` uiMap of Just t' -> when (t /= t') $ error $ "Uninterpreted constant " ++ show nm ++ " used at incompatible types\n" ++ " Current type : " ++ show t ++ "\n" ++ " Previously used at: " ++ show t' Nothing -> do modifyState st rUIMap (Map.insert nm t) $ noInteractive [ "Uninterpreted function introduction:" , " Named: " ++ nm , " Type : " ++ show t ] when (isJust mbCode) $ modifyState st rCgMap (Map.insert nm (fromJust mbCode)) (return ()) where validChar x = isAlphaNum x || x `elem` "_" enclosed = head nm == '|' && last nm == '|' && length nm > 2 && not (any (`elem` "|\\") (tail (init nm))) -- | Add a new sAssert based constraint addAssertion :: State -> Maybe CallStack -> String -> SW -> IO () addAssertion st cs msg cond = modifyState st rAsserts ((msg, cs, cond):) $ noInteractive [ "Named assertions (sAssert):" , " Tag: " ++ msg , " Loc: " ++ maybe "Unknown" show cs ] -- | Create an internal variable, which acts as an input but isn't visible to the user. -- Such variables are existentially quantified in a SAT context, and universally quantified -- in a proof context. internalVariable :: State -> Kind -> IO SW internalVariable st k = do (sw, nm) <- newSW st k rm <- readIORef (runMode st) let q = case rm of SMTMode _ True _ -> EX SMTMode _ False _ -> ALL CodeGen -> ALL Concrete{} -> ALL modifyState st rinps (first ((:) (q, (sw, "__internal_sbv_" ++ nm)))) $ noInteractive [ "Internal variable creation:" , " Named: " ++ nm ] return sw {-# INLINE internalVariable #-} -- | Create a new SW newSW :: State -> Kind -> IO (SW, String) newSW st k = do ctr <- incrementInternalCounter st let sw = SW k (NodeId ctr) registerKind st k return (sw, 's' : show ctr) {-# INLINE newSW #-} -- | Register a new kind with the system, used for uninterpreted sorts. -- NB: Is it safe to have new kinds in query mode? It could be that -- the new kind might introduce a constraint that effects the logic. For -- instance, if we're seeing 'Double' for the first time and using a BV -- logic, then things would fall apart. But this should be rare, and hopefully -- the 'success' checking mechanism will catch the rare cases where this -- is an issue. In either case, the user can always arrange for the right -- logic by calling 'setLogic' appropriately, so it seems safe to just -- allow for this. registerKind :: State -> Kind -> IO () registerKind st k | KUserSort sortName _ <- k, map toLower sortName `elem` smtLibReservedNames = error $ "SBV: " ++ show sortName ++ " is a reserved sort; please use a different name." | True = do ks <- readIORef (rUsedKinds st) unless (k `Set.member` ks) $ modifyState st rUsedKinds (Set.insert k) $ modifyIncState st rNewKinds (Set.insert k) -- | Register a new label with the system, making sure they are unique and have no '|'s in them registerLabel :: State -> String -> IO () registerLabel st nm | map toLower nm `elem` smtLibReservedNames = error $ "SBV: " ++ show nm ++ " is a reserved string; please use a different name." | '|' `elem` nm = error $ "SBV: " ++ show nm ++ " contains the character `|', which is not allowed!" | '\\' `elem` nm = error $ "SBV: " ++ show nm ++ " contains the character `\', which is not allowed!" | True = do old <- readIORef $ rUsedLbls st if nm `Set.member` old then error $ "SBV: " ++ show nm ++ " is used as a label multiple times. Please do not use duplicate names!" else modifyState st rUsedLbls (Set.insert nm) (return ()) -- | Create a new constant; hash-cons as necessary -- NB. For each constant, we also store weather it's negative-0 or not, -- as otherwise +0 == -0 and thus we'd confuse those entries. That's a -- bummer as we incur an extra boolean for this rare case, but it's simple -- and hopefully we don't generate a ton of constants in general. newConst :: State -> CW -> IO SW newConst st c = do constMap <- readIORef (rconstMap st) let key = (isNeg0 (cwVal c), c) case key `Map.lookup` constMap of Just sw -> return sw Nothing -> do let k = kindOf c (sw, _) <- newSW st k let ins = Map.insert key sw modifyState st rconstMap ins $ modifyIncState st rNewConsts ins return sw where isNeg0 (CWFloat f) = isNegativeZero f isNeg0 (CWDouble d) = isNegativeZero d isNeg0 _ = False {-# INLINE newConst #-} -- | Create a new table; hash-cons as necessary getTableIndex :: State -> Kind -> Kind -> [SW] -> IO Int getTableIndex st at rt elts = do let key = (at, rt, elts) tblMap <- readIORef (rtblMap st) case key `Map.lookup` tblMap of Just i -> return i _ -> do let i = Map.size tblMap upd = Map.insert key i modifyState st rtblMap upd $ modifyIncState st rNewTbls upd return i -- | Create a new expression; hash-cons as necessary newExpr :: State -> Kind -> SBVExpr -> IO SW newExpr st k app = do let e = reorder app exprMap <- readIORef (rexprMap st) case e `Map.lookup` exprMap of Just sw -> return sw Nothing -> do (sw, _) <- newSW st k let append (SBVPgm xs) = SBVPgm (xs S.|> (sw, e)) modifyState st spgm append $ modifyIncState st rNewAsgns append modifyState st rexprMap (Map.insert e sw) (return ()) return sw {-# INLINE newExpr #-} -- | Convert a symbolic value to a symbolic-word svToSW :: State -> SVal -> IO SW svToSW st (SVal _ (Left c)) = newConst st c svToSW st (SVal _ (Right f)) = uncache f st -- | Convert a symbolic value to an SW, inside the Symbolic monad svToSymSW :: SVal -> Symbolic SW svToSymSW sbv = do st <- ask liftIO $ svToSW st sbv ------------------------------------------------------------------------- -- * Symbolic Computations ------------------------------------------------------------------------- -- | A Symbolic computation. Represented by a reader monad carrying the -- state of the computation, layered on top of IO for creating unique -- references to hold onto intermediate results. newtype Symbolic a = Symbolic (ReaderT State IO a) deriving (Applicative, Functor, Monad, MonadIO, MonadReader State) -- | Create a symbolic value, based on the quantifier we have. If an -- explicit quantifier is given, we just use that. If not, then we -- pick the quantifier appropriately based on the run-mode. -- @randomCW@ is used for generating random values for this variable -- when used for 'quickCheck' or 'genTest' purposes. svMkSymVar :: Maybe Quantifier -> Kind -> Maybe String -> State -> IO SVal svMkSymVar = svMkSymVarGen False -- | Create an existentially quantified tracker variable svMkTrackerVar :: Kind -> String -> State -> IO SVal svMkTrackerVar k nm = svMkSymVarGen True (Just EX) k (Just nm) -- | Create a symbolic value, based on the quantifier we have. If an -- explicit quantifier is given, we just use that. If not, then we -- pick the quantifier appropriately based on the run-mode. -- @randomCW@ is used for generating random values for this variable -- when used for 'quickCheck' or 'genTest' purposes. svMkSymVarGen :: Bool -> Maybe Quantifier -> Kind -> Maybe String -> State -> IO SVal svMkSymVarGen isTracker mbQ k mbNm st = do rm <- readIORef (runMode st) let varInfo = case mbNm of Nothing -> ", of type " ++ show k Just nm -> ", while defining " ++ nm ++ " :: " ++ show k disallow what = error $ "Data.SBV: Unsupported: " ++ what ++ varInfo ++ " in mode: " ++ show rm noUI cont | isUninterpreted k = disallow "Uninterpreted sorts" | True = cont mkS q = do (sw, internalName) <- newSW st k let nm = fromMaybe internalName mbNm introduceUserName st isTracker nm k q sw mkC = do cw <- randomCW k do registerKind st k modifyState st rCInfo ((fromMaybe "_" mbNm, cw):) (return ()) return $ SVal k (Left cw) case (mbQ, rm) of (Just q, SMTMode{} ) -> mkS q (Nothing, SMTMode _ isSAT _) -> mkS (if isSAT then EX else ALL) (Just EX, CodeGen{}) -> disallow "Existentially quantified variables" (_ , CodeGen) -> noUI $ mkS ALL -- code generation, pick universal (Just EX, Concrete{}) -> disallow "Existentially quantified variables" (_ , Concrete{}) -> noUI mkC -- | Introduce a new user name. We die if repeated. introduceUserName :: State -> Bool -> String -> Kind -> Quantifier -> SW -> IO SVal introduceUserName st isTracker nm k q sw = do (is, ints) <- readIORef (rinps st) if nm `elem` [n | (_, (_, n)) <- is] ++ [n | (_, n) <- ints] then error $ "SBV: Repeated user given name: " ++ show nm ++ ". Please use unique names." else if isTracker && q == ALL then error $ "SBV: Impossible happened! A universally quantified tracker variable is being introduced: " ++ show nm else do let newInp olds = case q of EX -> (sw, nm) : olds ALL -> noInteractive [ "Adding a new universally quantified variable: " , " Name : " ++ show nm , " Kind : " ++ show k , " Quantifier: Universal" , " Node : " ++ show sw , "Only existential variables are supported in query mode." ] if isTracker then modifyState st rinps (second ((:) (sw, nm))) $ noInteractive ["Adding a new tracker variable in interactive mode: " ++ show nm] else modifyState st rinps (first ((:) (q, (sw, nm)))) $ modifyIncState st rNewInps newInp return $ SVal k $ Right $ cache (const (return sw)) -- | Add a user specified axiom to the generated SMT-Lib file. The first argument is a mere -- string, use for commenting purposes. The second argument is intended to hold the multiple-lines -- of the axiom text as expressed in SMT-Lib notation. Note that we perform no checks on the axiom -- itself, to see whether it's actually well-formed or is sensical by any means. -- A separate formalization of SMT-Lib would be very useful here. addAxiom :: String -> [String] -> Symbolic () addAxiom nm ax = do st <- ask liftIO $ modifyState st raxioms ((nm, ax) :) $ noInteractive [ "Adding a new axiom:" , " Named: " ++ show nm , " Axiom: " ++ unlines ax ] -- | Run a symbolic computation, and return a extra value paired up with the 'Result' runSymbolic :: SBVRunMode -> Symbolic a -> IO (a, Result) runSymbolic currentRunMode (Symbolic c) = do currTime <- getCurrentTime rm <- newIORef currentRunMode ctr <- newIORef (-2) -- start from -2; False and True will always occupy the first two elements cInfo <- newIORef [] pgm <- newIORef (SBVPgm S.empty) emap <- newIORef Map.empty cmap <- newIORef Map.empty inps <- newIORef ([], []) outs <- newIORef [] tables <- newIORef Map.empty arrays <- newIORef IMap.empty uis <- newIORef Map.empty cgs <- newIORef Map.empty axioms <- newIORef [] swCache <- newIORef IMap.empty aiCache <- newIORef IMap.empty usedKinds <- newIORef Set.empty usedLbls <- newIORef Set.empty cstrs <- newIORef [] smtOpts <- newIORef [] optGoals <- newIORef [] asserts <- newIORef [] istate <- newIORef =<< newIncState qstate <- newIORef Nothing let st = State { runMode = rm , startTime = currTime , pathCond = SVal KBool (Left trueCW) , rIncState = istate , rCInfo = cInfo , rctr = ctr , rUsedKinds = usedKinds , rUsedLbls = usedLbls , rinps = inps , routs = outs , rtblMap = tables , spgm = pgm , rconstMap = cmap , rArrayMap = arrays , rexprMap = emap , rUIMap = uis , rCgMap = cgs , raxioms = axioms , rSWCache = swCache , rAICache = aiCache , rConstraints = cstrs , rSMTOptions = smtOpts , rOptGoals = optGoals , rAsserts = asserts , queryState = qstate } _ <- newConst st falseCW -- s(-2) == falseSW _ <- newConst st trueCW -- s(-1) == trueSW r <- runReaderT c st res <- extractSymbolicSimulationState st -- Clean-up after ourselves qs <- readIORef qstate case qs of Nothing -> return () Just QueryState{queryTerminate} -> queryTerminate return (r, res) -- | Grab the program from a running symbolic simulation state. extractSymbolicSimulationState :: State -> IO Result extractSymbolicSimulationState st@State{ spgm=pgm, rinps=inps, routs=outs, rtblMap=tables, rArrayMap=arrays, rUIMap=uis, raxioms=axioms , rAsserts=asserts, rUsedKinds=usedKinds, rCgMap=cgs, rCInfo=cInfo, rConstraints=cstrs } = do SBVPgm rpgm <- readIORef pgm inpsO <- (reverse *** reverse) <$> readIORef inps outsO <- reverse <$> readIORef outs let swap (a, b) = (b, a) swapc ((_, a), b) = (b, a) cmp (a, _) (b, _) = a `compare` b arrange (i, (at, rt, es)) = ((i, at, rt), es) cnsts <- (sortBy cmp . map swapc . Map.toList) <$> readIORef (rconstMap st) tbls <- (map arrange . sortBy cmp . map swap . Map.toList) <$> readIORef tables arrs <- IMap.toAscList <$> readIORef arrays unint <- Map.toList <$> readIORef uis axs <- reverse <$> readIORef axioms knds <- readIORef usedKinds cgMap <- Map.toList <$> readIORef cgs traceVals <- reverse <$> readIORef cInfo extraCstrs <- reverse <$> readIORef cstrs assertions <- reverse <$> readIORef asserts return $ Result knds traceVals cgMap inpsO cnsts tbls arrs unint axs (SBVPgm rpgm) extraCstrs assertions outsO -- | Add a new option addNewSMTOption :: SMTOption -> Symbolic () addNewSMTOption o = do st <- ask liftIO $ modifyState st rSMTOptions (o:) (return ()) -- | Handling constraints imposeConstraint :: Maybe String -> SVal -> Symbolic () imposeConstraint mbNm c = do st <- ask rm <- liftIO $ readIORef (runMode st) case rm of CodeGen -> error "SBV: constraints are not allowed in code-generation" _ -> do () <- case mbNm of Nothing -> return () Just nm -> liftIO $ registerLabel st nm liftIO $ internalConstraint st mbNm c -- | Require a boolean condition to be true in the state. Only used for internal purposes. internalConstraint :: State -> Maybe String -> SVal -> IO () internalConstraint st mbNm b = do v <- svToSW st b modifyState st rConstraints ((mbNm, v):) $ noInteractive [ "Adding an internal constraint:" , " Named: " ++ fromMaybe "" mbNm ] -- | Add an optimization goal addSValOptGoal :: Objective SVal -> Symbolic () addSValOptGoal obj = do st <- ask -- create the tracking variable here for the metric let mkGoal nm orig = liftIO $ do origSW <- svToSW st orig track <- svMkTrackerVar (kindOf orig) nm st trackSW <- svToSW st track return (origSW, trackSW) let walk (Minimize nm v) = Minimize nm <$> mkGoal nm v walk (Maximize nm v) = Maximize nm <$> mkGoal nm v walk (AssertSoft nm v mbP) = flip (AssertSoft nm) mbP <$> mkGoal nm v obj' <- walk obj liftIO $ modifyState st rOptGoals (obj' :) $ noInteractive [ "Adding an optimization objective:" , " Objective: " ++ show obj ] -- | Mark an interim result as an output. Useful when constructing Symbolic programs -- that return multiple values, or when the result is programmatically computed. outputSVal :: SVal -> Symbolic () outputSVal (SVal _ (Left c)) = do st <- ask sw <- liftIO $ newConst st c liftIO $ modifyState st routs (sw:) (return ()) outputSVal (SVal _ (Right f)) = do st <- ask sw <- liftIO $ uncache f st liftIO $ modifyState st routs (sw:) (return ()) --------------------------------------------------------------------------------- -- * Symbolic Arrays --------------------------------------------------------------------------------- -- | Arrays implemented in terms of SMT-arrays: -- -- * Maps directly to SMT-lib arrays -- -- * Reading from an unintialized value is OK and yields an unspecified result -- -- * Can check for equality of these arrays -- -- * Cannot quick-check theorems using @SArr@ values -- -- * Typically slower as it heavily relies on SMT-solving for the array theory -- data SArr = SArr (Kind, Kind) (Cached ArrayIndex) -- | Read the array element at @a@ readSArr :: SArr -> SVal -> SVal readSArr (SArr (_, bk) f) a = SVal bk $ Right $ cache r where r st = do arr <- uncacheAI f st i <- svToSW st a newExpr st bk (SBVApp (ArrRead arr) [i]) -- | Update the element at @a@ to be @b@ writeSArr :: SArr -> SVal -> SVal -> SArr writeSArr (SArr ainfo f) a b = SArr ainfo $ cache g where g st = do arr <- uncacheAI f st addr <- svToSW st a val <- svToSW st b amap <- readIORef (rArrayMap st) let j = IMap.size amap upd = IMap.insert j ("array_" ++ show j, ainfo, ArrayMutate arr addr val) j `seq` modifyState st rArrayMap upd $ modifyIncState st rNewArrs upd return j -- | Merge two given arrays on the symbolic condition -- Intuitively: @mergeArrays cond a b = if cond then a else b@. -- Merging pushes the if-then-else choice down on to elements mergeSArr :: SVal -> SArr -> SArr -> SArr mergeSArr t (SArr ainfo a) (SArr _ b) = SArr ainfo $ cache h where h st = do ai <- uncacheAI a st bi <- uncacheAI b st ts <- svToSW st t amap <- readIORef (rArrayMap st) let k = IMap.size amap upd = IMap.insert k ("array_" ++ show k, ainfo, ArrayMerge ts ai bi) k `seq` modifyState st rArrayMap upd $ modifyIncState st rNewArrs upd return k -- | Create a named new array, with an optional initial value newSArr :: (Kind, Kind) -> (Int -> String) -> Symbolic SArr newSArr ainfo mkNm = do st <- ask amap <- liftIO $ readIORef $ rArrayMap st let i = IMap.size amap nm = mkNm i upd = IMap.insert i (nm, ainfo, ArrayFree) liftIO $ modifyState st rArrayMap upd $ modifyIncState st rNewArrs upd return $ SArr ainfo $ cache $ const $ return i -- | Compare two arrays for equality eqSArr :: SArr -> SArr -> SVal eqSArr (SArr _ a) (SArr _ b) = SVal KBool $ Right $ cache c where c st = do ai <- uncacheAI a st bi <- uncacheAI b st newExpr st KBool (SBVApp (ArrEq ai bi) []) --------------------------------------------------------------------------------- -- * Cached values --------------------------------------------------------------------------------- -- | We implement a peculiar caching mechanism, applicable to the use case in -- implementation of SBV's. Whenever we do a state based computation, we do -- not want to keep on evaluating it in the then-current state. That will -- produce essentially a semantically equivalent value. Thus, we want to run -- it only once, and reuse that result, capturing the sharing at the Haskell -- level. This is similar to the "type-safe observable sharing" work, but also -- takes into the account of how symbolic simulation executes. -- -- See Andy Gill's type-safe obervable sharing trick for the inspiration behind -- this technique: -- -- Note that this is *not* a general memo utility! newtype Cached a = Cached (State -> IO a) -- | Cache a state-based computation cache :: (State -> IO a) -> Cached a cache = Cached -- | Uncache a previously cached computation uncache :: Cached SW -> State -> IO SW uncache = uncacheGen rSWCache -- | An array index is simple an int value type ArrayIndex = Int -- | Uncache, retrieving array indexes uncacheAI :: Cached ArrayIndex -> State -> IO ArrayIndex uncacheAI = uncacheGen rAICache -- | Generic uncaching. Note that this is entirely safe, since we do it in the IO monad. uncacheGen :: (State -> IORef (Cache a)) -> Cached a -> State -> IO a uncacheGen getCache (Cached f) st = do let rCache = getCache st stored <- readIORef rCache sn <- f `seq` makeStableName f let h = hashStableName sn case maybe Nothing (sn `lookup`) (h `IMap.lookup` stored) of Just r -> return r Nothing -> do r <- f st r `seq` R.modifyIORef' rCache (IMap.insertWith (++) h [(sn, r)]) return r -- | Representation of SMTLib Program versions. As of June 2015, we're dropping support -- for SMTLib1, and supporting SMTLib2 only. We keep this data-type around in case -- SMTLib3 comes along and we want to support 2 and 3 simultaneously. data SMTLibVersion = SMTLib2 deriving (Bounded, Enum, Eq, Show) -- | The extension associated with the version smtLibVersionExtension :: SMTLibVersion -> String smtLibVersionExtension SMTLib2 = "smt2" -- | Representation of an SMT-Lib program. In between pre and post goes the refuted models data SMTLibPgm = SMTLibPgm SMTLibVersion [String] instance NFData SMTLibVersion where rnf a = a `seq` () instance NFData SMTLibPgm where rnf (SMTLibPgm v p) = rnf v `seq` rnf p `seq` () instance Show SMTLibPgm where show (SMTLibPgm _ pre) = intercalate "\n" pre -- Other Technicalities.. instance NFData CW where rnf (CW x y) = x `seq` y `seq` () instance NFData GeneralizedCW where rnf (ExtendedCW e) = e `seq` () rnf (RegularCW c) = c `seq` () #if MIN_VERSION_base(4,9,0) #else -- Can't really force this, but not a big deal instance NFData CallStack where rnf _ = () #endif instance NFData Result where rnf (Result kindInfo qcInfo cgs inps consts tbls arrs uis axs pgm cstr asserts outs) = rnf kindInfo `seq` rnf qcInfo `seq` rnf cgs `seq` rnf inps `seq` rnf consts `seq` rnf tbls `seq` rnf arrs `seq` rnf uis `seq` rnf axs `seq` rnf pgm `seq` rnf cstr `seq` rnf asserts `seq` rnf outs instance NFData Kind where rnf a = seq a () instance NFData ArrayContext where rnf a = seq a () instance NFData SW where rnf a = seq a () instance NFData SBVExpr where rnf a = seq a () instance NFData Quantifier where rnf a = seq a () instance NFData SBVType where rnf a = seq a () instance NFData SBVPgm where rnf a = seq a () instance NFData (Cached a) where rnf (Cached f) = f `seq` () instance NFData SVal where rnf (SVal x y) = rnf x `seq` rnf y `seq` () instance NFData SMTResult where rnf Unsatisfiable{} = () rnf (Satisfiable _ xs) = rnf xs `seq` () rnf (SatExtField _ xs) = rnf xs `seq` () rnf (Unknown _ xs) = rnf xs `seq` () rnf (ProofError _ xs) = rnf xs `seq` () instance NFData SMTModel where rnf (SMTModel objs assocs) = rnf objs `seq` rnf assocs `seq` () instance NFData SMTScript where rnf (SMTScript b m) = rnf b `seq` rnf m `seq` () -- | Translation tricks needed for specific capabilities afforded by each solver data SolverCapabilities = SolverCapabilities { supportsQuantifiers :: Bool -- ^ Support for SMT-Lib2 style quantifiers? , supportsUninterpretedSorts :: Bool -- ^ Support for SMT-Lib2 style uninterpreted-sorts , supportsUnboundedInts :: Bool -- ^ Support for unbounded integers? , supportsReals :: Bool -- ^ Support for reals? , supportsApproxReals :: Bool -- ^ Supports printing of approximations of reals? , supportsIEEE754 :: Bool -- ^ Support for floating point numbers? , supportsOptimization :: Bool -- ^ Support for optimization routines? , supportsPseudoBooleans :: Bool -- ^ Support for pseudo-boolean operations? , supportsCustomQueries :: Bool -- ^ Support for interactive queries per SMT-Lib? , supportsGlobalDecls :: Bool -- ^ Support for global decls, needed for push-pop. } -- | Rounding mode to be used for the IEEE floating-point operations. -- Note that Haskell's default is 'RoundNearestTiesToEven'. If you use -- a different rounding mode, then the counter-examples you get may not -- match what you observe in Haskell. data RoundingMode = RoundNearestTiesToEven -- ^ Round to nearest representable floating point value. -- If precisely at half-way, pick the even number. -- (In this context, /even/ means the lowest-order bit is zero.) | RoundNearestTiesToAway -- ^ Round to nearest representable floating point value. -- If precisely at half-way, pick the number further away from 0. -- (That is, for positive values, pick the greater; for negative values, pick the smaller.) | RoundTowardPositive -- ^ Round towards positive infinity. (Also known as rounding-up or ceiling.) | RoundTowardNegative -- ^ Round towards negative infinity. (Also known as rounding-down or floor.) | RoundTowardZero -- ^ Round towards zero. (Also known as truncation.) deriving (Eq, Ord, Show, Read, G.Data, Bounded, Enum) -- | 'RoundingMode' kind instance HasKind RoundingMode -- | Solver configuration. See also 'z3', 'yices', 'cvc4', 'boolector', 'mathSAT', etc. which are instantiations of this type for those solvers, with -- reasonable defaults. In particular, custom configuration can be created by varying those values. (Such as @z3{verbose=True}@.) -- -- Most fields are self explanatory. The notion of precision for printing algebraic reals stems from the fact that such values does -- not necessarily have finite decimal representations, and hence we have to stop printing at some depth. It is important to -- emphasize that such values always have infinite precision internally. The issue is merely with how we print such an infinite -- precision value on the screen. The field 'printRealPrec' controls the printing precision, by specifying the number of digits after -- the decimal point. The default value is 16, but it can be set to any positive integer. -- -- When printing, SBV will add the suffix @...@ at the and of a real-value, if the given bound is not sufficient to represent the real-value -- exactly. Otherwise, the number will be written out in standard decimal notation. Note that SBV will always print the whole value if it -- is precise (i.e., if it fits in a finite number of digits), regardless of the precision limit. The limit only applies if the representation -- of the real value is not finite, i.e., if it is not rational. -- -- The 'printBase' field can be used to print numbers in base 2, 10, or 16. If base 2 or 16 is used, then floating-point values will -- be printed in their internal memory-layout format as well, which can come in handy for bit-precise analysis. data SMTConfig = SMTConfig { verbose :: Bool -- ^ Debug mode , timing :: Timing -- ^ Print timing information on how long different phases took (construction, solving, etc.) , printBase :: Int -- ^ Print integral literals in this base (2, 10, and 16 are supported.) , printRealPrec :: Int -- ^ Print algebraic real values with this precision. (SReal, default: 16) , satCmd :: String -- ^ Usually "(check-sat)". However, users might tweak it based on solver characteristics. , allSatMaxModelCount :: Maybe Int -- ^ In an allSat call, return at most this many models. If nothing, return all. , isNonModelVar :: String -> Bool -- ^ When constructing a model, ignore variables whose name satisfy this predicate. (Default: (const False), i.e., don't ignore anything) , transcript :: Maybe FilePath -- ^ If Just, the entire interaction will be recorded as a playable file (for debugging purposes mostly) , smtLibVersion :: SMTLibVersion -- ^ What version of SMT-lib we use for the tool , solver :: SMTSolver -- ^ The actual SMT solver. , roundingMode :: RoundingMode -- ^ Rounding mode to use for floating-point conversions , solverSetOptions :: [SMTOption] -- ^ Options to set as we start the solver , ignoreExitCode :: Bool -- ^ If true, we shall ignore the exit code upon exit. Otherwise we require ExitSuccess. , redirectVerbose :: Maybe FilePath -- ^ Redirect the verbose output to this file if given. If Nothing, stdout is implied. } -- We're just seq'ing top-level here, it shouldn't really matter. (i.e., no need to go deeper.) instance NFData SMTConfig where rnf SMTConfig{} = () -- | A model, as returned by a solver data SMTModel = SMTModel { modelObjectives :: [(String, GeneralizedCW)] -- ^ Mapping of symbolic values to objective values. , modelAssocs :: [(String, CW)] -- ^ Mapping of symbolic values to constants. } deriving Show -- | The result of an SMT solver call. Each constructor is tagged with -- the 'SMTConfig' that created it so that further tools can inspect it -- and build layers of results, if needed. For ordinary uses of the library, -- this type should not be needed, instead use the accessor functions on -- it. (Custom Show instances and model extractors.) data SMTResult = Unsatisfiable SMTConfig -- ^ Unsatisfiable | Satisfiable SMTConfig SMTModel -- ^ Satisfiable with model | SatExtField SMTConfig SMTModel -- ^ Prover returned a model, but in an extension field containing Infinite/epsilon | Unknown SMTConfig String -- ^ Prover returned unknown, with the given reason | ProofError SMTConfig [String] -- ^ Prover errored out -- | A script, to be passed to the solver. data SMTScript = SMTScript { scriptBody :: String -- ^ Initial feed , scriptModel :: [String] -- ^ Continuation script, to extract results } -- | An SMT engine type SMTEngine = forall res. SMTConfig -- ^ current configuration -> State -- ^ the state in which to run the engine -> String -- ^ program -> (State -> IO res) -- ^ continuation -> IO res -- | Solvers that SBV is aware of data Solver = Z3 | Yices | Boolector | CVC4 | MathSAT | ABC deriving (Show, Enum, Bounded) -- | An SMT solver data SMTSolver = SMTSolver { name :: Solver -- ^ The solver in use , executable :: String -- ^ The path to its executable , options :: SMTConfig -> [String] -- ^ Options to provide to the solver , engine :: SMTEngine -- ^ The solver engine, responsible for interpreting solver output , capabilities :: SolverCapabilities -- ^ Various capabilities of the solver } {-# ANN type FPOp ("HLint: ignore Use camelCase" :: String) #-} {-# ANN type PBOp ("HLint: ignore Use camelCase" :: String) #-}