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Symbolic.hs
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Symbolic.hs
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-----------------------------------------------------------------------------
-- |
-- Module : Data.SBV.Core.Symbolic
-- Copyright : (c) Levent Erkok
-- License : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- Symbolic values
-----------------------------------------------------------------------------
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE CPP #-}
{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE DeriveDataTypeable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE NamedFieldPuns #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE StandaloneDeriving #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE ViewPatterns #-}
{-# OPTIONS_GHC -Wall -Werror -fno-warn-orphans #-}
module Data.SBV.Core.Symbolic
( NodeId(..)
, SV(..), swKind, trueSV, falseSV, contextOfSV
, Op(..), PBOp(..), OvOp(..), FPOp(..), NROp(..), StrOp(..), RegExOp(..), SeqOp(..), SetOp(..), SpecialRelOp(..)
, RegExp(..), regExpToSMTString
, Quantifier(..), needsExistentials, SBVContext(..), checkCompatibleContext, VarContext(..)
, RoundingMode(..)
, SBVType(..), svUninterpreted, svUninterpretedNamedArgs, newUninterpreted
, SVal(..)
, svMkSymVar, sWordN, sWordN_, sIntN, sIntN_
, ArrayContext(..), ArrayInfo
, svToSV, svToSymSV, forceSVArg
, SBVExpr(..), newExpr, isCodeGenMode, isSafetyCheckingIStage, isRunIStage, isSetupIStage
, Cached, cache, uncache, modifyState, modifyIncState
, ArrayIndex(..), uncacheAI
, NamedSymVar(..), Name, UserInputs, Inputs(..), getSV, swNodeId, namedNodeId
, addInternInput, addUserInput
, getUserName', getUserName
, lookupInput , getSValPathCondition, extendSValPathCondition
, getTableIndex, sObserve
, SBVPgm(..), MonadSymbolic(..), SymbolicT, Symbolic, runSymbolic, mkNewState, runSymbolicInState, State(..), SMTDef(..), smtDefGivenName, withNewIncState, IncState(..), incrementInternalCounter
, inSMTMode, SBVRunMode(..), IStage(..), Result(..), ResultInp(..), UICodeKind(..)
, registerKind, registerLabel, recordObservable
, addAssertion, addNewSMTOption, imposeConstraint, internalConstraint, internalVariable, lambdaVar, quantVar
, SMTLibPgm(..), SMTLibVersion(..), smtLibVersionExtension
, SolverCapabilities(..)
, extractSymbolicSimulationState, CnstMap
, OptimizeStyle(..), Objective(..), Penalty(..), objectiveName, addSValOptGoal
, MonadQuery(..), QueryT(..), Query, Queriable(..), Fresh(..), QueryState(..), QueryContext(..)
, SMTScript(..), Solver(..), SMTSolver(..), SMTResult(..), SMTModel(..), SMTConfig(..), SMTEngine
, validationRequested, outputSVal, ProgInfo(..), mustIgnoreVar, getRootState
) where
import Control.DeepSeq (NFData(..))
import Control.Monad (when)
import Control.Monad.Except (MonadError, ExceptT)
import Control.Monad.Reader (MonadReader(..), ReaderT, runReaderT,
mapReaderT)
import Control.Monad.State.Lazy (MonadState)
import Control.Monad.Trans (MonadIO(liftIO), MonadTrans(lift))
import Control.Monad.Trans.Maybe (MaybeT)
import Control.Monad.Writer.Strict (MonadWriter)
import Data.Char (isAlpha, isAlphaNum, toLower)
import Data.IORef (IORef, newIORef, readIORef)
import Data.List (intercalate, sortBy, isPrefixOf, isSuffixOf, nub)
import Data.Maybe (fromMaybe, mapMaybe)
import Data.String (IsString(fromString))
import Data.Kind (Type)
import Data.Time (getCurrentTime, UTCTime)
import Data.Int (Int64)
import GHC.Stack
import GHC.Stack.Types
import GHC.Generics (Generic)
import qualified Control.Exception as C
import qualified Control.Monad.State.Lazy as LS
import qualified Control.Monad.State.Strict as SS
import qualified Control.Monad.Writer.Lazy as LW
import qualified Control.Monad.Writer.Strict as SW
import qualified Data.IORef as R (modifyIORef')
import qualified Data.Generics as G (Data(..))
import qualified Data.Generics.Uniplate.Data as G
import qualified Data.IntMap.Strict as IMap (IntMap, empty, toAscList, lookup, insertWith)
import qualified Data.Map.Strict as Map (Map, empty, toList, lookup, insert, size)
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, (|>), (<|), lookup, elemIndexL)
import qualified Data.Text as T
import System.Mem.StableName
import System.Random
import Data.SBV.Core.Kind
import Data.SBV.Core.Concrete
import Data.SBV.SMT.SMTLibNames
import Data.SBV.Utils.TDiff (Timing)
import Data.SBV.Utils.Lib (stringToQFS, checkObservableName)
import Data.SBV.Control.Types
#if MIN_VERSION_base(4,11,0)
import Control.Monad.Fail as Fail
#endif
-- | Context identifier. 0 is reserved global context
newtype SBVContext = SBVContext Int64 deriving (Eq, Ord, G.Data, Show)
instance NFData SBVContext where
rnf (SBVContext i) = i `seq` ()
-- | Global context
globalSBVContext :: SBVContext
globalSBVContext = SBVContext 0
-- | Generate context. We make sure it isn't 0, i.e., the global context
-- The "hope" here is that each time we call this we get a different context number.
-- A random number doesn't necessarily have to do that, but I think the pseudo-generator
-- has a large enough period for this to go through OK.
genSBVContext :: IO SBVContext
genSBVContext = do ctx <- SBVContext <$> randomIO
if ctx == globalSBVContext -- unlikely, but possible
then genSBVContext
else pure ctx
-- | A symbolic node id
newtype NodeId = NodeId { getId :: (SBVContext, Int, Int) } -- Lambda-level, and node-id
deriving (Ord, G.Data)
-- Equality is pair-wise, except we accommodate for negative node-id; which is reserved for true/false
instance Eq NodeId where
NodeId n1@(_, _, i) == NodeId n2@(_, _, j)
| i < 0 && j < 0
= i == j
| True
= n1 == n2
-- | A symbolic word, tracking it's signedness and size.
data SV = SV !Kind !NodeId
deriving G.Data
-- | Which context are we using this var at?
contextOfSV :: SV -> SBVContext
contextOfSV (SV _ (NodeId (c, _, _))) = c
-- | For equality, we merely use the lambda-level/node-id
instance Eq SV where
SV _ n1 == SV _ n2 = n1 == n2
-- | Again, simply use the lambda-level/node-id for ordering
instance Ord SV where
SV _ n1 `compare` SV _ n2 = n1 `compare` n2
instance HasKind SV where
kindOf (SV k _) = k
instance Show SV where
show (SV _ (NodeId (_, l, n))) = case n of
-2 -> "false"
-1 -> "true"
_ -> prefix ++ 's' : show n
where prefix = case l of
0 -> ""
_ -> 'l' : show l ++ "_"
-- | Kind of a symbolic word.
swKind :: SV -> Kind
swKind (SV k _) = k
-- | retrieve the node id of a symbolic word
swNodeId :: SV -> NodeId
swNodeId (SV _ nid) = nid
-- | 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
forceSVArg :: SV -> IO ()
forceSVArg (SV k n) = k `seq` n `seq` return ()
-- | Constant False as an 'SV'. Note that this value always occupies slot -2 and level 0.
falseSV :: SV
falseSV = SV KBool $ NodeId (globalSBVContext, 0, -2)
-- | Constant True as an 'SV'. Note that this value always occupies slot -1 and level 0.
trueSV :: SV
trueSV = SV KBool $ NodeId (globalSBVContext, 0, -1)
-- | Symbolic operations
data Op = Plus
| Times
| Minus
| UNeg
| Abs
| Quot
| Rem
| Equal
| Implies
| 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
| ZeroExtend Int
| SignExtend Int
| LkUp (Int, Kind, Kind, Int) !SV !SV -- (table-index, arg-type, res-type, length of the table) index out-of-bounds-value
| ArrEq ArrayIndex ArrayIndex -- Array equality
| ArrRead ArrayIndex
| KindCast Kind Kind
| Uninterpreted String
| QuantifiedBool String -- When we generate a forall/exists (nested etc.) boolean value
| SpecialRelOp Kind SpecialRelOp -- Generate the equality to the internal operation
| Label String -- Essentially no-op; useful for code generation to emit comments.
| IEEEFP FPOp -- Floating-point ops, categorized separately
| NonLinear NROp -- Non-linear ops (mostly trigonometric), categorized separately
| OverflowOp OvOp -- Overflow-ops, categorized separately
| PseudoBoolean PBOp -- Pseudo-boolean ops, categorized separately
| RegExOp RegExOp -- RegEx operations, categorized separately
| StrOp StrOp -- String ops, categorized separately
| SeqOp SeqOp -- Sequence ops, categorized separately
| SetOp SetOp -- Set operations, categorized separately
| TupleConstructor Int -- Construct an n-tuple
| TupleAccess Int Int -- Access element i of an n-tuple; second argument is n
| EitherConstructor Kind Kind Bool -- Construct a sum; False: left, True: right
| EitherIs Kind Kind Bool -- Either branch tester; False: left, True: right
| EitherAccess Bool -- Either branch access; False: left, True: right
| RationalConstructor -- Construct a rational. Note that there's no access to numerator or denumerator, since we cannot store rationals in canonical form
| MaybeConstructor Kind Bool -- Construct a maybe value; False: Nothing, True: Just
| MaybeIs Kind Bool -- Maybe tester; False: nothing, True: just
| MaybeAccess -- Maybe branch access; grab the contents of the just
deriving (Eq, Ord, G.Data)
-- | Special relations supported by z3
data SpecialRelOp = IsPartialOrder String
| IsLinearOrder String
| IsTreeOrder String
| IsPiecewiseLinearOrder String
deriving (Eq, Ord, G.Data, Show)
instance NFData SpecialRelOp where
rnf (IsPartialOrder n) = rnf n
rnf (IsLinearOrder n) = rnf n
rnf (IsTreeOrder n) = rnf n
rnf (IsPiecewiseLinearOrder n) = rnf n
-- | Floating point operations
data FPOp = FP_Cast Kind Kind SV -- 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, G.Data)
-- 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 t of
KFloat -> "(_ to_fp 8 24)"
KDouble -> "(_ to_fp 11 53)"
KFP eb sb -> "(_ to_fp " ++ show eb ++ " " ++ show sb ++ ")"
_ -> 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"
-- | Non-linear operations
data NROp = NR_Sin
| NR_Cos
| NR_Tan
| NR_ASin
| NR_ACos
| NR_ATan
| NR_Sqrt
| NR_Sinh
| NR_Cosh
| NR_Tanh
| NR_Exp
| NR_Log
| NR_Pow
deriving (Eq, Ord, G.Data)
-- | The show instance carefully arranges for these to be printed as it can be understood by dreal
instance Show NROp where
show NR_Sin = "sin"
show NR_Cos = "cos"
show NR_Tan = "tan"
show NR_ASin = "asin"
show NR_ACos = "acos"
show NR_ATan = "atan"
show NR_Sinh = "sinh"
show NR_Cosh = "cosh"
show NR_Tanh = "tanh"
show NR_Sqrt = "sqrt"
show NR_Exp = "exp"
show NR_Log = "log"
show NR_Pow = "pow"
-- | 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, G.Data)
-- | Overflow operations
data OvOp = PlusOv Bool -- ^ Addition overflow. Bool is True if signed.
| SubOv Bool -- ^ Subtraction overflow. Bool is True if signed.
| MulOv Bool -- ^ Multiplication overflow. Bool is True if signed.
| DivOv -- ^ Division overflow. Only signed, since unsigned division does not overflow.
| NegOv -- ^ Unary negation overflow. Only signed, since unsigned negation does not overflow.
deriving (Eq, Ord, G.Data)
-- | Show instance. It's important that these follow the SMTLib names.
instance Show OvOp where
show (PlusOv signed) = "bv" ++ (if signed then "s" else "u") ++ "addo"
show (SubOv signed) = "bv" ++ (if signed then "s" else "u") ++ "subo"
show (MulOv signed) = "bv" ++ (if signed then "s" else "u") ++ "mulo"
show DivOv = "bvsdivo" -- This is confusing, the division is called bvsdivo, but negation is bvnego
show NegOv = "bvnego" -- But SMTLib's choice is deliberate: https://groups.google.com/u/0/g/smt-lib/c/J4D99wT0aKI
-- | String operations. Note that we do not define @StrAt@ as it translates to 'StrSubstr' trivially.
data StrOp = StrConcat -- ^ Concatenation of one or more strings
| StrLen -- ^ String length
| StrUnit -- ^ Unit string
| StrNth -- ^ Nth element
| StrSubstr -- ^ Retrieves substring of @s@ at @offset@
| StrIndexOf -- ^ Retrieves first position of @sub@ in @s@, @-1@ if there are no occurrences
| StrContains -- ^ Does @s@ contain the substring @sub@?
| StrPrefixOf -- ^ Is @pre@ a prefix of @s@?
| StrSuffixOf -- ^ Is @suf@ a suffix of @s@?
| StrReplace -- ^ Replace the first occurrence of @src@ by @dst@ in @s@
| StrStrToNat -- ^ Retrieve integer encoded by string @s@ (ground rewriting only)
| StrNatToStr -- ^ Retrieve string encoded by integer @i@ (ground rewriting only)
| StrToCode -- ^ Equivalent to Haskell's ord
| StrFromCode -- ^ Equivalent to Haskell's chr
| StrInRe RegExp -- ^ Check if string is in the regular expression
deriving (Eq, Ord, G.Data)
-- | Regular-expression operators. The only thing we can do is to compare for equality/disequality.
data RegExOp = RegExEq RegExp RegExp
| RegExNEq RegExp RegExp
deriving (Eq, Ord, G.Data)
-- | Regular expressions. Note that regular expressions themselves are
-- concrete, but the 'Data.SBV.RegExp.match' function from the 'Data.SBV.RegExp.RegExpMatchable' class
-- can check membership against a symbolic string/character. Also, we
-- are preferring a datatype approach here, as opposed to coming up with
-- some string-representation; there are way too many alternatives
-- already so inventing one isn't a priority. Please get in touch if you
-- would like a parser for this type as it might be easier to use.
data RegExp = Literal String -- ^ Precisely match the given string
| All -- ^ Accept every string
| AllChar -- ^ Accept every single character
| None -- ^ Accept no strings
| Range Char Char -- ^ Accept range of characters
| Conc [RegExp] -- ^ Concatenation
| KStar RegExp -- ^ Kleene Star: Zero or more
| KPlus RegExp -- ^ Kleene Plus: One or more
| Opt RegExp -- ^ Zero or one
| Comp RegExp -- ^ Complement of regular expression
| Diff RegExp RegExp -- ^ Difference of regular expressions
| Loop Int Int RegExp -- ^ From @n@ repetitions to @m@ repetitions
| Power Int RegExp -- ^ Exactly @n@ repetitions, i.e., nth power
| Union [RegExp] -- ^ Union of regular expressions
| Inter RegExp RegExp -- ^ Intersection of regular expressions
deriving (Eq, Ord, G.Data)
-- | With overloaded strings, we can have direct literal regular expressions.
instance IsString RegExp where
fromString = Literal
-- | Regular expressions as a 'Num' instance. Note that only some operations make sense and
-- not in the most obvious way. For instance, we would typically expect @a - b@ to be the
-- same as @a + negate b@, but that equality does not hold in general. So, use the @Num@
-- instance only as constructing syntax, not doing algebraic manipulations.
instance Num RegExp where
-- flatten the concats to make them simpler
Conc xs * y = Conc (xs ++ [y])
x * Conc ys = Conc (x : ys)
x * y = Conc [x, y]
-- flatten the unions to make them simpler
Union xs + y = Union (xs ++ [y])
x + Union ys = Union (x : ys)
x + y = Union [x, y]
x - y = Diff x y
abs = error "Num.RegExp: no abs method"
signum = error "Num.RegExp: no signum method"
fromInteger x
| x == 0 = None
| x == 1 = Literal "" -- Unit for concatenation is the empty string
| True = error $ "Num.RegExp: Only 0 and 1 makes sense as a reg-exp, no meaning for: " ++ show x
negate = Comp
-- | Convert a reg-exp to a Haskell-like string
instance Show RegExp where
show = regExpToString show
-- | Convert a reg-exp to a SMT-lib acceptable representation
regExpToSMTString :: RegExp -> String
regExpToSMTString = regExpToString (\s -> '"' : stringToQFS s ++ "\"")
-- | Convert a RegExp to a string, parameterized by how strings are converted
regExpToString :: (String -> String) -> RegExp -> String
regExpToString fs (Literal s) = "(str.to.re " ++ fs s ++ ")"
regExpToString _ All = "re.all"
regExpToString _ AllChar = "re.allchar"
regExpToString _ None = "re.nostr"
regExpToString fs (Range ch1 ch2) = "(re.range " ++ fs [ch1] ++ " " ++ fs [ch2] ++ ")"
regExpToString _ (Conc []) = show (1 :: Integer)
regExpToString fs (Conc [x]) = regExpToString fs x
regExpToString fs (Conc xs) = "(re.++ " ++ unwords (map (regExpToString fs) xs) ++ ")"
regExpToString fs (KStar r) = "(re.* " ++ regExpToString fs r ++ ")"
regExpToString fs (KPlus r) = "(re.+ " ++ regExpToString fs r ++ ")"
regExpToString fs (Opt r) = "(re.opt " ++ regExpToString fs r ++ ")"
regExpToString fs (Comp r) = "(re.comp " ++ regExpToString fs r ++ ")"
regExpToString fs (Diff r1 r2) = "(re.diff " ++ regExpToString fs r1 ++ " " ++ regExpToString fs r2 ++ ")"
regExpToString fs (Loop lo hi r)
| lo >= 0, hi >= lo = "((_ re.loop " ++ show lo ++ " " ++ show hi ++ ") " ++ regExpToString fs r ++ ")"
| True = error $ "Invalid regular-expression Loop with arguments: " ++ show (lo, hi)
regExpToString fs (Power n r)
| n >= 0 = regExpToString fs (Loop n n r)
| True = error $ "Invalid regular-expression Power with arguments: " ++ show n
regExpToString fs (Inter r1 r2) = "(re.inter " ++ regExpToString fs r1 ++ " " ++ regExpToString fs r2 ++ ")"
regExpToString _ (Union []) = "re.nostr"
regExpToString fs (Union [x]) = regExpToString fs x
regExpToString fs (Union xs) = "(re.union " ++ unwords (map (regExpToString fs) xs) ++ ")"
-- | Show instance for @StrOp@. Note that the mapping here is important to match the SMTLib equivalents.
instance Show StrOp where
show StrConcat = "str.++"
show StrLen = "str.len"
show StrUnit = "str.unit" -- NB. This is actually a no-op, since in SMTLib characters are the same as strings.
show StrNth = "str.at"
show StrSubstr = "str.substr"
show StrIndexOf = "str.indexof"
show StrContains = "str.contains"
show StrPrefixOf = "str.prefixof"
show StrSuffixOf = "str.suffixof"
show StrReplace = "str.replace"
show StrStrToNat = "str.to.int" -- NB. SMTLib uses "int" here though only nats are supported
show StrNatToStr = "int.to.str" -- NB. SMTLib uses "int" here though only nats are supported
show StrToCode = "str.to_code"
show StrFromCode = "str.from_code"
-- Note the breakage here with respect to argument order. We fix this explicitly later.
show (StrInRe s) = "str.in.re " ++ regExpToSMTString s
-- | Show instance for @RegExOp@.
instance Show RegExOp where
show (RegExEq r1 r2) = "(= " ++ regExpToSMTString r1 ++ " " ++ regExpToSMTString r2 ++ ")"
show (RegExNEq r1 r2) = "(distinct " ++ regExpToSMTString r1 ++ " " ++ regExpToSMTString r2 ++ ")"
-- | Sequence operations.
data SeqOp = SeqConcat -- ^ See StrConcat
| SeqLen -- ^ See StrLen
| SeqUnit -- ^ See StrUnit
| SeqNth -- ^ See StrNth
| SeqSubseq -- ^ See StrSubseq
| SeqIndexOf -- ^ See StrIndexOf
| SeqContains -- ^ See StrContains
| SeqPrefixOf -- ^ See StrPrefixOf
| SeqSuffixOf -- ^ See StrSuffixOf
| SeqReplace -- ^ See StrReplace
| SeqMap String -- ^ Mapping over sequences
| SeqMapI String -- ^ Mapping over sequences with offset
| SeqFoldLeft String -- ^ Folding of sequences
| SeqFoldLeftI String -- ^ Folding of sequences with offset
| SBVReverse Kind -- ^ Reversal of sequences. NB. Also works for strings; hence the name.
deriving (Eq, Ord, G.Data)
-- | Show instance for SeqOp. Again, mapping is important.
instance Show SeqOp where
show SeqConcat = "seq.++"
show SeqLen = "seq.len"
show SeqUnit = "seq.unit"
show SeqNth = "seq.nth"
show SeqSubseq = "seq.extract"
show SeqIndexOf = "seq.indexof"
show SeqContains = "seq.contains"
show SeqPrefixOf = "seq.prefixof"
show SeqSuffixOf = "seq.suffixof"
show SeqReplace = "seq.replace"
show (SeqMap s) = "seq.map " ++ s
show (SeqMapI s) = "seq.mapi " ++ s
show (SeqFoldLeft s) = "seq.foldl " ++ s
show (SeqFoldLeftI s) = "seq.foldli " ++ s
-- Note: This isn't part of SMTLib, we explicitly handle it
show (SBVReverse k) = "sbv.reverse[" ++ show k ++ "]"
-- | Set operations.
data SetOp = SetEqual
| SetMember
| SetInsert
| SetDelete
| SetIntersect
| SetUnion
| SetSubset
| SetDifference
| SetComplement
deriving (Eq, Ord, G.Data)
-- The show instance for 'SetOp' is merely for debugging, we map them separately so
-- the mapped strings are less important here.
instance Show SetOp where
show SetEqual = "=="
show SetMember = "Set.member"
show SetInsert = "Set.insert"
show SetDelete = "Set.delete"
show SetIntersect = "Set.intersect"
show SetUnion = "Set.union"
show SetSubset = "Set.subset"
show SetDifference = "Set.difference"
show SetComplement = "Set.complement"
-- 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 (QuantifiedBool i) = "[quantified boolean] " ++ i
show (Label s) = "[label] " ++ s
show (IEEEFP w) = show w
show (NonLinear w) = show w
show (PseudoBoolean p) = show p
show (OverflowOp o) = show o
show (StrOp s) = show s
show (RegExOp s) = show s
show (SeqOp s) = show s
show (SetOp s) = show s
show (TupleConstructor 0) = "mkSBVTuple0"
show (TupleConstructor n) = "mkSBVTuple" ++ show n
show (TupleAccess i n) = "proj_" ++ show i ++ "_SBVTuple" ++ show n
-- Remember, while we try to maintain SMTLib compabitibility here, these output
-- is merely for debugging purposes. For how we actually render these in SMTLib,
-- look at the file SBV/SMT/SMTLib2.hs for these constructors.
show (EitherConstructor k1 k2 False) = "(_ left_SBVEither " ++ show (KEither k1 k2) ++ ")"
show (EitherConstructor k1 k2 True ) = "(_ right_SBVEither " ++ show (KEither k1 k2) ++ ")"
show (EitherIs k1 k2 False) = "(_ is (left_SBVEither (" ++ show k1 ++ ") " ++ show (KEither k1 k2) ++ "))"
show (EitherIs k1 k2 True ) = "(_ is (right_SBVEither (" ++ show k2 ++ ") " ++ show (KEither k1 k2) ++ "))"
show (EitherAccess False) = "get_left_SBVEither"
show (EitherAccess True ) = "get_right_SBVEither"
show RationalConstructor = "SBV.Rational"
show (MaybeConstructor k False) = "(_ nothing_SBVMaybe " ++ show (KMaybe k) ++ ")"
show (MaybeConstructor k True) = "(_ just_SBVMaybe " ++ show (KMaybe k) ++ ")"
show (MaybeIs k False) = "(_ is (nothing_SBVMaybe () " ++ show (KMaybe k) ++ "))"
show (MaybeIs k True ) = "(_ is (just_SBVMaybe (" ++ show k ++ ") " ++ show (KMaybe k) ++ "))"
show MaybeAccess = "get_just_SBVMaybe"
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, "/="), (Implies, "=>")
, (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, G.Data)
-- | Show instance for 'Quantifier'
instance Show Quantifier where
show ALL = "Forall"
show EX = "Exists"
-- | Which context is this variable being created?
data VarContext = NonQueryVar (Maybe Quantifier) -- in this case, it can be quantified
| QueryVar -- in this case, it is always existential
-- | 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, G.Data)
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 ![SV]
deriving (Eq, Ord, G.Data)
-- | 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 (OverflowOp op) args) = unwords (show op : 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 (SV, SBVExpr)}
deriving G.Data
-- | Helper synonym for text, in case we switch to something else later.
type Name = T.Text
-- | 'NamedSymVar' pairs symbolic values and user given/automatically generated names
data NamedSymVar = NamedSymVar !SV !Name
deriving (Show, Generic, G.Data)
-- | For comparison purposes, we simply use the SV and ignore the name
instance Eq NamedSymVar where
(==) (NamedSymVar l _) (NamedSymVar r _) = l == r
instance Ord NamedSymVar where
compare (NamedSymVar l _) (NamedSymVar r _) = compare l r
-- | Convert to a named symvar, from string
toNamedSV' :: SV -> String -> NamedSymVar
toNamedSV' s = NamedSymVar s . T.pack
-- | Convert to a named symvar, from text
toNamedSV :: SV -> Name -> NamedSymVar
toNamedSV = NamedSymVar
-- | Get the node id from a named sym var
namedNodeId :: NamedSymVar -> NodeId
namedNodeId = swNodeId . getSV
-- | Get the SV from a named sym var
getSV :: NamedSymVar -> SV
getSV (NamedSymVar s _) = s
-- | Get the user-name typed value from named sym var
getUserName :: NamedSymVar -> Name
getUserName (NamedSymVar _ nm) = nm
-- | Get the string typed value from named sym var
getUserName' :: NamedSymVar -> String
getUserName' = T.unpack . getUserName
-- | 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.
| 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
| AssertWithPenalty 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 (AssertWithPenalty 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 :: Maybe C.SomeException -> IO ()
, queryTimeOutValue :: Maybe Int
, queryAssertionStackDepth :: Int
}
-- | Computations which support query operations.
class Monad m => MonadQuery m where
queryState :: m State
default queryState :: (MonadTrans t, MonadQuery m', m ~ t m') => m State
queryState = lift queryState
instance MonadQuery m => MonadQuery (ExceptT e m)
instance MonadQuery m => MonadQuery (MaybeT m)
instance MonadQuery m => MonadQuery (ReaderT r m)
instance MonadQuery m => MonadQuery (SS.StateT s m)
instance MonadQuery m => MonadQuery (LS.StateT s m)
instance (MonadQuery m, Monoid w) => MonadQuery (SW.WriterT w m)
instance (MonadQuery m, Monoid w) => MonadQuery (LW.WriterT w m)
-- | A query is a user-guided mechanism to directly communicate and extract
-- results from the solver. A generalization of 'Data.SBV.Query'.
newtype QueryT m a = QueryT { runQueryT :: ReaderT State m a }
deriving (Applicative, Functor, Monad, MonadIO, MonadTrans,
MonadError e, MonadState s, MonadWriter w)
instance Monad m => MonadQuery (QueryT m) where
queryState = QueryT ask
mapQueryT :: (ReaderT State m a -> ReaderT State n b) -> QueryT m a -> QueryT n b
mapQueryT f = QueryT . f . runQueryT
{-# INLINE mapQueryT #-}
-- | Create a fresh variable of some type in the underlying query monad transformer.
-- For further control on how these variables are projected and embedded, see the
-- 'Queriable' class.
class Fresh m a where
fresh :: QueryT m a
-- | An queriable value. This is a generalization of the 'Fresh' class, in case one needs
-- to be more specific about how projections/embeddings are done.
class Queriable m a where
type QueryResult a :: Type
-- | ^ Create a new symbolic value of type @a@
create :: QueryT m a
-- | ^ Extract the current value in a SAT context
project :: a -> QueryT m (QueryResult a)
-- | ^ Create a literal value. Morally, 'embed' and 'project' are inverses of each other
-- via the 'QueryT' monad transformer.
embed :: QueryResult a -> QueryT m a
-- Have to define this one by hand, because we use ReaderT in the implementation
instance MonadReader r m => MonadReader r (QueryT m) where
ask = lift ask
local f = mapQueryT $ mapReaderT $ local f
-- | A query is a user-guided mechanism to directly communicate and extract
-- results from the solver.
type Query = QueryT IO
instance MonadSymbolic Query where
symbolicEnv = queryState
instance NFData OptimizeStyle where
rnf x = x `seq` ()
instance NFData Penalty where
rnf DefaultPenalty = ()
rnf (Penalty p mbs) = rnf p `seq` rnf mbs
instance NFData a => NFData (Objective a) where
rnf (Minimize s a) = rnf s `seq` rnf a
rnf (Maximize s a) = rnf s `seq` rnf a
rnf (AssertWithPenalty s a p) = rnf s `seq` rnf a `seq` rnf p
-- | A result can either produce something at the top or as a lambda/constraint. Distinguish by inputs
data ResultInp = ResultTopInps ([NamedSymVar], [NamedSymVar]) -- user inputs -- trackers
| ResultLamInps [(Quantifier, NamedSymVar)] -- for constraints, we can have quantifiers
deriving G.Data
instance NFData ResultInp where
rnf (ResultTopInps xs) = rnf xs
rnf (ResultLamInps xs) = rnf xs
-- | Several data about the program
data ProgInfo = ProgInfo { hasQuants :: Bool
, progSpecialRels :: [SpecialRelOp]
, progTransClosures :: [(String, String)]
}
deriving G.Data
instance NFData ProgInfo where
rnf (ProgInfo a b c) = rnf a `seq` rnf b `seq` rnf c
deriving instance G.Data CallStack
deriving instance G.Data SrcLoc
-- | Result of running a symbolic computation
data Result = Result { progInfo :: ProgInfo -- ^ various info we collect about the program
, reskinds :: Set.Set Kind -- ^ kinds used in the program
, resTraces :: [(String, CV)] -- ^ quick-check counter-example information (if any)
, resObservables :: [(String, CV -> Bool, SV)] -- ^ observable expressions (part of the model)
, resUISegs :: [(String, [String])] -- ^ uninterpeted code segments
, resParams :: ResultInp -- ^ top-inputs or lambda params
, resConsts :: (CnstMap, [(SV, CV)]) -- ^ constants
, resTables :: [((Int, Kind, Kind), [SV])] -- ^ tables (automatically constructed) (tableno, index-type, result-type) elts
, resArrays :: [(Int, ArrayInfo)] -- ^ arrays (user specified)
, resUIConsts :: [(String, (Bool, Maybe [String], SBVType))] -- ^ uninterpreted constants
, resDefinitions :: [(SMTDef, SBVType)] -- ^ definitions created via smtFunction or lambda
, resAsgns :: SBVPgm -- ^ assignments
, resConstraints :: S.Seq (Bool, [(String, String)], SV) -- ^ additional constraints (boolean)
, resAssertions :: [(String, Maybe CallStack, SV)] -- ^ assertions
, resOutputs :: [SV] -- ^ outputs
}
deriving G.Data
-- 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
-- definition 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 params (_, cs) ts as uis defns xs cstrs asserts os) = intercalate "\n" $
(if null usorts then [] else "SORTS" : map (" " ++) usorts)
++ (case params of
ResultTopInps (i, t) -> "INPUTS" : map shn i ++ (if null t then [] else "TRACKER VARS" : map shn t)
ResultLamInps qs -> "LAMBDA-CONSTRAINT PARAMS" : map shq qs
)
++ ["CONSTANTS"]
++ concatMap shc cs
++ ["TABLES"]
++ map sht ts
++ ["ARRAYS"]
++ map sha as
++ ["UNINTERPRETED CONSTANTS"]
++ map shui uis
++ ["USER GIVEN CODE SEGMENTS"]
++ concatMap shcg cgs
++ ["AXIOMS-DEFINITIONS"]
++ map show defns
++ ["DEFINE"]
++ map (\(s, e) -> " " ++ shs s ++ " = " ++ show e) (F.toList (pgmAssignments xs))
++ ["CONSTRAINTS"]
++ map ((" " ++) . shCstr) (F.toList 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 Nothing = s
sh s (Just es) = s ++ " (" ++ intercalate ", " es ++ ")"
shs sv = show sv ++ " :: " ++ show (swKind sv)
sht ((i, at, rt), es) = " Table " ++ show i ++ " : " ++ show at ++ "->" ++ show rt ++ " = " ++ show es
shc (sv, cv)
| sv == falseSV || sv == trueSV
= []
| True
= [" " ++ show sv ++ " = " ++ show cv]
shcg (s, ss) = ("Variable: " ++ s) : map (" " ++) ss
shn (NamedSymVar sv nm) = " " <> ni <> " :: " ++ show (swKind sv) ++ alias
where ni = show sv
alias | ni == T.unpack nm = ""
| True = ", aliasing " ++ show nm
shq (q, v) = shn v ++ ", " ++ if q == ALL then "universal" else "existential"
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
shCstr (isSoft, [], c) = soft isSoft ++ show c
shCstr (isSoft, [(":named", nm)], c) = soft isSoft ++ nm ++ ": " ++ show c
shCstr (isSoft, attrs, c) = soft isSoft ++ show c ++ " (attributes: " ++ show attrs ++ ")"
soft True = "[SOFT] "
soft False = ""
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 (Either (Maybe SV) String) -- ^ A new array, the contents are initialized with the given value, if any, or the custom lambda given
| ArrayMutate ArrayIndex SV SV -- ^ An array created by mutating another array at a given cell
| ArrayMerge SV ArrayIndex ArrayIndex -- ^ An array created by symbolically merging two other arrays
deriving G.Data
instance Show ArrayContext where
show (ArrayFree (Left Nothing)) = " initialized with random elements"
show (ArrayFree (Left (Just sv))) = " initialized with " ++ show sv
show (ArrayFree (Right lambda)) = " initialized with " ++ show lambda
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 SV