---------------------------------------------------------------------------- -- | -- Module : Data.SBV.SMT.SMTLib2 -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- -- Conversion of symbolic programs to SMTLib format, Using v2 of the standard ----------------------------------------------------------------------------- {-# LANGUAGE PatternGuards #-} module Data.SBV.SMT.SMTLib2(cvt, addNonEqConstraints) where import Data.Bits (bit) import Data.Char (intToDigit) import Data.Function (on) import Data.Ord (comparing) import qualified Data.Foldable as F (toList) import qualified Data.Map as M import qualified Data.IntMap as IM import qualified Data.Set as Set import Data.List (intercalate, partition, groupBy, sortBy) import Numeric (showIntAtBase, showHex) import Data.SBV.BitVectors.AlgReals import Data.SBV.BitVectors.Data import Data.SBV.BitVectors.PrettyNum (showSMTFloat, showSMTDouble, smtRoundingMode) -- | Add constraints to generate /new/ models. This function is used to query the SMT-solver, while -- disallowing a previous model. addNonEqConstraints :: RoundingMode -> [(Quantifier, NamedSymVar)] -> [[(String, CW)]] -> SMTLibPgm -> Maybe String addNonEqConstraints rm qinps allNonEqConstraints (SMTLibPgm _ (aliasTable, pre, post)) | null allNonEqConstraints = Just $ intercalate "\n" $ pre ++ post | null refutedModel = Nothing | True = Just $ intercalate "\n" $ pre ++ [ "; --- refuted-models ---" ] ++ refutedModel ++ post where refutedModel = concatMap (nonEqs rm) (map (map intName) nonEqConstraints) intName (s, c) | Just sw <- s `lookup` aliasTable = (show sw, c) | True = (s, c) -- with existentials, we only add top-level existentials to the refuted-models list nonEqConstraints = filter (not . null) $ map (filter (\(s, _) -> s `elem` topUnivs)) allNonEqConstraints topUnivs = [s | (_, (_, s)) <- takeWhile (\p -> fst p == EX) qinps] nonEqs :: RoundingMode -> [(String, CW)] -> [String] nonEqs rm scs = format $ interp ps ++ disallow (map eqClass uninterpClasses) where (ups, ps) = partition (isUninterpreted . snd) scs format [] = [] format [m] = ["(assert " ++ m ++ ")"] format (m:ms) = ["(assert (or " ++ m] ++ map (" " ++) ms ++ [" ))"] -- Regular (or interpreted) sorts simply get a constraint that we disallow the current assignment interp = map $ nonEq rm -- Determine the equivalnce classes of uninterpreted sorts: uninterpClasses = filter (\l -> length l > 1) -- Only need this class if it has at least two members . map (map fst) -- throw away sorts, we only need the names . groupBy ((==) `on` snd) -- make sure they belong to the same sort and have the same value . sortBy (comparing snd) -- sort them according to their sorts first $ ups -- take the uninterpreted sorts -- Uninterpreted sorts get a constraint that says the equivalence classes as determined by the solver are disallowed: eqClass :: [String] -> String eqClass [] = error "SBV.allSat.nonEqs: Impossible happened, disallow received an empty list" eqClass cs = "(= " ++ unwords cs ++ ")" -- Now, take the conjunction of equivalence classes and assert it's negation: disallow = map $ \ec -> "(not " ++ ec ++ ")" nonEq :: RoundingMode -> (String, CW) -> String nonEq rm (s, c) = "(not (= " ++ s ++ " " ++ cvtCW rm c ++ "))" tbd :: String -> a tbd e = error $ "SBV.SMTLib2: Not-yet-supported: " ++ e -- | Translate a problem into an SMTLib2 script cvt :: RoundingMode -- ^ User selected rounding mode to be used for floating point arithmetic -> Maybe Logic -- ^ SMT-Lib logic, if requested by the user -> SolverCapabilities -- ^ capabilities of the current solver -> Set.Set Kind -- ^ kinds used -> Bool -- ^ is this a sat problem? -> [String] -- ^ extra comments to place on top -> [(Quantifier, NamedSymVar)] -- ^ inputs -> [Either SW (SW, [SW])] -- ^ skolemized version inputs -> [(SW, CW)] -- ^ constants -> [((Int, Kind, Kind), [SW])] -- ^ auto-generated tables -> [(Int, ArrayInfo)] -- ^ user specified arrays -> [(String, SBVType)] -- ^ uninterpreted functions/constants -> [(String, [String])] -- ^ user given axioms -> SBVPgm -- ^ assignments -> [SW] -- ^ extra constraints -> SW -- ^ output variable -> ([String], [String]) cvt rm smtLogic solverCaps kindInfo isSat comments inputs skolemInps consts tbls arrs uis axs (SBVPgm asgnsSeq) cstrs out = (pre, []) where -- the logic is an over-approaximation hasInteger = KUnbounded `Set.member` kindInfo hasReal = KReal `Set.member` kindInfo hasFloat = KFloat `Set.member` kindInfo hasDouble = KDouble `Set.member` kindInfo hasBVs = not $ null [() | KBounded{} <- Set.toList kindInfo] sorts = [s | KUninterpreted s <- Set.toList kindInfo] logic | Just l <- smtLogic = ["(set-logic " ++ show l ++ ") ; NB. User specified."] | hasDouble || hasFloat -- NB. We don't check for quantifiers here, we probably should.. = if hasBVs then ["(set-logic QF_FPABV)"] else ["(set-logic QF_FPA)"] | hasInteger || hasReal || not (null sorts) = case mbDefaultLogic solverCaps of Nothing -> ["; Has unbounded values (Int/Real) or sorts; no logic specified."] -- combination, let the solver pick Just l -> ["(set-logic " ++ l ++ ")"] | True = ["(set-logic " ++ qs ++ as ++ ufs ++ "BV)"] where qs | null foralls && null axs = "QF_" -- axioms are likely to contain quantifiers | True = "" as | null arrs = "" | True = "A" ufs | null uis && null tbls = "" -- we represent tables as UFs | True = "UF" getModels | supportsProduceModels solverCaps = ["(set-option :produce-models true)"] | True = [] pre = ["; Automatically generated by SBV. Do not edit."] ++ map ("; " ++) comments ++ getModels ++ logic ++ [ "; --- uninterpreted sorts ---" ] ++ map declSort sorts ++ [ "; --- literal constants ---" ] ++ concatMap (declConst (supportsMacros solverCaps)) consts ++ [ "; --- skolem constants ---" ] ++ [ "(declare-fun " ++ show s ++ " " ++ swFunType ss s ++ ")" ++ userName s | Right (s, ss) <- skolemInps] ++ [ "; --- constant tables ---" ] ++ concatMap constTable constTables ++ [ "; --- skolemized tables ---" ] ++ map (skolemTable (unwords (map swType foralls))) skolemTables ++ [ "; --- arrays ---" ] ++ concat arrayConstants ++ [ "; --- uninterpreted constants ---" ] ++ concatMap declUI uis ++ [ "; --- user given axioms ---" ] ++ map declAx axs ++ [ "; --- formula ---" ] ++ [if null foralls then "(assert ; no quantifiers" else "(assert (forall (" ++ intercalate "\n " ["(" ++ show s ++ " " ++ swType s ++ ")" | s <- foralls] ++ ")"] ++ map (letAlign . mkLet) asgns ++ map letAlign (if null delayedEqualities then [] else ("(and " ++ deH) : map (align 5) deTs) ++ [ impAlign (letAlign assertOut) ++ replicate noOfCloseParens ')' ] noOfCloseParens = length asgns + (if null foralls then 1 else 2) + (if null delayedEqualities then 0 else 1) (constTables, skolemTables) = ([(t, d) | (t, Left d) <- allTables], [(t, d) | (t, Right d) <- allTables]) allTables = [(t, genTableData rm skolemMap (not (null foralls), forallArgs) (map fst consts) t) | t <- tbls] (arrayConstants, allArrayDelayeds) = unzip $ map (declArray (not (null foralls)) (map fst consts) skolemMap) arrs delayedEqualities@(~(deH:deTs)) = concatMap snd skolemTables ++ concat allArrayDelayeds foralls = [s | Left s <- skolemInps] forallArgs = concatMap ((" " ++) . show) foralls letAlign s | null foralls = " " ++ s | True = " " ++ s impAlign s | null delayedEqualities = s | True = " " ++ s align n s = replicate n ' ' ++ s -- if sat, we assert cstrs /\ out -- if prove, we assert ~(cstrs => out) = cstrs /\ not out assertOut | null cstrs = o | True = "(and " ++ unwords (map mkConj cstrs ++ [o]) ++ ")" where mkConj = cvtSW skolemMap o | isSat = mkConj out | True = "(not " ++ mkConj out ++ ")" skolemMap = M.fromList [(s, ss) | Right (s, ss) <- skolemInps, not (null ss)] tableMap = IM.fromList $ map mkConstTable constTables ++ map mkSkTable skolemTables where mkConstTable (((t, _, _), _), _) = (t, "table" ++ show t) mkSkTable (((t, _, _), _), _) = (t, "table" ++ show t ++ forallArgs) asgns = F.toList asgnsSeq mkLet (s, e) = "(let ((" ++ show s ++ " " ++ cvtExp rm skolemMap tableMap e ++ "))" declConst useDefFun (s, c) | useDefFun = ["(define-fun " ++ varT ++ " " ++ cvtCW rm c ++ ")"] | True = [ "(declare-fun " ++ varT ++ ")" , "(assert (= " ++ show s ++ " " ++ cvtCW rm c ++ "))" ] where varT = show s ++ " " ++ swFunType [] s declSort s = "(declare-sort " ++ s ++ " 0)" userName s = case s `lookup` map snd inputs of Just u | show s /= u -> " ; tracks user variable " ++ show u _ -> "" declUI :: (String, SBVType) -> [String] declUI (i, t) = ["(declare-fun " ++ i ++ " " ++ cvtType t ++ ")"] -- NB. We perform no check to as to whether the axiom is meaningful in any way. declAx :: (String, [String]) -> String declAx (nm, ls) = (";; -- user given axiom: " ++ nm ++ "\n") ++ intercalate "\n" ls constTable :: (((Int, Kind, Kind), [SW]), [String]) -> [String] constTable (((i, ak, rk), _elts), is) = decl : map wrap is where t = "table" ++ show i decl = "(declare-fun " ++ t ++ " (" ++ smtType ak ++ ") " ++ smtType rk ++ ")" wrap s = "(assert " ++ s ++ ")" skolemTable :: String -> (((Int, Kind, Kind), [SW]), [String]) -> String skolemTable qsIn (((i, ak, rk), _elts), _) = decl where qs = if null qsIn then "" else qsIn ++ " " t = "table" ++ show i decl = "(declare-fun " ++ t ++ " (" ++ qs ++ smtType ak ++ ") " ++ smtType rk ++ ")" -- Left if all constants, Right if otherwise genTableData :: RoundingMode -> SkolemMap -> (Bool, String) -> [SW] -> ((Int, Kind, Kind), [SW]) -> Either [String] [String] genTableData rm skolemMap (_quantified, args) consts ((i, aknd, _), elts) | null post = Left (map (topLevel . snd) pre) | True = Right (map (nested . snd) (pre ++ post)) where ssw = cvtSW skolemMap (pre, post) = partition fst (zipWith mkElt elts [(0::Int)..]) t = "table" ++ show i mkElt x k = (isReady, (idx, ssw x)) where idx = cvtCW rm (mkConstCW aknd k) isReady = x `elem` consts topLevel (idx, v) = "(= (" ++ t ++ " " ++ idx ++ ") " ++ v ++ ")" nested (idx, v) = "(= (" ++ t ++ args ++ " " ++ idx ++ ") " ++ v ++ ")" -- TODO: We currently do not support non-constant arrays when quantifiers are present, as -- we might have to skolemize those. Implement this properly. -- The difficulty is with the ArrayReset/Mutate/Merge: We have to postpone an init if -- the components are themselves postponed, so this cannot be implemented as a simple map. declArray :: Bool -> [SW] -> SkolemMap -> (Int, ArrayInfo) -> ([String], [String]) declArray quantified consts skolemMap (i, (_, (aKnd, bKnd), ctx)) = (adecl : map wrap pre, map snd post) where topLevel = not quantified || case ctx of ArrayFree Nothing -> True ArrayFree (Just sw) -> sw `elem` consts ArrayReset _ sw -> sw `elem` consts ArrayMutate _ a b -> all (`elem` consts) [a, b] ArrayMerge c _ _ -> c `elem` consts (pre, post) = partition fst ctxInfo nm = "array_" ++ show i ssw sw | topLevel || sw `elem` consts = cvtSW skolemMap sw | True = tbd "Non-constant array initializer in a quantified context" adecl = "(declare-fun " ++ nm ++ " () (Array " ++ smtType aKnd ++ " " ++ smtType bKnd ++ "))" ctxInfo = case ctx of ArrayFree Nothing -> [] ArrayFree (Just sw) -> declA sw ArrayReset _ sw -> declA sw ArrayMutate j a b -> [(all (`elem` consts) [a, b], "(= " ++ nm ++ " (store array_" ++ show j ++ " " ++ ssw a ++ " " ++ ssw b ++ "))")] ArrayMerge t j k -> [(t `elem` consts, "(= " ++ nm ++ " (ite " ++ ssw t ++ " array_" ++ show j ++ " array_" ++ show k ++ "))")] declA sw = let iv = nm ++ "_freeInitializer" in [ (True, "(declare-fun " ++ iv ++ " () " ++ smtType aKnd ++ ")") , (sw `elem` consts, "(= (select " ++ nm ++ " " ++ iv ++ ") " ++ ssw sw ++ ")") ] wrap (False, s) = s wrap (True, s) = "(assert " ++ s ++ ")" swType :: SW -> String swType s = smtType (kindOf s) swFunType :: [SW] -> SW -> String swFunType ss s = "(" ++ unwords (map swType ss) ++ ") " ++ swType s smtType :: Kind -> String smtType KBool = "Bool" smtType (KBounded _ sz) = "(_ BitVec " ++ show sz ++ ")" smtType KUnbounded = "Int" smtType KReal = "Real" smtType KFloat = "(_ FP 8 24)" smtType KDouble = "(_ FP 11 53)" smtType (KUninterpreted s) = s cvtType :: SBVType -> String cvtType (SBVType []) = error "SBV.SMT.SMTLib2.cvtType: internal: received an empty type!" cvtType (SBVType xs) = "(" ++ unwords (map smtType body) ++ ") " ++ smtType ret where (body, ret) = (init xs, last xs) type SkolemMap = M.Map SW [SW] type TableMap = IM.IntMap String cvtSW :: SkolemMap -> SW -> String cvtSW skolemMap s | Just ss <- s `M.lookup` skolemMap = "(" ++ show s ++ concatMap ((" " ++) . show) ss ++ ")" | True = show s -- Carefully code hex numbers, SMTLib is picky about lengths of hex constants. For the time -- being, SBV only supports sizes that are multiples of 4, but the below code is more robust -- in case of future extensions to support arbitrary sizes. hex :: Int -> Integer -> String hex 1 v = "#b" ++ show v hex sz v | sz `mod` 4 == 0 = "#x" ++ pad (sz `div` 4) (showHex v "") | True = "#b" ++ pad sz (showBin v "") where pad n s = replicate (n - length s) '0' ++ s showBin = showIntAtBase 2 intToDigit cvtCW :: RoundingMode -> CW -> String cvtCW rm x | isBoolean x, CWInteger w <- cwVal x = if w == 0 then "false" else "true" | isUninterpreted x, CWUninterpreted s <- cwVal x = s | isReal x, CWAlgReal r <- cwVal x = algRealToSMTLib2 r | isFloat x, CWFloat f <- cwVal x = showSMTFloat rm f | isDouble x, CWDouble d <- cwVal x = showSMTDouble rm d | not (isBounded x), CWInteger w <- cwVal x = if w >= 0 then show w else "(- " ++ show (abs w) ++ ")" | not (hasSign x) , CWInteger w <- cwVal x = hex (intSizeOf x) w -- signed numbers (with 2's complement representation) is problematic -- since there's no way to put a bvneg over a positive number to get minBound.. -- Hence, we punt and use binary notation in that particular case | hasSign x , CWInteger w <- cwVal x = if w == negate (2 ^ intSizeOf x) then mkMinBound (intSizeOf x) else negIf (w < 0) $ hex (intSizeOf x) (abs w) | True = error $ "SBV.cvtCW: Impossible happened: Kind/Value disagreement on: " ++ show (kindOf x, x) negIf :: Bool -> String -> String negIf True a = "(bvneg " ++ a ++ ")" negIf False a = a -- anamoly at the 2's complement min value! Have to use binary notation here -- as there is no positive value we can provide to make the bvneg work.. (see above) mkMinBound :: Int -> String mkMinBound i = "#b1" ++ replicate (i-1) '0' getTable :: TableMap -> Int -> String getTable m i | Just tn <- i `IM.lookup` m = tn | True = error $ "SBV.SMTLib2: Cannot locate table " ++ show i cvtExp :: RoundingMode -> SkolemMap -> TableMap -> SBVExpr -> String cvtExp rm skolemMap tableMap expr@(SBVApp _ arguments) = sh expr where ssw = cvtSW skolemMap bvOp = all isBounded arguments intOp = any isInteger arguments realOp = any isReal arguments doubleOp = any isDouble arguments floatOp = any isFloat arguments boolOp = all isBoolean arguments bad | intOp = error $ "SBV.SMTLib2: Unsupported operation on unbounded integers: " ++ show expr | True = error $ "SBV.SMTLib2: Unsupported operation on real values: " ++ show expr ensureBVOrBool = bvOp || boolOp || bad ensureBV = bvOp || bad addRM s = s ++ " " ++ smtRoundingMode rm lift2 o _ [x, y] = "(" ++ o ++ " " ++ x ++ " " ++ y ++ ")" lift2 o _ sbvs = error $ "SBV.SMTLib2.sh.lift2: Unexpected arguments: " ++ show (o, sbvs) -- lift a binary operation with rounding-mode added; used for floating-point arithmetic lift2WM o | doubleOp || floatOp = lift2 (addRM o) | True = lift2 o lift2B bOp vOp | boolOp = lift2 bOp | True = lift2 vOp lift1B bOp vOp | boolOp = lift1 bOp | True = lift1 vOp eqBV sgn sbvs | boolOp = lift2 "=" sgn sbvs | True = "(= " ++ lift2 "bvcomp" sgn sbvs ++ " #b1)" neqBV sgn sbvs = "(not " ++ eqBV sgn sbvs ++ ")" equal sgn sbvs | doubleOp = lift2 "==" sgn sbvs | floatOp = lift2 "==" sgn sbvs | True = lift2 "=" sgn sbvs notEqual sgn sbvs | doubleOp = "(not " ++ equal sgn sbvs ++ ")" | floatOp = "(not " ++ equal sgn sbvs ++ ")" | True = lift2 "distinct" sgn sbvs lift2S oU oS sgn = lift2 (if sgn then oS else oU) sgn lift1 o _ [x] = "(" ++ o ++ " " ++ x ++ ")" lift1 o _ sbvs = error $ "SBV.SMT.SMTLib2.sh.lift1: Unexpected arguments: " ++ show (o, sbvs) sh (SBVApp Ite [a, b, c]) = "(ite " ++ ssw a ++ " " ++ ssw b ++ " " ++ ssw c ++ ")" sh (SBVApp (LkUp (t, aKnd, _, l) i e) []) | needsCheck = "(ite " ++ cond ++ ssw e ++ " " ++ lkUp ++ ")" | True = lkUp where needsCheck = case aKnd of KBool -> (2::Integer) > fromIntegral l KBounded _ n -> (2::Integer)^n > fromIntegral l KUnbounded -> True KReal -> error "SBV.SMT.SMTLib2.cvtExp: unexpected real valued index" KFloat -> error "SBV.SMT.SMTLib2.cvtExp: unexpected float valued index" KDouble -> error "SBV.SMT.SMTLib2.cvtExp: unexpected double valued index" KUninterpreted s -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected uninterpreted valued index: " ++ s lkUp = "(" ++ getTable tableMap t ++ " " ++ ssw i ++ ")" cond | hasSign i = "(or " ++ le0 ++ " " ++ gtl ++ ") " | True = gtl ++ " " (less, leq) = case aKnd of KBool -> error "SBV.SMT.SMTLib2.cvtExp: unexpected boolean valued index" KBounded{} -> if hasSign i then ("bvslt", "bvsle") else ("bvult", "bvule") KUnbounded -> ("<", "<=") KReal -> ("<", "<=") KFloat -> ("<", "<=") KDouble -> ("<", "<=") KUninterpreted s -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected uninterpreted valued index: " ++ s mkCnst = cvtCW rm . mkConstCW (kindOf i) le0 = "(" ++ less ++ " " ++ ssw i ++ " " ++ mkCnst 0 ++ ")" gtl = "(" ++ leq ++ " " ++ mkCnst l ++ " " ++ ssw i ++ ")" sh (SBVApp (ArrEq i j) []) = "(= array_" ++ show i ++ " array_" ++ show j ++")" sh (SBVApp (ArrRead i) [a]) = "(select array_" ++ show i ++ " " ++ ssw a ++ ")" sh (SBVApp (Uninterpreted nm) []) = nm sh (SBVApp (Uninterpreted nm) args) = "(" ++ nm' ++ " " ++ unwords (map ssw args) ++ ")" where -- slight hack needed here to take advantage of custom floating-point functions.. sigh. fpSpecials = ["squareRoot", "fusedMA"] nm' | (floatOp || doubleOp) && (nm `elem` fpSpecials) = addRM nm | True = nm sh (SBVApp (Extract 0 0) [a]) -- special SInteger -> SReal conversion | kindOf a == KUnbounded = "(to_real " ++ ssw a ++ ")" sh (SBVApp (Extract i j) [a]) | ensureBV = "((_ extract " ++ show i ++ " " ++ show j ++ ") " ++ ssw a ++ ")" sh (SBVApp (Rol i) [a]) | bvOp = rot ssw "rotate_left" i a | intOp = sh (SBVApp (Shl i) [a]) -- Haskell treats rotateL as shiftL for unbounded values | True = bad sh (SBVApp (Ror i) [a]) | bvOp = rot ssw "rotate_right" i a | intOp = sh (SBVApp (Shr i) [a]) -- Haskell treats rotateR as shiftR for unbounded values | True = bad sh (SBVApp (Shl i) [a]) | bvOp = shft rm ssw "bvshl" "bvshl" i a | i < 0 = sh (SBVApp (Shr (-i)) [a]) -- flip sign/direction | intOp = "(* " ++ ssw a ++ " " ++ show (bit i :: Integer) ++ ")" -- Implement shiftL by multiplication by 2^i | True = bad sh (SBVApp (Shr i) [a]) | bvOp = shft rm ssw "bvlshr" "bvashr" i a | i < 0 = sh (SBVApp (Shl (-i)) [a]) -- flip sign/direction | intOp = "(div " ++ ssw a ++ " " ++ show (bit i :: Integer) ++ ")" -- Implement shiftR by division by 2^i | True = bad sh (SBVApp op args) | Just f <- lookup op smtBVOpTable, ensureBVOrBool = f (any hasSign args) (map ssw args) where -- The first 4 operators below do make sense for Integer's in Haskell, but there's -- no obvious counterpart for them in the SMTLib translation. -- TODO: provide support for these. smtBVOpTable = [ (And, lift2B "and" "bvand") , (Or, lift2B "or" "bvor") , (XOr, lift2B "xor" "bvxor") , (Not, lift1B "not" "bvnot") , (Join, lift2 "concat") ] sh inp@(SBVApp op args) | intOp, Just f <- lookup op smtOpIntTable = f True (map ssw args) | bvOp, Just f <- lookup op smtOpBVTable = f (any hasSign args) (map ssw args) | realOp, Just f <- lookup op smtOpRealTable = f (any hasSign args) (map ssw args) | floatOp || doubleOp, Just f <- lookup op smtOpFloatDoubleTable = f (any hasSign args) (map ssw args) | Just f <- lookup op uninterpretedTable = f (map ssw args) | True = error $ "SBV.SMT.SMTLib2.cvtExp.sh: impossible happened; can't translate: " ++ show inp where smtOpBVTable = [ (Plus, lift2 "bvadd") , (Minus, lift2 "bvsub") , (Times, lift2 "bvmul") , (Quot, lift2S "bvudiv" "bvsdiv") , (Rem, lift2S "bvurem" "bvsrem") , (Equal, eqBV) , (NotEqual, neqBV) , (LessThan, lift2S "bvult" "bvslt") , (GreaterThan, lift2S "bvugt" "bvsgt") , (LessEq, lift2S "bvule" "bvsle") , (GreaterEq, lift2S "bvuge" "bvsge") ] smtOpRealTable = smtIntRealShared ++ [ (Quot, lift2WM "/") ] smtOpIntTable = smtIntRealShared ++ [ (Quot, lift2 "div") , (Rem, lift2 "mod") ] smtOpFloatDoubleTable = smtIntRealShared ++ [(Quot, lift2WM "/")] smtIntRealShared = [ (Plus, lift2WM "+") , (Minus, lift2WM "-") , (Times, lift2WM "*") , (Equal, equal) , (NotEqual, notEqual) , (LessThan, lift2S "<" "<") , (GreaterThan, lift2S ">" ">") , (LessEq, lift2S "<=" "<=") , (GreaterEq, lift2S ">=" ">=") ] -- equality is the only thing that works on uninterpreted sorts uninterpretedTable = [ (Equal, lift2S "=" "=" True) , (NotEqual, lift2S "distinct" "distinct" True) ] rot :: (SW -> String) -> String -> Int -> SW -> String rot ssw o c x = "((_ " ++ o ++ " " ++ show c ++ ") " ++ ssw x ++ ")" shft :: RoundingMode -> (SW -> String) -> String -> String -> Int -> SW -> String shft rm ssw oW oS c x = "(" ++ o ++ " " ++ ssw x ++ " " ++ cvtCW rm c' ++ ")" where s = hasSign x c' = mkConstCW (kindOf x) c o = if s then oS else oW