sbv-14.2: Data/SBV/SMT/SMTLib2.hs
-----------------------------------------------------------------------------
-- |
-- 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 NamedFieldPuns #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ViewPatterns #-}
{-# OPTIONS_GHC -Wall -Werror #-}
module Data.SBV.SMT.SMTLib2(cvt, cvtExp, cvtCV, cvtInc, declUserFuns, constructTables, setSMTOption) where
import Data.List (intercalate, partition, nub, elemIndex)
import Data.Maybe (listToMaybe, catMaybes)
import qualified Data.Foldable as F (toList, foldl')
import qualified Data.Map.Strict as M
import qualified Data.IntMap.Strict as IM
import Data.Set (Set)
import qualified Data.Set as Set
import qualified Data.Text as T
import Data.Text (Text)
import Data.SBV.Core.Data
import Data.SBV.Core.Kind (smtType, needsFlattening, expandKinds, substituteADTVars)
import Data.SBV.Control.Types
import Data.SBV.SMT.Utils
import Data.SBV.Core.Symbolic ( QueryContext(..), SetOp(..), getUserName, getUserName', getSV, regExpToSMTString, NROp(..)
, SMTDef(..), SMTLambda(..), ResultInp(..), ProgInfo(..), SpecialRelOp(..), ADTOp(..)
)
import Data.SBV.Utils.PrettyNum (smtRoundingMode, cvToSMTLib)
import Data.SBV.Utils.Lib (showText)
import qualified Data.Generics.Uniplate.Data as G
import qualified Data.Graph as DG
-- Check that all ADT subkinds are registered. If not, tell the user to do so
-- NB. This should not be the case as we "automatically" register the subkinds
-- as we encounter them. But this is mostly a if-something-goes-wrong check.
checkKinds :: [Kind] -> Maybe String
checkKinds ks = case [m | m@(n, _) <- apps, n `notElem` defs] of
[] -> Nothing
xs@(f:_) -> let (h, cnt) = case [p | p@(_, i) <- xs, i > 0] of
(p:_) -> p
_ -> f
plu | length xs > 1 = "s are"
| True = " is"
msg = T.unlines $ [
"Data.SBV.mkSymbolic: Impossible happened! Unregistered subkinds."
, "***"
, "*** The following kind" <> plu <> " not registered: " <> T.unwords (map (T.pack . fst) xs)
, "***"
, "*** Please report this as a bug."
, "***"
, "*** As a workaround, you can try registering each ADT subfield, using: "
, "***"
, "*** {-# LANGUAGE TypeApplications #-}"
, "***"
, "*** import Data.Proxy"
, "*** registerType (Proxy @" <> mkProxy h cnt <> ")"
]
++ extras cnt
++ [ "***"
, "*** Even if the workaround does the trick for you, it should not"
, "*** be needed. Please report this as a bug!"
]
in Just $ T.unpack msg
where apps = nub [(n, length as) | KApp n as <- concatMap expandKinds ks]
defs = nub [n | KADT n _ _ <- ks]
mkProxy h 0 = T.pack h
mkProxy h n = "(" <> T.unwords (T.pack h : replicate n "Integer") <> ")"
extras 0 = []
extras _ = [ "***"
, "*** NB. You can use any base type as arguments, not just 'Integer'."
, "*** It does not need to match the actual use cases, just one instance"
, "*** at some base type is sufficent."
]
-- | Translate a problem into an SMTLib2 script
cvt :: SMTLibConverter (Text, Text)
cvt ctx curProgInfo kindInfo isSat comments allInputs (_, consts) tbls uis defs (SBVPgm asgnsSeq) cstrs out cfg
| Just s <- checkKinds allKinds
= error s
| True
= (T.intercalate "\n" pgm, T.intercalate "\n" exportedDefs)
where allKinds = Set.toList kindInfo
-- Below can simply be defined as: nub (sort (G.universeBi asgnsSeq))
-- Alas, it turns out this is really expensive when we have nested lambdas, so we do an explicit walk
allTopOps = Set.toList $ F.foldl' (\sofar (_, SBVApp o _) -> Set.insert o sofar) Set.empty asgnsSeq
hasInteger = KUnbounded `Set.member` kindInfo
hasArrays = not (null [() | KArray{} <- allKinds])
hasNonBVArrays = not (null [() | KArray k1 k2 <- allKinds, not (isBounded k1 && isBounded k2)])
hasReal = KReal `Set.member` kindInfo
hasFP = not (null [() | KFP{} <- allKinds])
|| KFloat `Set.member` kindInfo
|| KDouble `Set.member` kindInfo
hasString = KString `Set.member` kindInfo
hasRegExp = (not . null) [() | (_ :: RegExOp) <- G.universeBi allTopOps]
hasChar = KChar `Set.member` kindInfo
hasRounding = any isRoundingMode allKinds
hasBVs = not (null [() | KBounded{} <- allKinds])
adtsNoRM = [(s, ps, cs) | k@(KADT s ps cs) <- allKinds, not (isRoundingMode k)]
tupleArities = findTupleArities kindInfo
hasOverflows = (not . null) [() | (_ :: OvOp) <- G.universeBi allTopOps]
hasQuantBools = (not . null) [() | QuantifiedBool{} <- G.universeBi allTopOps]
hasList = any isList kindInfo
hasSets = any isSet kindInfo
hasTuples = not . null $ tupleArities
hasRational = any isRational kindInfo
hasADTs = not . null $ adtsNoRM
solverCaps = capabilities (solver cfg)
(needsQuantifiers, needsSpecialRels) = case curProgInfo of
ProgInfo hasQ srs tcs -> (hasQ, not (null srs && null tcs))
-- Is there a reason why we can't handle this problem?
-- NB. There's probably a lot more checking we can do here, but this is a start:
doesntHandle = listToMaybe [nope w | (w, have, need) <- checks, need && not (have solverCaps)]
where checks = [ ("data types", supportsDataTypes, hasTuples || hasADTs)
, ("set operations", supportsSets, hasSets)
, ("bit vectors", supportsBitVectors, hasBVs)
, ("special relations", supportsSpecialRels, needsSpecialRels)
, ("needs quantifiers", supportsQuantifiers, needsQuantifiers)
, ("unbounded integers", supportsUnboundedInts, hasInteger)
, ("algebraic reals", supportsReals, hasReal)
, ("floating-point numbers", supportsIEEE754, hasFP)
, ("has data-types/sorts", supportsADTs, not (null adtsNoRM))
]
nope w = [ "*** Given problem requires support for " <> T.pack w
, "*** But the chosen solver (" <> showText (name (solver cfg)) <> ") doesn't support this feature."
]
-- Some cases require all, some require none.
setAll reason = [logicString cfg Logic_ALL <> " ; " <> T.pack reason <> ", using catch-all."]
-- Determining the logic is surprisingly tricky!
logic :: [Text]
logic
-- user told us what to do: so just take it:
| Just l <- case [l | SetLogic l <- solverSetOptions cfg] of
[] -> Nothing
[l] -> Just l
ls -> error $ T.unpack $ T.unlines [ ""
, "*** Only one setOption call to 'setLogic' is allowed, found: " <> showText (length ls)
, "*** " <> T.unwords (map showText ls)
]
= case l of
Logic_NONE -> ["; NB. Not setting the logic per user request of Logic_NONE"]
_ -> [logicString cfg l <> " ; NB. User specified."]
-- There's a reason why we can't handle this problem:
| Just cantDo <- doesntHandle
= let msg = T.unlines $ [ ""
, "*** SBV is unable to choose a proper solver configuration:"
, "***"
]
<> cantDo
<> [ "***"
, "*** Please report this as a feature request, either for SBV or the backend solver."
]
in error $ T.unpack msg
-- Otherwise, we try to determine the most suitable logic.
-- NB. This isn't really fool proof!
-- we never set QF_S (ALL seems to work better in all cases)
| needsSpecialRels = ["; has special relations, no logic set."]
-- Things that require ALL
| hasInteger = setAll "has unbounded values"
| hasRational = setAll "has rational values"
| hasReal = setAll "has algebraic reals"
| hasADTs = setAll "has user-defined data-types"
| hasNonBVArrays = setAll "has non-bitvector arrays"
| hasTuples = setAll "has tuples"
| hasSets = setAll "has sets"
| hasList = setAll "has lists"
| hasChar = setAll "has chars"
| hasString = setAll "has strings"
| hasRegExp = setAll "has regular expressions"
| hasOverflows = setAll "has overflow checks"
| hasQuantBools = setAll "has quantified booleans"
| hasFP || hasRounding
= if needsQuantifiers
then [logicString cfg Logic_ALL]
else [logicString cfg (if hasBVs then QF_FPBV else QF_FP)]
-- If we're in a user query context, we'll pick ALL, otherwise
-- we'll stick to some bit-vector logic based on what we see in the problem.
-- This is controversial, but seems to work well in practice.
| True
= case ctx of
QueryExternal -> [logicString cfg Logic_ALL <> " ; external query, using all logics."]
QueryInternal -> if supportsBitVectors solverCaps
then [logicString cfg picked]
else [logicString cfg Logic_ALL] -- fall-thru
where picked
| needsQuantifiers = Logic_ALL
| True = case (hasArrays, null uis && null tbls) of
(False, False) -> QF_UFBV
(False, True) -> QF_BV
(True, False) -> QF_AUFBV
(True, True) -> QF_ABV
-- SBV always requires the production of models!
getModels :: [Text]
getModels = "(set-option :produce-models true)"
: concat [map T.pack flattenConfig | any needsFlattening kindInfo, Just flattenConfig <- [supportsFlattenedModels solverCaps]]
-- process all other settings we're given. If an option cannot be repeated, we only take the last one.
userSettings = map (setSMTOption cfg) $ filter (not . isLogic) $ foldr comb [] $ solverSetOptions cfg
where -- Logic is already processed, so drop it:
isLogic SetLogic{} = True
isLogic _ = False
-- SBV sets diagnostic-output channel on some solvers. If the user also gives it, let's just
-- take it by only taking the last one
isDiagOutput DiagnosticOutputChannel{} = True
isDiagOutput _ = False
comb o rest
| isDiagOutput o && any isDiagOutput rest = rest
| True = o : rest
settings = userSettings -- NB. Make sure this comes first!
<> getModels
<> logic
(inputs, trackerVars)
= case allInputs of
ResultTopInps ists -> ists
ResultLamInps ps -> error $ unlines [ ""
, "*** Data.SBV.smtLib2: Unexpected lambda inputs in conversion"
, "***"
, "*** Saw: " ++ show ps
]
pgm = map (T.pack . ("; " <>)) comments
<> settings
<> [ "; --- tuples ---" ]
<> concatMap declTuple tupleArities
<> [ "; --- sums ---" ]
<> (if containsRationals kindInfo then declRationals else [])
<> [ "; --- ADTs --- " | not (null adtsNoRM)]
<> declADT adtsNoRM
<> [ "; --- literal constants ---" ]
<> concatMap (declConst cfg) consts
<> [ "; --- top level inputs ---"]
<> concat [declareFun s (SBVType [kindOf s]) (userName s) | var <- inputs, let s = getSV var]
<> [ "; --- optimization tracker variables ---" | not (null trackerVars) ]
<> concat [declareFun s (SBVType [kindOf s]) (Just ("tracks " <> getUserName var)) | var <- trackerVars, let s = getSV var]
<> [ "; --- constant tables ---" ]
<> concatMap (uncurry (:) . mkTable) constTables
<> [ "; --- non-constant tables ---" ]
<> map nonConstTable nonConstTables
<> [ "; --- uninterpreted constants ---" ]
<> concatMap (declUI curProgInfo) uis
<> [ "; --- user defined functions ---"]
<> userDefs
<> [ "; --- assignments ---" ]
<> concatMap (declDef curProgInfo cfg tableMap) asgns
<> [ "; --- delayedEqualities ---" ]
<> map (\s -> "(assert " <> s <> ")") delayedEqualities
<> [ "; --- formula ---" ]
<> finalAssert
userDefs = declUserFuns defs
exportedDefs
| null userDefs
= ["; No calls to 'smtFunction' found."]
| True
= "; Automatically generated by SBV. Do not modify!" : userDefs
(tableMap, constTables, nonConstTables) = constructTables consts tbls
delayedEqualities = concatMap snd nonConstTables
finalAssert
| noConstraints = []
| True = map (\(attr, v) -> "(assert " <> addAnnotations attr (mkLiteral v) <> ")") hardAsserts
<> map (\(attr, v) -> "(assert-soft " <> addAnnotations attr (mkLiteral v) <> ")") softAsserts
where mkLiteral (Left v) = cvtSV v
mkLiteral (Right v) = "(not " <> cvtSV v <> ")"
(noConstraints, assertions) = finalAssertions
hardAsserts, softAsserts :: [([(String, String)], Either SV SV)]
hardAsserts = [(attr, v) | (False, attr, v) <- assertions]
softAsserts = [(attr, v) | (True, attr, v) <- assertions]
finalAssertions :: (Bool, [(Bool, [(String, String)], Either SV SV)]) -- If Left: positive, Right: negative
finalAssertions
| null finals = (True, [(False, [], Left trueSV)])
| True = (False, finals)
where finals = cstrs' ++ maybe [] (\r -> [(False, [], r)]) mbO
cstrs' = [(isSoft, attrs, c') | (isSoft, attrs, c) <- F.toList cstrs, Just c' <- [pos c]]
mbO | isSat = pos out
| True = neg out
neg s
| s == falseSV = Nothing
| s == trueSV = Just $ Left falseSV
| True = Just $ Right s
pos s
| s == trueSV = Nothing
| s == falseSV = Just $ Left falseSV
| True = Just $ Left s
asgns = F.toList asgnsSeq
userNameMap = M.fromList $ map (\nSymVar -> (getSV nSymVar, getUserName' nSymVar)) inputs
userName s = case M.lookup s userNameMap of
Just u | show s /= u -> Just $ "tracks user variable " <> showText u
_ -> Nothing
-- | Declare ADTs
declADT :: [(String, [(String, Kind)], [(String, [Kind])])] -> [Text]
declADT = concatMap declGroup . DG.stronglyConnComp . map mkNode
where mkNode adt@(n, pks, cstrs) = (adt, n, [s | KApp s _ <- concatMap expandKinds (map snd pks ++ concatMap snd cstrs)])
declGroup (DG.AcyclicSCC d ) = singleADT d
declGroup (DG.CyclicSCC ds)
= case ds of
[] -> error "Data.SBV.declADT: Impossible happened: an empty cyclic group was returned!"
[d] -> singleADT d
_ -> multiADT ds
parParens :: [(String, Kind)] -> (Text, Text)
parParens [] = ("", "")
parParens ps = (" (par (" <> T.unwords (map (T.pack . fst) ps) <> ")", ")")
mkC (nm, []) = T.pack nm
mkC (nm, ts) = T.pack nm <> " " <> T.unwords ['(' `T.cons` mkF (nm <> "_" <> show i) t <> ")" | (i, t) <- zip [(1::Int)..] ts]
where mkF a t = "get" <> T.pack a <> " " <> smtType t
singleADT :: (String, [(String, Kind)], [(String, [Kind])]) -> [Text]
singleADT (tName, [], []) = ["(declare-sort " <> T.pack tName <> " 0) ; N.B. Uninterpreted sort."]
singleADT (tName, pks, cstrs) = ("; User defined ADT: " <> T.pack tName) : decl
where decl = ("(declare-datatype " <> T.pack tName <> parOpen <> " (")
: [" (" <> mkC c <> ")" | c <- cstrs]
<> ["))" <> parClose]
(parOpen, parClose) = parParens pks
multiADT :: [(String, [(String, Kind)], [(String, [Kind])])] -> [Text]
multiADT adts = ("; User defined mutually-recursive ADTs: " <> T.intercalate ", " (map (\(a, _, _) -> T.pack a) adts)) : decl
where decl = ("(declare-datatypes (" <> typeDecls <> ") (")
: concatMap adtBody adts
<> ["))"]
typeDecls = T.unwords ['(' `T.cons` T.pack name <> " " <> showText (length pks) <> ")" | (name, pks, _) <- adts]
adtBody (_, pks, cstrs) = body
where (parOpen, parClose) = parParens pks
body = (" " <> parOpen <> " (")
: [" (" <> mkC c <> ")" | c <- cstrs]
<> [" )" <> parClose]
-- | Declare tuple datatypes
--
-- eg:
--
-- @
-- (declare-datatypes ((SBVTuple2 2)) ((par (T1 T2)
-- ((mkSBVTuple2 (proj_1_SBVTuple2 T1)
-- (proj_2_SBVTuple2 T2))))))
-- @
declTuple :: Int -> [Text]
declTuple arity
| arity == 0 = ["(declare-datatypes ((SBVTuple0 0)) (((mkSBVTuple0))))"]
| arity == 1 = error "Data.SBV.declTuple: Unexpected one-tuple"
| True = (l1 <> "(par (" <> T.unwords [param i | i <- [1..arity]] <> ")")
: [pre i <> proj i <> post i | i <- [1..arity]]
where l1 = "(declare-datatypes ((SBVTuple" <> showText arity <> " " <> showText arity <> ")) ("
l2 = T.replicate (T.length l1) " " <> "((mkSBVTuple" <> showText arity <> " "
tab = T.replicate (T.length l2) " "
pre 1 = l2
pre _ = tab
proj i = "(proj_" <> showText i <> "_SBVTuple" <> showText arity <> " " <> param i <> ")"
post i = if i == arity then ")))))" else ""
param i = "T" <> showText i
-- | Find the set of tuple sizes to declare, eg (2-tuple, 5-tuple).
-- NB. We do *not* need to recursively go into list/tuple kinds here,
-- because register-kind function automatically registers all subcomponent
-- kinds, thus everything we need is available at the top-level.
findTupleArities :: Set Kind -> [Int]
findTupleArities ks = Set.toAscList
$ Set.map length
$ Set.fromList [ tupKs | KTuple tupKs <- Set.toList ks ]
-- | Is @Rational@ being used?
containsRationals :: Set Kind -> Bool
containsRationals = not . Set.null . Set.filter isRational
-- Internally, we do *not* keep the rationals in reduced form! So, the boolean operators explicitly do the math
-- to make sure equivalent values are treated correctly.
declRationals :: [Text]
declRationals = [ "(declare-datatype SBVRational ((SBV.Rational (sbv.rat.numerator Int) (sbv.rat.denominator Int))))"
, ""
, "(define-fun sbv.rat.eq ((x SBVRational) (y SBVRational)) Bool"
, " (= (* (sbv.rat.numerator x) (sbv.rat.denominator y))"
, " (* (sbv.rat.denominator x) (sbv.rat.numerator y)))"
, ")"
, ""
, "(define-fun sbv.rat.notEq ((x SBVRational) (y SBVRational)) Bool"
, " (not (sbv.rat.eq x y))"
, ")"
]
-- | Convert in a query context.
-- NB. We do not store everything in @newKs@ below, but only what we need
-- to do as an extra in the incremental context. See `Data.SBV.Core.Symbolic.registerKind`
-- for a list of what we include, in case something doesn't show up
-- and you need it!
cvtInc :: SMTLibIncConverter [Text]
cvtInc curProgInfo inps newKs (_, consts) tbls uis (SBVPgm asgnsSeq) cstrs cfg =
-- any new settings?
settings
-- sorts
<> declADT [(s, pks, cs) | k@(KADT s pks cs) <- newKinds, not (isRoundingMode k)]
-- tuples. NB. Only declare the new sizes, old sizes persist.
<> concatMap declTuple (findTupleArities newKs)
-- constants
<> concatMap (declConst cfg) consts
-- inputs
<> concatMap declInp inps
-- uninterpreteds
<> concatMap (declUI curProgInfo) uis
-- table declarations
<> tableDecls
-- expressions
<> concatMap (declDef curProgInfo cfg tableMap) asgnsSeq
-- table setups
<> concat tableAssigns
-- extra constraints
<> map (\(isSoft, attr, v) -> "(assert" <> (if isSoft then "-soft " else " ") <> addAnnotations attr (cvtSV v) <> ")") (F.toList cstrs)
where newKinds = Set.toList newKs
declInp (getSV -> s) = declareFun s (SBVType [kindOf s]) Nothing
(tableMap, allTables) = (tm, ct <> nct)
where (tm, ct, nct) = constructTables consts tbls
(tableDecls, tableAssigns) = unzip $ map mkTable allTables
-- If we need flattening in models, do emit the required lines if preset
settings
| any needsFlattening newKinds
= concat (catMaybes [map T.pack <$> supportsFlattenedModels solverCaps])
| True
= []
where solverCaps = capabilities (solver cfg)
declDef :: ProgInfo -> SMTConfig -> TableMap -> (SV, SBVExpr) -> [Text]
declDef curProgInfo cfg tableMap (s, expr) =
case expr of
SBVApp (Label m) [e] -> defineFun cfg (s, cvtSV e) (Just $ T.pack m)
e -> defineFun cfg (s, cvtExp cfg curProgInfo caps rm tableMap e) Nothing
where caps = capabilities (solver cfg)
rm = roundingMode cfg
defineFun :: SMTConfig -> (SV, Text) -> Maybe Text -> [Text]
defineFun cfg (s, def) mbComment
| hasDefFun = ["(define-fun " <> varT <> " " <> def <> ")" <> cmnt]
| True = [ "(declare-fun " <> varT <> ")" <> cmnt
, "(assert (= " <> var <> " " <> def <> "))"
]
where var = showText s
varT = var <> " " <> svFunType [] s
cmnt = maybe "" (" ; " <>) mbComment
hasDefFun = supportsDefineFun $ capabilities (solver cfg)
-- Declare constants. NB. We don't declare true/false; but just inline those as necessary
declConst :: SMTConfig -> (SV, CV) -> [Text]
declConst cfg (s, c)
| s == falseSV || s == trueSV
= []
| True
= defineFun cfg (s, cvtCV c) Nothing
-- Make a function equality of nm against the internal function fun
mkRelEq :: Text -> (Text, Text) -> Kind -> Text
mkRelEq nm (fun, order) ak = res
where lhs = "(" <> nm <> " x y)"
rhs = "((_ " <> fun <> " " <> order <> ") x y)"
tk = smtType ak
res = "(forall ((x " <> tk <> ") (y " <> tk <> ")) (= " <> lhs <> " " <> rhs <> "))"
declUI :: ProgInfo -> (String, (Bool, Maybe [String], SBVType)) -> [Text]
declUI ProgInfo{progTransClosures} (i, (_, _, t)) = declareName (T.pack i) t Nothing <> declClosure
where declClosure | Just external <- lookup i progTransClosures
= declareName (T.pack external) t Nothing
<> ["(assert " <> mkRelEq (T.pack external) ("transitive-closure", T.pack i) (argKind t) <> ")"]
| True
= []
argKind (SBVType [ka, _, KBool]) = ka
argKind _ = error $ "declUI: Unexpected type for name: " <> show (i, t)
-- Note that even though we get all user defined-functions here (i.e., lambda and axiom), we can only have defined-functions
-- and axioms. We spit axioms as is; and topologically sort the definitions.
declUserFuns :: [(String, (SMTDef, SBVType))] -> [Text]
declUserFuns ds = map declGroup sorted
where mkNode d = (d, fst d, getDeps d)
getDeps (_, (SMTDef _ d _ _, _)) = d
mkDecl Nothing rt = "() " <> rt
mkDecl (Just p) rt = p <> " " <> rt
sorted = DG.stronglyConnComp (map mkNode ds)
declGroup (DG.AcyclicSCC b) = declUserDef False b
declGroup (DG.CyclicSCC bs) = case bs of
[] -> error "Data.SBV.declFuns: Impossible happened: an empty cyclic group was returned!"
[x] -> declUserDef True x
xs -> declUserDefMulti xs
declUserDef isRec (nm, (SMTDef fk deps param body, ty)) =
"; " <> T.pack nm <> " :: " <> showText ty <> recursive <> frees <> "\n" <> s
where (recursive, definer) | isRec = (" [Recursive]", "define-fun-rec")
| True = ("", "define-fun")
otherDeps = filter (/= nm) deps
frees | null otherDeps = ""
| True = " [Refers to: " <> T.intercalate ", " (map T.pack otherDeps) <> "]"
decl = mkDecl param (smtType fk)
s = "(" <> definer <> " " <> T.pack nm <> " " <> decl <> "\n" <> body 2 <> ")"
-- declare a bunch of mutually-recursive functions
declUserDefMulti bs = render $ map collect bs
where collect (nm, (SMTDef fk deps param body, ty)) = (deps, nm, ty, "(" <> T.pack nm <> " " <> decl <> ")", body 3)
where decl = mkDecl param (smtType fk)
render defs = T.intercalate "\n" $
[ "; " <> T.intercalate ", " [T.pack n <> " :: " <> showText ty | (_, n, ty, _, _) <- defs]
, "(define-funs-rec"
]
<> [ open i <> param d <> close1 i | (i, d) <- zip [1..] defs]
<> [ open i <> dump d <> close2 i | (i, d) <- zip [1..] defs]
where open 1 = " ("
open _ = " "
param (_deps, _nm, _ty, p, _body) = p
dump (deps, nm, ty, _, body) = "; Definition of: " <> T.pack nm <> " :: " <> showText ty <> ". [Refers to: " <> T.intercalate ", " (map T.pack deps) <> "]"
<> "\n" <> body
ld = length defs
close1 n = if n == ld then ")" else ""
close2 n = if n == ld then "))" else ""
mkTable :: (((Int, Kind, Kind), [SV]), [Text]) -> (Text, [Text])
mkTable (((i, ak, rk), _elts), is) = (decl, zipWith wrap [(0::Int)..] is <> setup)
where t = "table" <> showText i
decl = "(declare-fun " <> t <> " (" <> smtType ak <> ") " <> smtType rk <> ")"
-- Arrange for initializers
mkInit idx = "table" <> showText i <> "_initializer_" <> showText (idx :: Int)
initializer = "table" <> showText i <> "_initializer"
wrap index s = "(define-fun " <> mkInit index <> " () Bool " <> s <> ")"
lis = length is
setup
| lis == 0 = [ "(define-fun " <> initializer <> " () Bool true) ; no initialization needed"
]
| lis == 1 = [ "(define-fun " <> initializer <> " () Bool " <> mkInit 0 <> ")"
, "(assert " <> initializer <> ")"
]
| True = [ "(define-fun " <> initializer <> " () Bool (and " <> T.unwords (map mkInit [0..lis - 1]) <> "))"
, "(assert " <> initializer <> ")"
]
nonConstTable :: (((Int, Kind, Kind), [SV]), [Text]) -> Text
nonConstTable (((i, ak, rk), _elts), _) = decl
where t = "table" <> showText i
decl = "(declare-fun " <> t <> " (" <> smtType ak <> ") " <> smtType rk <> ")"
constructTables :: [(SV, CV)] -> [((Int, Kind, Kind), [SV])]
-> ( IM.IntMap Text -- table enumeration
, [(((Int, Kind, Kind), [SV]), [Text])] -- constant tables
, [(((Int, Kind, Kind), [SV]), [Text])] -- non-constant tables
)
constructTables consts tbls = (tableMap, constTables, nonConstTables)
where allTables = [(t, genTableData (map fst consts) t) | t <- tbls]
constTables = [(t, d) | (t, Left d) <- allTables]
nonConstTables = [(t, d) | (t, Right d) <- allTables]
tableMap = IM.fromList $ map grab allTables
grab (((t, _, _), _), _) = (t, "table" <> showText t)
-- Left if all constants, Right if otherwise
genTableData :: [SV] -> ((Int, Kind, Kind), [SV]) -> Either [Text] [Text]
genTableData consts ((i, aknd, _), elts)
| null post = Left (map (mkEntry . snd) pre)
| True = Right (map (mkEntry . snd) (pre ++ post))
where (pre, post) = partition fst (zipWith mkElt elts [(0::Int)..])
t = "table" <> showText i
mkElt x k = (isReady, (idx, cvtSV x))
where idx = cvtCV (mkConstCV aknd k)
isReady = x `Set.member` constsSet
mkEntry (idx, v) = "(= (" <> t <> " " <> idx <> ") " <> v <> ")"
constsSet = Set.fromList consts
svType :: SV -> Text
svType s = smtType (kindOf s)
svFunType :: [SV] -> SV -> Text
svFunType ss s = "(" <> T.unwords (map svType ss) <> ") " <> svType s
cvtType :: SBVType -> Text
cvtType (SBVType []) = error "SBV.SMT.SMTLib2.cvtType: internal: received an empty type!"
cvtType (SBVType xs) = "(" <> T.unwords (map smtType body) <> ") " <> smtType ret
where (body, ret) = (init xs, last xs)
type TableMap = IM.IntMap Text
-- Present an SV, simply show
cvtSV :: SV -> Text
cvtSV = showText
cvtCV :: CV -> Text
cvtCV = cvToSMTLib
getTable :: TableMap -> Int -> Text
getTable m i
| Just tn <- i `IM.lookup` m = tn
| True = "table" <> showText i
cvtExp :: SMTConfig -> ProgInfo -> SolverCapabilities -> RoundingMode -> TableMap -> SBVExpr -> Text
cvtExp cfg curProgInfo caps rm tableMap expr@(SBVApp _ arguments) = sh expr
where hasPB = supportsPseudoBooleans caps
hasDistinct = supportsDistinct caps
specialRels = progSpecialRels curProgInfo
bvOp = all isBounded arguments
intOp = any isUnbounded arguments
ratOp = any isRational arguments
realOp = any isReal arguments
fpOp = any (\a -> isDouble a || isFloat a || isFP a) arguments
boolOp = all isBoolean arguments
charOp = any isChar arguments
stringOp = any isString arguments
listOp = any isList 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
isZ3 = case name (solver cfg) of
Z3 -> True
_ -> False
isCVC5 = case name (solver cfg) of
CVC5 -> True
_ -> False
hd _ (a:_) = a
hd w [] = error $ "Impossible: " ++ w ++ ": Received empty list of args!"
-- lift a binary op
lift2 o _ [x, y] = "(" <> o <> " " <> x <> " " <> y <> ")"
lift2 o _ sbvs = error $ "SBV.SMTLib2.sh.lift2: Unexpected arguments: " ++ show (o, sbvs)
-- lift an arbitrary arity operator
liftN o _ xs = "(" <> o <> " " <> T.unwords xs <> ")"
-- lift a binary operation with rounding-mode added; used for floating-point arithmetic
lift2WM o fo | fpOp = lift2 (addRM fo)
| True = lift2 o
lift1FP o fo | fpOp = lift1 fo
| True = lift1 o
liftAbs sgned args | fpOp = lift1 "fp.abs" sgned args
| intOp = lift1 "abs" sgned args
| bvOp, sgned = mkAbs fArg "bvslt" "bvneg"
| bvOp = fArg
| True = mkAbs fArg "<" "-"
where fArg = hd "liftAbs" args
mkAbs x cmp neg = "(ite " <> ltz <> " " <> nx <> " " <> x <> ")"
where ltz = "(" <> cmp <> " " <> x <> " " <> z <> ")"
nx = "(" <> neg <> " " <> x <> ")"
z = cvtCV (mkConstCV (kindOf (hd "liftAbs.arguments" arguments)) (0::Integer))
lift2B bOp vOp
| boolOp = lift2 bOp
| True = lift2 vOp
lift1B bOp vOp
| boolOp = lift1 bOp
| True = lift1 vOp
eqBV = lift2 "="
neqBV = liftN "distinct"
equal sgn sbvs
| fpOp = lift2 "fp.eq" sgn sbvs
| True = lift2 "=" sgn sbvs
-- Do not use distinct on floats; because +0/-0, and NaNs mess
-- up the meaning. Just go with reqular equals.
notEqual sgn sbvs
| fpOp || not hasDistinct = liftP sbvs
| True = liftN "distinct" sgn sbvs
where liftP xs@[_, _] = "(not " <> equal sgn xs <> ")"
liftP args = "(and " <> T.unwords (walk args) <> ")"
walk [] = []
walk (e:es) = map (\e' -> liftP [e, e']) es <> walk es
lift2S oU oS sgn = lift2 (if sgn then oS else oU) sgn
liftNS oU oS sgn = liftN (if sgn then oS else oU) sgn
lift2Cmp o fo | fpOp = lift2 fo
| True = lift2 o
stringOrChar KString = True
stringOrChar KChar = True
stringOrChar _ = False
stringCmp swap o [a, b]
| stringOrChar (kindOf (hd "stringCmp" arguments))
= let (a1, a2) | swap = (b, a)
| True = (a, b)
in "(" <> o <> " " <> a1 <> " " <> a2 <> ")"
stringCmp _ o sbvs = error $ "SBV.SMT.SMTLib2.sh.stringCmp: Unexpected arguments: " ++ show (o, sbvs)
-- NB. Likewise for sequences
seqCmp swap o [a, b]
| KList{} <- kindOf (hd "seqCmp" arguments)
= let (a1, a2) | swap = (b, a)
| True = (a, b)
in "(" <> o <> " " <> a1 <> " " <> a2 <> ")"
seqCmp _ o sbvs = error $ "SBV.SMT.SMTLib2.sh.seqCmp: Unexpected arguments: " ++ show (o, sbvs)
lift1 o _ [x] = "(" <> o <> " " <> x <> ")"
lift1 o _ sbvs = error $ "SBV.SMTLib2.sh.lift1: Unexpected arguments: " ++ show (o, sbvs)
sh (SBVApp Ite [a, b, c]) = "(ite " <> cvtSV a <> " " <> cvtSV b <> " " <> cvtSV c <> ")"
sh (SBVApp (LkUp (t, aKnd, _, l) i e) [])
| needsCheck = "(ite " <> cond <> cvtSV e <> " " <> lkUp <> ")"
| True = lkUp
where unexpected = error $ "SBV.SMT.SMTLib2.cvtExp: Unexpected: " ++ show aKnd
needsCheck = case aKnd of
KVar{} -> unexpected
KBool -> (2::Integer) > fromIntegral l
KBounded _ n -> (2::Integer)^n > fromIntegral l
KUnbounded -> True
KApp _ _ -> unexpected
KADT _ _ _ -> unexpected
KReal -> unexpected
KFloat -> unexpected
KDouble -> unexpected
KFP _ _ -> unexpected
KRational -> unexpected
KChar -> unexpected
KString -> unexpected
KList _ -> unexpected
KSet _ -> unexpected
KTuple _ -> unexpected
KArray _ _ -> unexpected
lkUp = "(" <> getTable tableMap t <> " " <> cvtSV i <> ")"
cond
| hasSign i = "(or " <> le0 <> " " <> gtl <> ") "
| True = gtl <> " "
(less, leq) = case aKnd of
KVar{} -> error "SBV.SMT.SMTLib2.cvtExp: unexpected variable index"
KBool -> error "SBV.SMT.SMTLib2.cvtExp: unexpected boolean valued index"
KBounded{} -> if hasSign i then ("bvslt", "bvsle") else ("bvult", "bvule")
KUnbounded -> ("<", "<=")
KReal -> ("<", "<=")
KFloat -> ("fp.lt", "fp.leq")
KDouble -> ("fp.lt", "fp.leq")
KRational -> ("sbv.rat.lt", "sbv.rat.leq")
KFP{} -> ("fp.lt", "fp.leq")
KChar -> error "SBV.SMT.SMTLib2.cvtExp: unexpected string valued index"
KString -> error "SBV.SMT.SMTLib2.cvtExp: unexpected string valued index"
KApp s _ -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected ADT applied index: " ++ s
KADT s _ _ -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected ADT valued index: " ++ s
KList k -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected sequence valued index: " ++ show k
KSet k -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected set valued index: " ++ show k
KTuple k -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected tuple valued index: " ++ show k
KArray k1 k2 -> error $ "SBV.SMT.SMTLib2.cvtExp: unexpected array valued index: " ++ show (k1, k2)
mkCnst = cvtCV . mkConstCV (kindOf i)
le0 = "(" <> less <> " " <> cvtSV i <> " " <> mkCnst 0 <> ")"
gtl = "(" <> leq <> " " <> mkCnst l <> " " <> cvtSV i <> ")"
sh (SBVApp (KindCast f t) [a]) = handleKindCast f t (cvtSV a)
sh (SBVApp (ArrayInit (Left (f, t))) [a]) = "((as const (Array " <> smtType f <> " " <> smtType t <> ")) " <> cvtSV a <> ")"
sh (SBVApp (ArrayInit (Right (SMTLambda s))) []) = s
sh (SBVApp ReadArray [a, i]) = "(select " <> cvtSV a <> " " <> cvtSV i <> ")"
sh (SBVApp WriteArray [a, i, e]) = "(store " <> cvtSV a <> " " <> cvtSV i <> " " <> cvtSV e <> ")"
sh (SBVApp (Uninterpreted nm) []) = nm
sh (SBVApp (Uninterpreted nm) args) = "(" <> nm <> " " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (ADTOp aop) args) = handleADT caps aop args
sh (SBVApp (QuantifiedBool i) []) = i
sh (SBVApp (QuantifiedBool i) args) = error $ "SBV.SMT.SMTLib2.cvtExp: unexpected arguments to quantified boolean: " ++ show (T.unpack i, args)
sh a@(SBVApp (SpecialRelOp k o) args)
| not (null args)
= error $ "SBV.SMT.SMTLib2.cvtExp: unexpected arguments to special op: " ++ show a
| True
= let order = case o `elemIndex` specialRels of
Just i -> i
Nothing -> error $ unlines [ "SBV.SMT.SMTLib2.cvtExp: Cannot find " ++ show o ++ " in the special-relations list."
, "Known relations: " ++ intercalate ", " (map show specialRels)
]
asrt nm fun = mkRelEq (T.pack nm) (T.pack fun, showText order) k
in case o of
IsPartialOrder nm -> asrt nm "partial-order"
IsLinearOrder nm -> asrt nm "linear-order"
IsTreeOrder nm -> asrt nm "tree-order"
IsPiecewiseLinearOrder nm -> asrt nm "piecewise-linear-order"
sh (SBVApp (Divides n) [a]) = "((_ divisible " <> showText n <> ") " <> cvtSV a <> ")"
sh (SBVApp (Extract i j) [a]) | ensureBV = "((_ extract " <> showText i <> " " <> showText j <> ") " <> cvtSV a <> ")"
sh (SBVApp (Rol i) [a])
| bvOp = rot "rotate_left" i a
| True = bad
sh (SBVApp (Ror i) [a])
| bvOp = rot "rotate_right" i a
| True = bad
sh (SBVApp Shl [a, i])
| bvOp = shft "bvshl" "bvshl" a i
| True = bad
sh (SBVApp Shr [a, i])
| bvOp = shft "bvlshr" "bvashr" a i
| True = bad
sh (SBVApp (ZeroExtend i) [a])
| bvOp = "((_ zero_extend " <> showText i <> ") " <> cvtSV a <> ")"
| True = bad
sh (SBVApp (SignExtend i) [a])
| bvOp = "((_ sign_extend " <> showText i <> ") " <> cvtSV a <> ")"
| True = bad
sh (SBVApp op args)
| Just f <- lookup op smtBVOpTable, ensureBVOrBool
= f (any hasSign args) (map cvtSV 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 (SBVApp (Label _) [a]) = cvtSV a -- This won't be reached; but just in case!
sh (SBVApp (IEEEFP (FP_Cast kFrom kTo m)) args) = handleFPCast kFrom kTo (cvtSV m) (T.unwords (map cvtSV args))
sh (SBVApp (IEEEFP w ) args) = "(" <> showText w <> " " <> T.unwords (map cvtSV args) <> ")"
-- Some non-linear operators are supported by z3/CVC5 specifically, so do the custom translation Otherwise
-- we pass them along.
sh (SBVApp (NonLinear NR_Sqrt) [a]) | isZ3 = "(^ " <> cvtSV a <> " 0.5)"
| isCVC5 = "(sqrt " <> cvtSV a <> ")"
sh (SBVApp (NonLinear NR_Pow) [a, b]) | isZ3 || isCVC5 = "(^ " <> cvtSV a <> " " <> cvtSV b <> ")"
sh (SBVApp (NonLinear w) args) = "(" <> showText w <> " " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (PseudoBoolean pb) args)
| hasPB = handlePB pb args'
| True = reducePB pb args'
where args' = map cvtSV args
sh (SBVApp (OverflowOp op) args) = "(" <> showText op <> " " <> T.unwords (map cvtSV args) <> ")"
-- Note the unfortunate reversal in StrInRe..
sh (SBVApp (StrOp (StrInRe r)) args) = "(str.in_re " <> T.unwords (map cvtSV args) <> " " <> regExpToSMTString r <> ")"
sh (SBVApp (StrOp op) args) = "(" <> showText op <> " " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (RegExOp o@RegExEq{}) []) = showText o
sh (SBVApp (RegExOp o@RegExNEq{}) []) = showText o
-- Sequences. The only interesting thing here is that unit over KChar is a no-op since SMTLib doesn't distinguish
-- Strings and Characters, but SBV does.
sh (SBVApp (SeqOp (SeqUnit KChar)) [a]) = cvtSV a
sh (SBVApp (SeqOp op) args) = "(" <> showText op <> " " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (SetOp SetEqual) args) = "(= " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (SetOp SetMember) [e, s]) = "(select " <> cvtSV s <> " " <> cvtSV e <> ")"
sh (SBVApp (SetOp SetInsert) [e, s]) = "(store " <> cvtSV s <> " " <> cvtSV e <> " true)"
sh (SBVApp (SetOp SetDelete) [e, s]) = "(store " <> cvtSV s <> " " <> cvtSV e <> " false)"
sh (SBVApp (SetOp SetIntersect) args) = "(intersection " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (SetOp SetUnion) args) = "(union " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (SetOp SetSubset) args) = "(subset " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (SetOp SetDifference) args) = "(setminus " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (SetOp SetComplement) args) = "(complement " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (TupleConstructor 0) []) = "mkSBVTuple0"
sh (SBVApp (TupleConstructor n) args) = "((as mkSBVTuple" <> showText n <> " " <> smtType (KTuple (map kindOf args)) <> ") " <> T.unwords (map cvtSV args) <> ")"
sh (SBVApp (TupleAccess i n) [tup]) = "(proj_" <> showText i <> "_SBVTuple" <> showText n <> " " <> cvtSV tup <> ")"
sh (SBVApp RationalConstructor [t, b]) = "(SBV.Rational " <> cvtSV t <> " " <> cvtSV b <> ")"
sh (SBVApp Implies [a, b]) = "(=> " <> cvtSV a <> " " <> cvtSV b <> ")"
sh inp@(SBVApp op args)
| intOp, Just f <- lookup op smtOpIntTable
= f True (map cvtSV args)
| boolOp, Just f <- lookup op boolComps
= f (map cvtSV args)
| bvOp, Just f <- lookup op smtOpBVTable
= f (any hasSign args) (map cvtSV args)
| realOp, Just f <- lookup op smtOpRealTable
= f (any hasSign args) (map cvtSV args)
| ratOp, Just f <- lookup op ratOpTable
= f (map cvtSV args)
| fpOp, Just f <- lookup op smtOpFloatDoubleTable
= f (any hasSign args) (map cvtSV args)
| charOp || stringOp, Just f <- lookup op smtStringTable
= f (map cvtSV args)
| listOp, Just f <- lookup op smtListTable
= f (map cvtSV args)
| Just f <- lookup op uninterpretedTable
= f (map cvtSV args)
| True
= error $ unlines [ ""
, "*** SBV.SMT.SMTLib2.cvtExp.sh: impossible happened; can't translate: " ++ show inp
, "***"
, "*** Applied to arguments of type: " ++ intercalate ", " (nub (map (show . kindOf) args))
, "***"
, "*** This can happen if the Num instance isn't properly defined for a lifted kind."
, "*** (See https://github.com/LeventErkok/sbv/issues/698 for a discussion.)"
, "***"
, "*** If you believe this is in error, please report!"
]
where smtOpBVTable = [ (Plus, lift2 "bvadd")
, (Minus, lift2 "bvsub")
, (Times, lift2 "bvmul")
, (UNeg, lift1B "not" "bvneg")
, (Abs, liftAbs)
, (Quot, lift2S "bvudiv" "bvsdiv")
, (Rem, lift2S "bvurem" "bvsrem")
, (Equal True, eqBV)
, (Equal False, eqBV)
, (NotEqual, neqBV)
, (LessThan, lift2S "bvult" "bvslt")
, (GreaterThan, lift2S "bvugt" "bvsgt")
, (LessEq, lift2S "bvule" "bvsle")
, (GreaterEq, lift2S "bvuge" "bvsge")
]
-- Boolean comparisons.. SMTLib's bool type doesn't do comparisons, but Haskell does.. Sigh
boolComps = [ (LessThan, blt)
, (GreaterThan, blt . swp)
, (LessEq, blq)
, (GreaterEq, blq . swp)
]
where blt [x, y] = "(and (not " <> x <> ") " <> y <> ")"
blt xs = error $ "SBV.SMT.SMTLib2.boolComps.blt: Impossible happened, incorrect arity (expected 2): " ++ show xs
blq [x, y] = "(or (not " <> x <> ") " <> y <> ")"
blq xs = error $ "SBV.SMT.SMTLib2.boolComps.blq: Impossible happened, incorrect arity (expected 2): " ++ show xs
swp [x, y] = [y, x]
swp xs = error $ "SBV.SMT.SMTLib2.boolComps.swp: Impossible happened, incorrect arity (expected 2): " ++ show xs
smtOpRealTable = smtIntRealShared
++ [ (Quot, lift2WM "/" "fp.div")
]
smtOpIntTable = smtIntRealShared
++ [ (Quot, lift2 "div")
, (Rem, lift2 "mod")
]
smtOpFloatDoubleTable = smtIntRealShared
++ [(Quot, lift2WM "/" "fp.div")]
smtIntRealShared = [ (Plus, lift2WM "+" "fp.add")
, (Minus, lift2WM "-" "fp.sub")
, (Times, lift2WM "*" "fp.mul")
, (UNeg, lift1FP "-" "fp.neg")
, (Abs, liftAbs)
, (Equal True, equal)
, (Equal False, equal)
, (NotEqual, notEqual)
, (LessThan, lift2Cmp "<" "fp.lt")
, (GreaterThan, lift2Cmp ">" "fp.gt")
, (LessEq, lift2Cmp "<=" "fp.leq")
, (GreaterEq, lift2Cmp ">=" "fp.geq")
]
ratOpTable = [ (Equal True, lift2Rat "sbv.rat.eq")
, (Equal False, lift2Rat "sbv.rat.eq")
, (NotEqual, lift2Rat "sbv.rat.notEq")
]
where lift2Rat o [x, y] = "(" <> o <> " " <> x <> " " <> y <> ")"
lift2Rat o sbvs = error $ "SBV.SMTLib2.sh.lift2Rat: Unexpected arguments: " ++ show (o, sbvs)
-- equality and comparisons are the only thing that works on uninterpreted sorts and pretty much everything else
uninterpretedTable = [ (Equal True, lift2S "=" "=" True)
, (Equal False, lift2S "=" "=" True)
, (NotEqual, liftNS "distinct" "distinct" True)
]
-- For strings, equality and comparisons are the only operators
smtStringTable = [ (Equal True, lift2S "=" "=" True)
, (Equal False, lift2S "=" "=" True)
, (NotEqual, liftNS "distinct" "distinct" True)
, (LessThan, stringCmp False "str.<")
, (GreaterThan, stringCmp True "str.<")
, (LessEq, stringCmp False "str.<=")
, (GreaterEq, stringCmp True "str.<=")
]
-- For lists, equality is really the only operator. Also, not strong-equality due to lists of floats.
-- Likewise here, things might change for comparisons
smtListTable = [ (Equal False, lift2S "=" "=" True)
, (NotEqual, liftNS "distinct" "distinct" True)
, (LessThan, seqCmp False "seq.<")
, (GreaterThan, seqCmp True "seq.<")
, (LessEq, seqCmp False "seq.<=")
, (GreaterEq, seqCmp True "seq.<=")
]
declareFun :: SV -> SBVType -> Maybe Text -> [Text]
declareFun sv = declareName (showText sv)
-- If we have a char, we have to make sure it's and SMTLib string of length exactly one
-- If we have a rational, we have to make sure the denominator is > 0
-- Otherwise, we just declare the name
declareName :: Text -> SBVType -> Maybe Text -> [Text]
declareName s t@(SBVType inputKS) mbCmnt = decl : restrict
where decl = "(declare-fun " <> s <> " " <> cvtType t <> ")" <> maybe "" (" ; " <>) mbCmnt
(args, result) = case inputKS of
[] -> error $ "SBV.declareName: Unexpected empty type for: " ++ T.unpack s
_ -> (init inputKS, last inputKS)
-- Does the kind KChar and KRational *not* occur in the kind anywhere?
charRatFree k = all notCharOrRat (expandKinds k)
where notCharOrRat KChar = False
notCharOrRat KRational = False
notCharOrRat _ = True
noCharOrRat = charRatFree result
needsQuant = not $ null args
resultVar | needsQuant = "result"
| True = s
argList = ["a" <> showText i | (i, _) <- zip [1::Int ..] args]
argTList = ["(" <> a <> " " <> smtType k <> ")" | (a, k) <- zip argList args]
resultExp = "(" <> s <> " " <> T.unwords argList <> ")"
restrict | noCharOrRat = []
| needsQuant = [ "(assert (forall (" <> T.unwords argTList <> ")"
, " (let ((" <> resultVar <> " " <> resultExp <> "))"
]
<> (case constraints of
[] -> [ " true"]
[x] -> [ " " <> x]
(x:xs) -> ( " (and " <> x)
: [ " " <> c | c <- xs]
<> [ " )"])
<> [ " )))"]
| True = case constraints of
[] -> []
[x] -> ["(assert " <> x <> ")"]
(x:xs) -> ( "(assert (and " <> x)
: [ " " <> c | c <- xs]
<> [ " ))"]
constraints = walk 0 resultVar cstr result
where cstr KChar nm = ["(= 1 (str.len " <> nm <> "))"]
cstr KRational nm = ["(< 0 (sbv.rat.denominator " <> nm <> "))"]
cstr _ _ = []
mkAnd [] _context = []
mkAnd [c] context = context c
mkAnd cs context = context $ "(and " <> T.unwords cs <> ")"
walk :: Int -> Text -> (Kind -> Text -> [Text]) -> Kind -> [Text]
walk _d nm f k@KVar {} = f k nm
walk _d nm f k@KBool {} = f k nm
walk _d nm f k@KBounded {} = f k nm
walk _d nm f k@KUnbounded{} = f k nm
walk _d nm f k@KReal {} = f k nm
walk _d nm f k@KApp {} = f k nm
walk _d nm f k@KFloat {} = f k nm
walk _d nm f k@KDouble {} = f k nm
walk _d nm f k@KRational {} = f k nm
walk _d nm f k@KFP {} = f k nm
walk _d nm f k@KChar {} = f k nm
walk _d nm f k@KString {} = f k nm
walk d nm f (KList k)
| charRatFree k = []
| True = let fnm = "seq" <> showText d
cstrs = walk (d+1) ("(seq.nth " <> nm <> " " <> fnm <> ")") f k
in mkAnd cstrs $ \hole -> ["(forall ((" <> fnm <> " " <> smtType KUnbounded <> ")) (=> (and (>= " <> fnm <> " 0) (< " <> fnm <> " (seq.len " <> nm <> "))) " <> hole <> "))"]
walk d nm f (KSet k)
| charRatFree k = []
| True = let fnm = "set" <> showText d
cstrs = walk (d+1) nm (\sk snm -> ["(=> (select " <> snm <> " " <> fnm <> ") " <> c <> ")" | c <- f sk fnm]) k
in mkAnd cstrs $ \hole -> ["(forall ((" <> fnm <> " " <> smtType k <> ")) " <> hole <> ")"]
walk d nm f (KTuple ks) = let tt = "SBVTuple" <> showText (length ks)
project i = "(proj_" <> showText i <> "_" <> tt <> " " <> nm <> ")"
nmks = [(project i, k) | (i, k) <- zip [1::Int ..] ks]
in concatMap (\(n, k) -> walk (d+1) n f k) nmks
walk d nm f (KArray k1 k2)
| all charRatFree [k1, k2] = []
| True = let fnm = "array" <> showText d
cstrs = walk (d+1) ("(select " <> nm <> " " <> fnm <> ")") f k2
in mkAnd cstrs $ \hole -> ["(forall ((" <> fnm <> " " <> smtType k1 <> ")) " <> hole <> ")"]
walk d nm f (KADT ty dict pureFS) = let fs = [(c, map (substituteADTVars ty dict) ks) | (c, ks) <- pureFS]
nmks = [("(get" <> T.pack c <> "_" <> showText i <> " " <> nm <> ")", k) | (c, ks) <- fs, (i, k) <- zip [(1::Int)..] ks]
in concatMap (\(n, k) -> walk (d+1) n f k) nmks
-----------------------------------------------------------------------------------------------
-- Casts supported by SMTLib. (From: <https://smt-lib.org/theories-FloatingPoint.shtml>)
-- ; from another floating point sort
-- ((_ to_fp eb sb) RoundingMode (_ FloatingPoint mb nb) (_ FloatingPoint eb sb))
--
-- ; from real
-- ((_ to_fp eb sb) RoundingMode Real (_ FloatingPoint eb sb))
--
-- ; from signed machine integer, represented as a 2's complement bit vector
-- ((_ to_fp eb sb) RoundingMode (_ BitVec m) (_ FloatingPoint eb sb))
--
-- ; from unsigned machine integer, represented as bit vector
-- ((_ to_fp_unsigned eb sb) RoundingMode (_ BitVec m) (_ FloatingPoint eb sb))
--
-- ; to unsigned machine integer, represented as a bit vector
-- ((_ fp.to_ubv m) RoundingMode (_ FloatingPoint eb sb) (_ BitVec m))
--
-- ; to signed machine integer, represented as a 2's complement bit vector
-- ((_ fp.to_sbv m) RoundingMode (_ FloatingPoint eb sb) (_ BitVec m))
--
-- ; to real
-- (fp.to_real (_ FloatingPoint eb sb) Real)
-----------------------------------------------------------------------------------------------
handleFPCast :: Kind -> Kind -> Text -> Text -> Text
handleFPCast kFromIn kToIn rm input
| kFrom == kTo
= input
| True
= "(" <> cast kFrom kTo input <> ")"
where addRM a s = s <> " " <> rm <> " " <> a
kFrom = simplify kFromIn
kTo = simplify kToIn
simplify KFloat = KFP 8 24
simplify KDouble = KFP 11 53
simplify k = k
size (eb, sb) = showText eb <> " " <> showText sb
-- To go and back from Ints, we detour through reals
cast KUnbounded (KFP eb sb) a = "(_ to_fp " <> size (eb, sb) <> ") " <> rm <> " (to_real " <> a <> ")"
cast KFP{} KUnbounded a = "to_int (fp.to_real (fp.roundToIntegral " <> rm <> " " <> a <> "))"
-- To floats
cast (KBounded False _) (KFP eb sb) a = addRM a $ "(_ to_fp_unsigned " <> size (eb, sb) <> ")"
cast (KBounded True _) (KFP eb sb) a = addRM a $ "(_ to_fp " <> size (eb, sb) <> ")"
cast KReal (KFP eb sb) a = addRM a $ "(_ to_fp " <> size (eb, sb) <> ")"
cast KFP{} (KFP eb sb) a = addRM a $ "(_ to_fp " <> size (eb, sb) <> ")"
-- From float/double
cast KFP{} (KBounded False m) a = addRM a $ "(_ fp.to_ubv " <> showText m <> ")"
cast KFP{} (KBounded True m) a = addRM a $ "(_ fp.to_sbv " <> showText m <> ")"
-- To real
cast KFP{} KReal a = "fp.to_real" <> " " <> a
-- Nothing else should come up:
cast f d _ = error $ "SBV.SMTLib2: Unexpected FPCast from: " ++ show f ++ " to " ++ show d
rot :: Text -> Int -> SV -> Text
rot o c x = "((_ " <> o <> " " <> showText c <> ") " <> cvtSV x <> ")"
shft :: Text -> Text -> SV -> SV -> Text
shft oW oS x c = "(" <> o <> " " <> cvtSV x <> " " <> cvtSV c <> ")"
where o = if hasSign x then oS else oW
-- ADT operations
handleADT :: SolverCapabilities -> ADTOp -> [SV] -> Text
handleADT caps op args = case args of
[] -> f
_ -> "(" <> f <> " " <> T.unwords (map cvtSV args) <> ")"
where f = case op of
ADTConstructor nm k -> ascribe nm k
ADTTester nm k -> if supportsDirectTesters caps
then nm
else ascribe nm k
ADTAccessor nm _ -> nm
ascribe nm k = "(as " <> nm <> " " <> smtType k <> ")"
-- Various casts
handleKindCast :: Kind -> Kind -> Text -> Text
handleKindCast kFrom kTo a
| kFrom == kTo
= a
| True
= case kFrom of
KBounded s m -> case kTo of
KBounded _ n -> fromBV (if s then signExtend else zeroExtend) m n
KUnbounded -> if s then "(sbv_to_int " <> a <> ")"
else "(ubv_to_int " <> a <> ")"
_ -> tryFPCast
KUnbounded -> case kTo of
KReal -> "(to_real " <> a <> ")"
KBounded _ n -> "((_ int_to_bv " <> showText n <> ") " <> a <> ")"
_ -> tryFPCast
KReal -> case kTo of
KUnbounded -> "(to_int " <> a <> ")"
_ -> tryFPCast
_ -> tryFPCast
where -- See if we can push this down to a float-cast, using sRNE. This happens if one of the kinds is a float/double.
-- Otherwise complain
tryFPCast
| any (\k -> isFloat k || isDouble k) [kFrom, kTo]
= handleFPCast kFrom kTo (smtRoundingMode RoundNearestTiesToEven) a
| True
= error $ "SBV.SMTLib2: Unexpected cast from: " ++ show kFrom ++ " to " ++ show kTo
fromBV upConv m n
| n > m = upConv (n - m)
| m == n = a
| True = extract (n - 1)
signExtend i = "((_ sign_extend " <> showText i <> ") " <> a <> ")"
zeroExtend i = "((_ zero_extend " <> showText i <> ") " <> a <> ")"
extract i = "((_ extract " <> showText i <> " 0) " <> a <> ")"
-- Translation of pseudo-booleans, in case the solver supports them
handlePB :: PBOp -> [Text] -> Text
handlePB (PB_AtMost k) args = "((_ at-most " <> showText k <> ") " <> T.unwords args <> ")"
handlePB (PB_AtLeast k) args = "((_ at-least " <> showText k <> ") " <> T.unwords args <> ")"
handlePB (PB_Exactly k) args = "((_ pbeq " <> T.unwords (map showText (k : replicate (length args) 1)) <> ") " <> T.unwords args <> ")"
handlePB (PB_Eq cs k) args = "((_ pbeq " <> T.unwords (map showText (k : cs)) <> ") " <> T.unwords args <> ")"
handlePB (PB_Le cs k) args = "((_ pble " <> T.unwords (map showText (k : cs)) <> ") " <> T.unwords args <> ")"
handlePB (PB_Ge cs k) args = "((_ pbge " <> T.unwords (map showText (k : cs)) <> ") " <> T.unwords args <> ")"
-- Translation of pseudo-booleans, in case the solver does *not* support them
reducePB :: PBOp -> [Text] -> Text
reducePB op args = case op of
PB_AtMost k -> "(<= " <> addIf (repeat 1) <> " " <> showText k <> ")"
PB_AtLeast k -> "(>= " <> addIf (repeat 1) <> " " <> showText k <> ")"
PB_Exactly k -> "(= " <> addIf (repeat 1) <> " " <> showText k <> ")"
PB_Le cs k -> "(<= " <> addIf cs <> " " <> showText k <> ")"
PB_Ge cs k -> "(>= " <> addIf cs <> " " <> showText k <> ")"
PB_Eq cs k -> "(= " <> addIf cs <> " " <> showText k <> ")"
where addIf :: [Int] -> Text
addIf cs = "(+ " <> T.unwords ["(ite " <> a <> " " <> showText c <> " 0)" | (a, c) <- zip args cs] <> ")"
-- | Translate an option setting to SMTLib. Note the SetLogic/SetInfo discrepancy.
setSMTOption :: SMTConfig -> SMTOption -> Text
setSMTOption cfg = set
where set (DiagnosticOutputChannel f) = opt [":diagnostic-output-channel", showText f]
set (ProduceAssertions b) = opt [":produce-assertions", smtBool b]
set (ProduceAssignments b) = opt [":produce-assignments", smtBool b]
set (ProduceProofs b) = opt [":produce-proofs", smtBool b]
set (ProduceInterpolants b) = opt [":produce-interpolants", smtBool b]
set (ProduceUnsatAssumptions b) = opt [":produce-unsat-assumptions", smtBool b]
set (ProduceUnsatCores b) = opt [":produce-unsat-cores", smtBool b]
set (ProduceAbducts b) = opt [":produce-abducts", smtBool b]
set (RandomSeed i) = opt [":random-seed", showText i]
set (ReproducibleResourceLimit i) = opt [":reproducible-resource-limit", showText i]
set (SMTVerbosity i) = opt [":verbosity", showText i]
set (OptionKeyword k as) = opt (T.pack k : map T.pack as)
set (SetLogic l) = logicString cfg l
set (SetInfo k as) = info (T.pack k : map T.pack as)
set (SetTimeOut i) = opt $ timeOut i
opt xs = "(set-option " <> T.unwords xs <> ")"
info xs = "(set-info " <> T.unwords xs <> ")"
-- timeout is not standard. We distinguish between CVC/Z3. All else follows z3
-- The value is in milliseconds, which is how z3/CVC interpret it
timeOut i = case name (solver cfg) of
CVC4 -> [":tlimit-per", showText i]
CVC5 -> [":tlimit-per", showText i]
_ -> [":timeout", showText i]
-- SMTLib's True/False is spelled differently than Haskell's.
smtBool :: Bool -> Text
smtBool True = "true"
smtBool False = "false"
-- | Set the logic, accounting for solver inconsistencies.
logicString :: SMTConfig -> Logic -> Text
logicString cfg = pick
where
slvr = name (solver cfg)
-- This is more or less showText, but with exceptions:
--
-- Logic_ALL : HO_ALL for CVC5 to get support for higher-order features.
-- QF_FPBV : Bitwuzla calls it QF_BVFP. See: https://github.com/LeventErkok/sbv/issues/774
-- Logic_NONE: Sets nothing, just sets a comment
pick Logic_ALL | CVC5 <- slvr = wrap "HO_ALL"
pick QF_FPBV | Bitwuzla <- slvr = wrap "QF_BVFP"
pick Logic_NONE = "; NB. not setting the logic per user request of Logic_NONE"
-- Fall thru
pick l = wrap (showText l)
wrap l = "(set-logic " <> l <> ")"
{- HLint ignore module "Use record patterns" -}