----------------------------------------------------------------------------- -- | -- Module : Data.SBV.Lambda -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer: erkokl@gmail.com -- Stability : experimental -- -- Generating lambda-expressions, constraints, and named functions, for (limited) -- higher-order function support in SBV. ----------------------------------------------------------------------------- {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE NamedFieldPuns #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE UndecidableInstances #-} {-# OPTIONS_GHC -Wall -Werror -fno-warn-orphans #-} module Data.SBV.Lambda ( lambda, lambdaStr , namedLambda, namedLambdaStr , constraint, constraintStr ) where import Control.Monad (join) import Control.Monad.Trans (liftIO, MonadIO) import Data.SBV.Core.Data import Data.SBV.Core.Kind import Data.SBV.SMT.SMTLib2 import Data.SBV.Utils.PrettyNum import Data.SBV.Core.Symbolic hiding (mkNewState, fresh) import qualified Data.SBV.Core.Symbolic as S (mkNewState) import Data.IORef (readIORef, modifyIORef') import Data.List import qualified Data.Foldable as F import qualified Data.Map.Strict as M import qualified Data.Generics.Uniplate.Data as G data Defn = Defn [String] -- The uninterpreted names referred to in the body (Maybe [(Quantifier, String)]) -- Param declaration groups, if any (Int -> String) -- Body, given the tab amount. -- | Maka a new substate from the incoming state, sharing parts as necessary inSubState :: MonadIO m => State -> (State -> m b) -> m b inSubState inState comp = do ll <- liftIO $ readIORef (rLambdaLevel inState) stEmpty <- S.mkNewState (stCfg inState) (LambdaGen (ll + 1)) let share fld = fld inState -- reuse the field from the parent-context fresh fld = fld stEmpty -- create a new field here -- freshen certain fields, sharing some from the parent, and run the comp -- Here's the guidance: -- -- * Anything that's "shared" updates the calling context. It better be the case -- that the caller can handle that info. -- * Anything that's "fresh" will be used in this substate, and will be forgotten. -- It better be the case that in "toLambda" below, you do something with it. -- -- Note the above applies to all the IORefs, which is most of the state, though -- not all. For the time being, those are pathCond, stCfg, and startTime; which -- don't really impact anything. comp State { -- These are not IORefs; so we share by copying the value; changes won't be copied back sbvContext = share sbvContext , pathCond = share pathCond , startTime = share startTime -- These are shared IORef's; and is shared, so they will be copied back to the parent state , rProgInfo = share rProgInfo , rIncState = share rIncState , rCInfo = share rCInfo , rUsedKinds = share rUsedKinds , rUsedLbls = share rUsedLbls , rUIMap = share rUIMap , rUserFuncs = share rUserFuncs , rCgMap = share rCgMap , rDefns = share rDefns , rSMTOptions = share rSMTOptions , rOptGoals = share rOptGoals , rAsserts = share rAsserts , rOutstandingAsserts = share rOutstandingAsserts , rPartitionVars = share rPartitionVars -- Everything else is fresh in the substate; i.e., will not copy back , stCfg = fresh stCfg , runMode = fresh runMode , rctr = fresh rctr , rLambdaLevel = fresh rLambdaLevel , rtblMap = fresh rtblMap , rArrayMap = fresh rArrayMap , rAICache = fresh rAICache , rinps = fresh rinps , rlambdaInps = fresh rlambdaInps , rConstraints = fresh rConstraints , rObservables = fresh rObservables , routs = fresh routs , spgm = fresh spgm , rconstMap = fresh rconstMap , rexprMap = fresh rexprMap , rSVCache = fresh rSVCache , rQueryState = fresh rQueryState -- keep track of our parent , parentState = Just inState } -- In this case, we expect just one group of parameters, with universal quantification extractAllUniversals :: [(Quantifier, String)] -> String extractAllUniversals [(ALL, s)] = s extractAllUniversals other = error $ unlines [ "" , "*** Data.SBV.Lambda: Impossible happened. Got existential quantifiers." , "***" , "*** Params: " ++ show other , "***" , "*** Please report this as a bug!" ] -- | Generic creator for anonymous lamdas. lambdaGen :: (MonadIO m, Lambda (SymbolicT m) a) => (Defn -> b) -> State -> Kind -> a -> m b lambdaGen trans inState fk f = inSubState inState $ \st -> trans <$> convert st fk (mkLambda st f) -- | Create an SMTLib lambda, in the given state. lambda :: (MonadIO m, Lambda (SymbolicT m) a) => State -> Kind -> a -> m SMTDef lambda inState fk = lambdaGen mkLam inState fk where mkLam (Defn frees params body) = SMTLam fk frees (extractAllUniversals <$> params) body -- | Create an anonymous lambda, rendered as n SMTLib string lambdaStr :: (MonadIO m, Lambda (SymbolicT m) a) => State -> Kind -> a -> m String lambdaStr = lambdaGen mkLam where mkLam (Defn _frees Nothing body) = body 0 mkLam (Defn _frees (Just params) body) = "(lambda " ++ extractAllUniversals params ++ "\n" ++ body 2 ++ ")" -- | Generaic creator for named functions, namedLambdaGen :: (MonadIO m, Lambda (SymbolicT m) a) => (Defn -> b) -> State -> Kind -> a -> m b namedLambdaGen trans inState fk f = inSubState inState $ \st -> trans <$> convert st fk (mkLambda st f) -- | Create a named SMTLib function, in the given state. namedLambda :: (MonadIO m, Lambda (SymbolicT m) a) => State -> String -> Kind -> a -> m SMTDef namedLambda inState nm fk = namedLambdaGen mkDef inState fk where mkDef (Defn frees params body) = SMTDef nm fk frees (extractAllUniversals <$> params) body -- | Create a named SMTLib function, in the given state, string version namedLambdaStr :: (MonadIO m, Lambda (SymbolicT m) a) => State -> String -> SBVType -> a -> m String namedLambdaStr inState nm t = namedLambdaGen mkDef inState fk where mkDef (Defn frees params body) = concat $ declUserFuns [(SMTDef nm fk frees (extractAllUniversals <$> params) body, t)] fk = case t of SBVType [] -> error $ "namedLambdaStr: Invalid type for " ++ show nm ++ ", empty!" SBVType xs -> last xs -- | Generic constraint generator. constraintGen :: (MonadIO m, Constraint (SymbolicT m) a) => ([String] -> (Int -> String) -> b) -> State -> a -> m b constraintGen trans inState@State{rProgInfo} f = do -- indicate we have quantifiers liftIO $ modifyIORef' rProgInfo (\u -> u{hasQuants = True}) let mkDef (Defn deps Nothing body) = trans deps body mkDef (Defn deps (Just params) body) = trans deps $ \i -> unwords (map mkGroup params) ++ "\n" ++ body (i + 2) ++ replicate (length params) ')' mkGroup (ALL, s) = "(forall " ++ s mkGroup (EX, s) = "(exists " ++ s inSubState inState $ \st -> mkDef <$> convert st KBool (mkConstraint st f >>= output >> pure ()) -- | A constraint can be turned into a boolean instance Constraint Symbolic a => QuantifiedBool a where quantifiedBool qb = SBV $ SVal KBool $ Right $ cache f where f st = liftIO $ constraint st qb -- | Generate a constraint. constraint :: (MonadIO m, Constraint (SymbolicT m) a) => State -> a -> m SV constraint st = join . constraintGen mkSV st where mkSV _deps d = liftIO $ newExpr st KBool (SBVApp (QuantifiedBool (d 0)) []) -- | Generate a constraint, string version constraintStr :: (MonadIO m, Constraint (SymbolicT m) a) => State -> a -> m String constraintStr = constraintGen toStr where toStr deps body = intercalate "\n" [ "; user defined axiom: " ++ depInfo deps , "(assert " ++ body 2 ++ ")" ] depInfo [] = "" depInfo ds = "[Refers to: " ++ intercalate ", " ds ++ "]" -- | Convert to an appropriate SMTLib representation. convert :: MonadIO m => State -> Kind -> SymbolicT m () -> m Defn convert st expectedKind comp = do ((), res) <- runSymbolicInState st comp curProgInfo <- liftIO $ readIORef (rProgInfo st) pure $ toLambda curProgInfo (stCfg st) expectedKind res -- | Convert the result of a symbolic run to a more abstract representation toLambda :: ProgInfo -> SMTConfig -> Kind -> Result -> Defn toLambda curProgInfo cfg expectedKind result@Result{resAsgns = SBVPgm asgnsSeq} = sh result where tbd xs = error $ unlines $ "*** Data.SBV.lambda: Unsupported construct." : map ("*** " ++) ("" : xs ++ ["", report]) bad xs = error $ unlines $ "*** Data.SBV.lambda: Impossible happened." : map ("*** " ++) ("" : xs ++ ["", bugReport]) report = "Please request this as a feature at https://github.com/LeventErkok/sbv/issues" bugReport = "Please report this at https://github.com/LeventErkok/sbv/issues" sh (Result _hasQuants -- Has quantified booleans? Does not apply _ki -- Kind info, we're assuming that all the kinds used are already available in the surrounding context. -- There's no way to create a new kind in a lambda. If a new kind is used, it should be registered. _qcInfo -- Quickcheck info, does not apply, ignored observables -- Observables: There's no way to display these, so ignore _codeSegs -- UI code segments: Again, shouldn't happen; if present, error out is -- Inputs ( _allConsts -- Not needed, consts are sufficient for this translation , consts -- constants used ) tbls -- Tables _arrs -- Arrays : nothing to do with them _uis -- Uninterpeted constants: nothing to do with them _axs -- Axioms definitions : nothing to do with them pgm -- Assignments cstrs -- Additional constraints: Not currently supported inside lambda's assertions -- Assertions: Not currently supported inside lambda's outputs -- Outputs of the lambda (should be singular) ) | not (null cstrs) = tbd [ "Constraints." , " Saw: " ++ show (length cstrs) ++ " additional constraint(s)." ] | not (null assertions) = tbd [ "Assertions." , " Saw: " ++ intercalate ", " [n | (n, _, _) <- assertions] ] | not (null observables) = tbd [ "Observables." , " Saw: " ++ intercalate ", " [n | (n, _, _) <- observables] ] | kindOf out /= expectedKind = bad [ "Expected kind and final kind do not match" , " Saw : " ++ show (kindOf out) , " Expected: " ++ show expectedKind ] | True = res where res = Defn (nub [nm | Uninterpreted nm <- G.universeBi asgnsSeq]) mbParam (intercalate "\n" . body) params = case is of ResultTopInps as -> bad [ "Top inputs" , " Saw: " ++ show as ] ResultLamInps xs -> map (\(q, v) -> (q, getSV v)) xs mbParam | null params = Nothing | True = Just [(q, paramList (map snd l)) | l@((q, _) : _) <- pGroups] where pGroups = groupBy (\(q1, _) (q2, _) -> q1 == q2) params paramList ps = '(' : unwords (map (\p -> '(' : show p ++ " " ++ smtType (kindOf p) ++ ")") ps) ++ ")" body tabAmnt | null constTables , null nonConstTables , Just e <- simpleBody (constBindings ++ svBindings) out = [tab ++ e] | True = map (tab ++) $ [mkLet sv | sv <- constBindings] ++ [mkTable t | t <- constTables] ++ walk svBindings nonConstTables ++ [show out ++ replicate totalClose ')'] where tab = replicate tabAmnt ' ' mkBind l r = "(let ((" ++ l ++ " " ++ r ++ "))" mkLet (s, v) = mkBind (show s) v mkTable (((i, ak, rk), elts), _) = mkBind nm (lambdaTable (map (const ' ') nm) ak rk elts) where nm = "table" ++ show i totalClose = length constBindings + length svBindings + length constTables + length nonConstTables walk [] [] = [] walk [] remaining = error $ "Data.SBV: Impossible: Ran out of bindings, but tables remain: " ++ show remaining walk (cur@(SV _ nd, _) : rest) remaining = map (mkTable . snd) ready ++ [mkLet cur] ++ walk rest notReady where (ready, notReady) = partition (\(need, _) -> need < getLLI nd) remaining getLLI :: NodeId -> (Int, Int) getLLI (NodeId (_, l, i)) = (l, i) -- if we have just one definition returning it, simplify simpleBody :: [(SV, String)] -> SV -> Maybe String simpleBody [(v, e)] o | v == o = Just e simpleBody _ _ = Nothing assignments = F.toList (pgmAssignments pgm) constants = filter ((`notElem` [falseSV, trueSV]) . fst) consts constBindings, svBindings :: [(SV, String)] constBindings = map mkConst constants svBindings = map mkAsgn assignments mkConst :: (SV, CV) -> (SV, String) mkConst (sv, cv) = (sv, cvToSMTLib (roundingMode cfg) cv) out :: SV out = case outputs of [o] -> o _ -> bad [ "Unexpected non-singular output" , " Saw: " ++ show outputs ] rm = roundingMode cfg -- NB. The following is dead-code, since we ensure tbls is empty -- We used to support this, but there are issues, so dropping support -- See, for instance, https://github.com/LeventErkok/sbv/issues/664 (tableMap, constTables, nonConstTablesUnindexed) = constructTables rm consts tbls -- Index each non-const table with the largest index of SV it needs nonConstTables = [ (maximum ((0, 0) : [getLLI n | SV _ n <- elts]), nct) | nct@((_, elts), _) <- nonConstTablesUnindexed] lambdaTable :: String -> Kind -> Kind -> [SV] -> String lambdaTable extraSpace ak rk elts = "(lambda ((" ++ lv ++ " " ++ smtType ak ++ "))" ++ space ++ chain 0 elts ++ ")" where cnst k i = cvtCV rm (mkConstCV k (i::Integer)) lv = "idx" -- If more than 5 elts, use new-lines long = not (null (drop 5 elts)) space | long = "\n " ++ extraSpace | True = " " chain _ [] = cnst rk 0 chain _ [x] = show x chain i (x:xs) = "(ite (= " ++ lv ++ " " ++ cnst ak i ++ ") " ++ show x ++ space ++ chain (i+1) xs ++ ")" mkAsgn (sv, e) = (sv, converter e) converter = cvtExp curProgInfo solverCaps rm tableMap funcMap where solverCaps = capabilities (solver cfg) funcMap = M.empty {- HLint ignore module "Use second" -}