liquid-fixpoint-0.9.6.3.1: src/Language/Fixpoint/SortCheck.hs
{-# LANGUAGE CPP #-}
{-# LANGUAGE Strict #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TupleSections #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternGuards #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE RankNTypes #-}
-- | This module has the functions that perform sort-checking, and related
-- operations on Fixpoint expressions and predicates.
module Language.Fixpoint.SortCheck (
-- * Sort Substitutions
TVSubst
, Env
, mkSearchEnv
-- * Checking Well-Formedness
, checkSorted
, checkSortedReft
, checkSortedReftFull
, checkSortFull
, pruneUnsortedReft
-- * Sort inference
, sortExpr
, checkSortExpr
, exprSort
, exprSortMaybe
-- * Unify
, unifyFast
, unifySorts
, unifyTo1
, unifys
-- * Apply Substitution
, apply
, defuncEApp
-- * Exported Sorts
, boolSort
, strSort
-- * Sort-Directed Transformations
, Elaborate (..)
, applySorts
, elabApply
, elabExpr
, elabNumeric
, unApply
, unElab
, unElabSortedReft
, unApplySortedReft
, unApplyAt
, toInt
-- * Predicates on Sorts
, isFirstOrder
, isMono
, runCM0
) where
-- import Control.DeepSeq
import Control.Exception (Exception, catch, try, throwIO)
import Control.Monad
import Control.Monad.Reader
import qualified Data.HashMap.Strict as M
import Data.IORef
import qualified Data.List as L
import Data.Maybe (mapMaybe, fromMaybe, catMaybes, isJust)
import Language.Fixpoint.Types.PrettyPrint
import Language.Fixpoint.Misc
import Language.Fixpoint.Types hiding (subst, GInfo(..), senv)
import qualified Language.Fixpoint.Types.Visitor as Vis
import qualified Language.Fixpoint.Smt.Theories as Thy
import Text.PrettyPrint.HughesPJ.Compat
import Text.Printf
import GHC.Stack
import qualified Language.Fixpoint.Types as F
import System.IO.Unsafe (unsafePerformIO)
--import Debug.Trace as Debug
-- If set to 'True', enable precise logging via CallStacks.
debugLogs :: Bool
debugLogs = False
traced :: HasCallStack => (HasCallStack => String) -> String
traced str =
if debugLogs
then let prettified = prettyCallStack (popCallStack callStack)
in str <> " (at " <> prettified <> ")"
else str
--------------------------------------------------------------------------------
-- | Predicates on Sorts -------------------------------------------------------
--------------------------------------------------------------------------------
isMono :: Sort -> Bool
--------------------------------------------------------------------------------
isMono = null . Vis.foldSort fv []
where
fv vs (FVar i) = i : vs
fv vs _ = vs
--------------------------------------------------------------------------------
-- | Elaborate: make polymorphic instantiation explicit via casts,
-- make applications monomorphic for SMTLIB. This deals with
-- polymorphism by `elaborate`-ing all refinements except for
-- KVars. THIS IS NOW MANDATORY as sort-variables can be
-- instantiated to `int` and `bool`.
--------------------------------------------------------------------------------
class Elaborate a where
elaborate :: Located String -> SymEnv -> a -> a
instance (Loc a) => Elaborate (SInfo a) where
elaborate msg senv si = si
{ F.cm = elaborate msg senv <$> F.cm si
, F.bs = elaborate msg senv $ F.bs si
, F.asserts = elaborate msg senv <$> F.asserts si
}
instance (Elaborate e) => (Elaborate (Triggered e)) where
elaborate msg env t = fmap (elaborate msg env) t
instance (Elaborate a) => (Elaborate (Maybe a)) where
elaborate msg env t = fmap (elaborate msg env) t
instance Elaborate Sort where
elaborate _ _ = go
where
go s | isString s = strSort
go (FAbs i s) = FAbs i (go s)
go (FFunc s1 s2) = funSort (go s1) (go s2)
go (FApp s1 s2) = FApp (go s1) (go s2)
go s = s
funSort :: Sort -> Sort -> Sort
funSort = FApp . FApp funcSort
instance Elaborate AxiomEnv where
elaborate msg env ae = ae
{ aenvEqs = elaborate msg env (aenvEqs ae)
-- MISSING SORTS OOPS, aenvSimpl = elaborate msg env (aenvSimpl ae)
}
instance Elaborate Rewrite where
elaborate msg env rw = rw { smBody = skipElabExpr msg env' (smBody rw) }
where
env' = insertsSymEnv env undefined
instance Elaborate Equation where
elaborate msg env eq = eq { eqBody = skipElabExpr msg env' (eqBody eq) }
where
env' = insertsSymEnv env (eqArgs eq)
instance Elaborate Expr where
elaborate msg env =
elabNumeric . elabApply env' . elabExpr msg env' . elabFSet
where
env' = coerceEnv env
skipElabExpr :: Located String -> SymEnv -> Expr -> Expr
skipElabExpr msg env e = case elabExprE msg env e of
Left _ -> e
Right e' -> elabNumeric . elabApply env $ e'
instance Elaborate (Symbol, Sort) where
elaborate msg env (x, s) = (x, elaborate msg env s)
instance Elaborate a => Elaborate [a] where
elaborate msg env xs = elaborate msg env <$> xs
elabNumeric :: Expr -> Expr
elabNumeric = Vis.mapExprOnExpr go
where
go (ETimes e1 e2)
| exprSort "txn1" e1 == FReal
, exprSort "txn2" e2 == FReal
= ERTimes e1 e2
go (EDiv e1 e2)
| exprSort ("txn3: " ++ showpp e1) e1 == FReal
, exprSort "txn4" e2 == FReal
= ERDiv e1 e2
go e
= e
instance Elaborate SortedReft where
elaborate msg env (RR s (Reft (v, e))) = RR s (Reft (v, e'))
where
e' = elaborate msg env' e
env' = insertSymEnv v s env
instance (Loc a) => Elaborate (BindEnv a) where
elaborate msg env = mapBindEnv (\i (x, sr, l) -> (x, elaborate (msg' l i x sr) env sr, l))
where
msg' l i x sr = atLoc l (val msg ++ unwords [" elabBE", show i, show x, show sr])
instance (Loc a) => Elaborate (SimpC a) where
elaborate msg env c = c {_crhs = elaborate msg' env (_crhs c) }
where msg' = atLoc c (val msg)
---------------------------------------------------------------------------------
-- | 'elabFSet' replaces all finset theory operations with array-based encodings.
---------------------------------------------------------------------------------
elabFSet :: Expr -> Expr
elabFSet (EApp h@(EVar f) e)
| f == Thy.setEmpty = EApp (EVar Thy.arrConst) PFalse
| f == Thy.setEmp = PAtom Eq (EApp (EVar Thy.arrConst) PFalse) (elabFSet e)
| f == Thy.setSng = EApp (EApp (EApp (EVar Thy.arrStore) (EApp (EVar Thy.arrConst) PFalse)) (elabFSet e)) PTrue
| f == Thy.setCom = EApp (EVar Thy.arrMapNot) (elabFSet e)
| otherwise = EApp (elabFSet h) (elabFSet e)
elabFSet (EApp (EApp h@(EVar f) e1) e2)
| f == Thy.setMem = EApp (EApp (EVar Thy.arrSelect) (elabFSet e2)) (elabFSet e1)
| f == Thy.setCup = EApp (EApp (EVar Thy.arrMapOr) (elabFSet e1)) (elabFSet e2)
| f == Thy.setCap = EApp (EApp (EVar Thy.arrMapAnd) (elabFSet e1)) (elabFSet e2)
| f == Thy.setAdd = EApp (EApp (EApp (EVar Thy.arrStore) (elabFSet e1)) (elabFSet e2)) PTrue
-- A \ B == A /\ ~B == ~(A => B)
| f == Thy.setDif = EApp (EApp (EVar Thy.arrMapAnd) (elabFSet e1)) (EApp (EVar Thy.arrMapNot) (elabFSet e2))
| f == Thy.setSub = PAtom Eq (EApp (EVar Thy.arrConst) PTrue) (EApp (EApp (EVar Thy.arrMapImp) (elabFSet e1)) (elabFSet e2))
| otherwise = EApp (EApp (elabFSet h) (elabFSet e1)) (elabFSet e2)
elabFSet (EApp e1 e2) = EApp (elabFSet e1) (elabFSet e2)
elabFSet (ENeg e) = ENeg (elabFSet e)
elabFSet (EBin b e1 e2) = EBin b (elabFSet e1) (elabFSet e2)
elabFSet (EIte e1 e2 e3) = EIte (elabFSet e1) (elabFSet e2) (elabFSet e3)
elabFSet (ECst e t) = ECst (elabFSet e) t
elabFSet (ELam b e) = ELam b (elabFSet e)
elabFSet (ETApp e t) = ETApp (elabFSet e) t
elabFSet (ETAbs e t) = ETAbs (elabFSet e) t
elabFSet (PAnd es) = PAnd (elabFSet <$> es)
elabFSet (POr es) = POr (elabFSet <$> es)
elabFSet (PNot e) = PNot (elabFSet e)
elabFSet (PImp e1 e2) = PImp (elabFSet e1) (elabFSet e2)
elabFSet (PIff e1 e2) = PIff (elabFSet e1) (elabFSet e2)
elabFSet (PAtom r e1 e2) = PAtom r (elabFSet e1) (elabFSet e2)
elabFSet (PAll bs e) = PAll bs (elabFSet e)
elabFSet (PExist bs e) = PExist bs (elabFSet e)
elabFSet (PGrad k su i e) = PGrad k su i (elabFSet e)
elabFSet (ECoerc a t e) = ECoerc a t (elabFSet e)
elabFSet e = e
--------------------------------------------------------------------------------
-- | 'elabExpr' adds "casts" to decorate polymorphic instantiation sites.
--------------------------------------------------------------------------------
elabExpr :: Located String -> SymEnv -> Expr -> Expr
elabExpr msg env e = case elabExprE msg env e of
Left ex -> die ex
Right e' -> F.notracepp ("elabExp " ++ showpp e) e'
elabExprE :: Located String -> SymEnv -> Expr -> Either Error Expr
elabExprE msg env e =
case runCM0 (srcSpan msg) (elab (env, envLookup) e) of
Left (ChError f') ->
let e' = f' ()
in Left $ err (srcSpan e') (d (val e'))
Right s -> Right (fst s)
where
sEnv = seSort env
envLookup = (`lookupSEnvWithDistance` sEnv)
d m = vcat [ "elaborate" <+> text (val msg) <+> "failed on:"
, nest 4 (pprint e)
, "with error"
, nest 4 (text m)
, "in environment"
, nest 4 (pprint $ subEnv sEnv e)
]
--------------------------------------------------------------------------------
-- | 'elabApply' replaces all direct function calls indirect calls via `apply`
--------------------------------------------------------------------------------
elabApply :: SymEnv -> Expr -> Expr
elabApply env = go
where
go e = case splitArgs e of
(e', []) -> step e'
(f , es) -> defuncEApp env (go f) (mapFst go <$> es)
step (PAnd []) = PTrue
step (POr []) = PFalse
step (ENeg e) = ENeg (go e)
step (EBin o e1 e2) = EBin o (go e1) (go e2)
step (EIte e1 e2 e3) = EIte (go e1) (go e2) (go e3)
step (ECst e t) = ECst (go e) t
step (PAnd ps) = PAnd (go <$> ps)
step (POr ps) = POr (go <$> ps)
step (PNot p) = PNot (go p)
step (PImp p q) = PImp (go p) (go q)
step (PIff p q) = PIff (go p) (go q)
step (PExist bs p) = PExist bs (go p)
step (PAll bs p) = PAll bs (go p)
step (PAtom r e1 e2) = PAtom r (go e1) (go e2)
step e@EApp {} = go e
step (ELam b e) = ELam b (go e)
step (ECoerc a t e) = ECoerc a t (go e)
step (PGrad k su i e) = PGrad k su i (go e)
step e@PKVar{} = e
step e@ESym{} = e
step e@ECon{} = e
step e@EVar{} = e
-- ETApp, ETAbs, PAll, PExist
step e = error $ "TODO elabApply: " ++ showpp e
--------------------------------------------------------------------------------
-- | Sort Inference ------------------------------------------------------------
--------------------------------------------------------------------------------
sortExpr :: SrcSpan -> SEnv Sort -> Expr -> Sort
sortExpr l γ e = case runCM0 l (checkExpr f e) of
Left (ChError f') -> die $ err l (d (val (f' ())))
Right s -> s
where
f = (`lookupSEnvWithDistance` γ)
d m = vcat [ "sortExpr failed on expression:"
, nest 4 (pprint e)
, "with error:"
, nest 4 (text m)
, "in environment"
, nest 4 (pprint γ)
]
checkSortExpr :: SrcSpan -> SEnv Sort -> Expr -> Maybe Sort
checkSortExpr sp γ e = case runCM0 sp (checkExpr f e) of
Left _ -> Nothing
Right s -> Just s
where
f x = case lookupSEnv x γ of
Just z -> Found z
Nothing -> Alts []
subEnv :: (Subable e) => SEnv a -> e -> SEnv a
subEnv g e = intersectWithSEnv const g g'
where
g' = fromListSEnv $ (, ()) <$> syms e
--------------------------------------------------------------------------------
-- | Checking Refinements ------------------------------------------------------
--------------------------------------------------------------------------------
-- | Types used throughout checker
type CheckM = ReaderT ChState IO
-- We guard errors with a lambda to prevent accidental eager
-- evaluation of the payload. This module is using -XStrict.
-- See also Note [Lazy error messages].
newtype ChError = ChError (() -> Located String)
instance Show ChError where
show (ChError f) = show (f ())
instance Exception ChError where
data ChState = ChS { chCount :: IORef Int, chSpan :: SrcSpan }
type Env = Symbol -> SESearch Sort
type ElabEnv = (SymEnv, Env)
--------------------------------------------------------------------------------
mkSearchEnv :: SEnv a -> Symbol -> SESearch a
--------------------------------------------------------------------------------
mkSearchEnv env x = lookupSEnvWithDistance x env
-- withError :: CheckM a -> ChError -> CheckM a
-- act `withError` e' = act `catchError` (\e -> throwError (atLoc e (val e ++ "\n because\n" ++ val e')))
withError :: HasCallStack => CheckM a -> String -> CheckM a
act `withError` msg = do
r <- ask
liftIO $ runReaderT act r `catch`
(\(ChError f) ->
throwIO $ ChError $ \_ ->
let e = f ()
in atLoc e (val e ++ "\n because\n" ++ msg)
)
-- XXX: Why start at 42?
{-# NOINLINE varCounterRef #-}
varCounterRef :: IORef Int
varCounterRef = unsafePerformIO $ newIORef 42
-- XXX: Since 'varCounterRef' was made global, this
-- function is not referentially transparent.
-- Each evaluation of the function starts with a different
-- value of counter.
runCM0 :: SrcSpan -> CheckM a -> Either ChError a
runCM0 sp act = unsafePerformIO $ do
try (runReaderT act (ChS varCounterRef sp))
fresh :: CheckM Int
fresh = do
rn <- asks chCount
liftIO $ atomicModifyIORef' rn $ \n -> (n+1, n)
--------------------------------------------------------------------------------
-- | Checking Refinements ------------------------------------------------------
--------------------------------------------------------------------------------
checkSortedReft :: SEnv SortedReft -> [Symbol] -> SortedReft -> Maybe Doc
checkSortedReft env xs sr = applyNonNull Nothing oops unknowns
where
oops = Just . (text "Unknown symbols:" <+>) . toFix
unknowns = [ x | x <- syms sr, x `notElem` v : xs, not (x `memberSEnv` env)]
Reft (v,_) = sr_reft sr
checkSortedReftFull :: Checkable a => SrcSpan -> SEnv SortedReft -> a -> Maybe Doc
checkSortedReftFull sp γ t =
case runCM0 sp (check γ' t) of
Left (ChError f) -> Just (text (val (f ())))
Right _ -> Nothing
where
γ' = sr_sort <$> γ
checkSortFull :: Checkable a => SrcSpan -> SEnv SortedReft -> Sort -> a -> Maybe Doc
checkSortFull sp γ s t =
case runCM0 sp (checkSort γ' s t) of
Left (ChError f) -> Just (text (val (f ())))
Right _ -> Nothing
where
γ' = sr_sort <$> γ
checkSorted :: Checkable a => SrcSpan -> SEnv Sort -> a -> Maybe Doc
checkSorted sp γ t =
case runCM0 sp (check γ t) of
Left (ChError f) -> Just (text (val (f ())))
Right _ -> Nothing
pruneUnsortedReft :: SEnv Sort -> Templates -> SortedReft -> SortedReft
pruneUnsortedReft _ t r
| isEmptyTemplates t
= r
pruneUnsortedReft γ t (RR s (Reft (v, p)))
| isAnyTemplates t
-- this is the old code that checks everything
= RR s (Reft (v, tx filterAny p))
| otherwise
= RR s (Reft (v, tx (filter filterWithTemplate) p))
where
filterAny = mapMaybe (checkPred' f)
filterWithTemplate e = not (matchesTemplates t e) || isJust (checkPred' f e)
tx f' = pAnd . f' . conjuncts
f = (`lookupSEnvWithDistance` γ')
γ' = insertSEnv v s γ
-- wmsg t r = "WARNING: prune unsorted reft:\n" ++ showFix r ++ "\n" ++ t
checkPred' :: Env -> Expr -> Maybe Expr
checkPred' f p = res -- traceFix ("checkPred: p = " ++ showFix p) $ res
where
res = case runCM0 dummySpan (checkPred f p) of
Left _err -> notracepp ("Removing" ++ showpp p) Nothing
Right _ -> Just p
class Checkable a where
check :: SEnv Sort -> a -> CheckM ()
checkSort :: SEnv Sort -> Sort -> a -> CheckM ()
checkSort γ _ = check γ
instance Checkable Expr where
check γ e = void $ checkExpr f e
where f = (`lookupSEnvWithDistance` coerceSortEnv γ)
checkSort γ s e = void $ checkExpr f (ECst e (coerceSetToArray s))
where f = (`lookupSEnvWithDistance` coerceSortEnv γ)
instance Checkable SortedReft where
check γ (RR s (Reft (v, ra))) = check γ' ra
where
γ' = insertSEnv v s γ
--------------------------------------------------------------------------------
-- | Checking Expressions ------------------------------------------------------
--------------------------------------------------------------------------------
checkExpr :: Env -> Expr -> CheckM Sort
checkExpr _ (ESym _) = return strSort
checkExpr _ (ECon (I _)) = return FInt
checkExpr _ (ECon (R _)) = return FReal
checkExpr _ (ECon (L _ s)) = return s
checkExpr f (EVar x) = checkSym f x
checkExpr f (ENeg e) = checkNeg f e
checkExpr f (EBin o e1 e2) = checkOp f e1 o e2
checkExpr f (EIte p e1 e2) = checkIte f p e1 e2
checkExpr f (ECst e t) = checkCst f t e
checkExpr f (EApp g e) = checkApp f Nothing g e
checkExpr f (PNot p) = checkPred f p >> return boolSort
checkExpr f (PImp p p') = mapM_ (checkPred f) [p, p'] >> return boolSort
checkExpr f (PIff p p') = mapM_ (checkPred f) [p, p'] >> return boolSort
checkExpr f (PAnd ps) = mapM_ (checkPred f) ps >> return boolSort
checkExpr f (POr ps) = mapM_ (checkPred f) ps >> return boolSort
checkExpr f (PAtom r e e') = checkRel f r e e' >> return boolSort
checkExpr _ PKVar{} = return boolSort
checkExpr f (PGrad _ _ _ e) = checkPred f e >> return boolSort
checkExpr f (PAll bs e ) = checkExpr (addEnv f bs) e
checkExpr f (PExist bs e) = checkExpr (addEnv f bs) e
checkExpr f (ELam (x,t) e) = FFunc t <$> checkExpr (addEnv f [(x,t)]) e
checkExpr f (ECoerc s t e) = checkExpr f (ECst e s) >> return t
checkExpr _ (ETApp _ _) = error "SortCheck.checkExpr: TODO: implement ETApp"
checkExpr _ (ETAbs _ _) = error "SortCheck.checkExpr: TODO: implement ETAbs"
addEnv :: Eq a => (a -> SESearch b) -> [(a, b)] -> a -> SESearch b
addEnv f bs x
= case L.lookup x bs of
Just s -> Found s
Nothing -> f x
--------------------------------------------------------------------------------
-- | Elaborate expressions with types to make polymorphic instantiation explicit.
--------------------------------------------------------------------------------
{-# SCC elab #-}
elab :: ElabEnv -> Expr -> CheckM (Expr, Sort)
--------------------------------------------------------------------------------
elab f@(_, g) e@(EBin o e1 e2) = do
(e1', s1) <- elab f e1
(e2', s2) <- elab f e2
s <- checkOpTy g e s1 s2
return (EBin o (eCst e1' s1) (eCst e2' s2), s)
elab f (EApp e1@(EApp _ _) e2) = do
(e1', _, e2', s2, s) <- notracepp "ELAB-EAPP" <$> elabEApp f e1 e2
let e = eAppC s e1' (eCst e2' s2)
let θ = unifyExpr (snd f) e
return (applyExpr θ e, maybe s (`apply` s) θ)
elab f (EApp e1 e2) = do
(e1', s1, e2', s2, s) <- elabEApp f e1 e2
let e = eAppC s (eCst e1' s1) (eCst e2' s2)
let θ = unifyExpr (snd f) e
return (applyExpr θ e, maybe s (`apply` s) θ)
elab _ e@(ESym _) =
return (e, strSort)
elab _ e@(ECon (I _)) =
return (e, FInt)
elab _ e@(ECon (R _)) =
return (e, FReal)
elab _ e@(ECon (L _ s)) =
return (e, s)
elab _ e@(PKVar _ _) =
return (e, boolSort)
elab f (PGrad k su i e) =
(, boolSort) . PGrad k su i . fst <$> elab f e
elab (_, f) e@(EVar x) =
(e,) <$> checkSym f x
elab f (ENeg e) = do
(e', s) <- elab f e
return (ENeg e', s)
elab f@(_,g) (ECst (EIte p e1 e2) t) = do
(p', _) <- elab f p
(e1', s1) <- elab f (eCst e1 t)
(e2', s2) <- elab f (eCst e2 t)
s <- checkIteTy g p e1' e2' s1 s2
return (EIte p' (eCst e1' s) (eCst e2' s), t)
elab f@(_,g) (EIte p e1 e2) = do
t <- getIte g e1 e2
(p', _) <- elab f p
(e1', s1) <- elab f (eCst e1 t)
(e2', s2) <- elab f (eCst e2 t)
s <- checkIteTy g p e1' e2' s1 s2
return (EIte p' (eCst e1' s) (eCst e2' s), s)
elab f (ECst e t) = do
(e', _) <- elab f e
return (eCst e' t, t)
elab f (PNot p) = do
(e', _) <- elab f p
return (PNot e', boolSort)
elab f (PImp p1 p2) = do
(p1', _) <- elab f p1
(p2', _) <- elab f p2
return (PImp p1' p2', boolSort)
elab f (PIff p1 p2) = do
(p1', _) <- elab f p1
(p2', _) <- elab f p2
return (PIff p1' p2', boolSort)
elab f (PAnd ps) = do
ps' <- mapM (elab f) ps
return (PAnd (fst <$> ps'), boolSort)
elab f (POr ps) = do
ps' <- mapM (elab f) ps
return (POr (fst <$> ps'), boolSort)
elab f@(_,g) e@(PAtom eq e1 e2) | eq == Eq || eq == Ne = do
t1 <- checkExpr g e1
t2 <- checkExpr g e2
(t1',t2') <- unite g e t1 t2 `withError` errElabExpr e
e1' <- elabAs f t1' e1
e2' <- elabAs f t2' e2
e1'' <- eCstAtom f e1' t1'
e2'' <- eCstAtom f e2' t2'
return (PAtom eq e1'' e2'' , boolSort)
elab f (PAtom r e1 e2)
| r == Ueq || r == Une = do
(e1', _) <- elab f e1
(e2', _) <- elab f e2
return (PAtom r e1' e2', boolSort)
elab f@(env,_) (PAtom r e1 e2) = do
e1' <- uncurry (toInt env) <$> elab f e1
e2' <- uncurry (toInt env) <$> elab f e2
return (PAtom r e1' e2', boolSort)
elab f (PExist bs e) = do
(e', s) <- elab (elabAddEnv f bs) e
let bs' = elaborate "PExist Args" mempty bs
return (PExist bs' e', s)
elab f (PAll bs e) = do
(e', s) <- elab (elabAddEnv f bs) e
let bs' = elaborate "PAll Args" mempty bs
return (PAll bs' e', s)
elab f (ELam (x,t) e) = do
(e', s) <- elab (elabAddEnv f [(x, t)]) e
let t' = elaborate "ELam Arg" mempty t
return (ELam (x, t') (eCst e' s), FFunc t s)
elab f (ECoerc s t e) = do
(e', _) <- elab f e
return (ECoerc s t e', t)
elab _ (ETApp _ _) =
error "SortCheck.elab: TODO: implement ETApp"
elab _ (ETAbs _ _) =
error "SortCheck.elab: TODO: implement ETAbs"
-- | 'eCstAtom' is to support tests like `tests/pos/undef00.fq`
eCstAtom :: ElabEnv -> Expr -> Sort -> CheckM Expr
eCstAtom f@(sym,g) (EVar x) t
| Found s <- g x
, isUndef s
, not (isInt sym t) = (`ECst` t) <$> elabAs f t (EApp (eVar tyCastName) (eVar x))
eCstAtom _ e t = return (ECst e t)
isUndef :: Sort -> Bool
isUndef s = case bkAbs s of
(is, FVar j) -> j `elem` is
_ -> False
elabAddEnv :: Eq a => (t, a -> SESearch b) -> [(a, b)] -> (t, a -> SESearch b)
elabAddEnv (g, f) bs = (g, addEnv f bs)
elabAs :: ElabEnv -> Sort -> Expr -> CheckM Expr
elabAs f t e = notracepp _msg <$> go e
where
_msg = "elabAs: t = " ++ showpp t ++ "; e = " ++ showpp e
go (EApp e1 e2) = elabAppAs f t e1 e2
go e' = fst <$> elab f e'
-- DUPLICATION with `checkApp'`
elabAppAs :: ElabEnv -> Sort -> Expr -> Expr -> CheckM Expr
elabAppAs env@(_, f) t g e = do
gT <- checkExpr f g
eT <- checkExpr f e
(iT, oT, isu) <- checkFunSort gT
let ge = Just (EApp g e)
su <- unifyMany f ge isu [oT, iT] [t, eT]
let tg = apply su gT
g' <- elabAs env tg g
let te = apply su eT
e' <- elabAs env te e
pure $ EApp (ECst g' tg) (ECst e' te)
elabEApp :: ElabEnv -> Expr -> Expr -> CheckM (Expr, Sort, Expr, Sort, Sort)
elabEApp f@(_, g) e1 e2 = do
(e1', s1) <- {- notracepp ("elabEApp: e1 = " ++ showpp e1) <$> -} elab f e1
(e2', s2) <- elab f e2
(e1'', e2'', s1', s2', s) <- elabAppSort g e1' e2' s1 s2
return (e1'', s1', e2'', s2', s)
elabAppSort :: Env -> Expr -> Expr -> Sort -> Sort -> CheckM (Expr, Expr, Sort, Sort, Sort)
elabAppSort f e1 e2 s1 s2 = do
let e = Just (EApp e1 e2)
(sIn, sOut, su) <- checkFunSort s1
su' <- unify1 f e su sIn s2
return (applyExpr (Just su') e1 , applyExpr (Just su') e2, apply su' s1, apply su' s2, apply su' sOut)
--------------------------------------------------------------------------------
-- | defuncEApp monomorphizes function applications.
--------------------------------------------------------------------------------
defuncEApp :: SymEnv -> Expr -> [(Expr, Sort)] -> Expr
defuncEApp _ e [] = e
defuncEApp env e es = eCst (L.foldl' makeApplication e' es') (snd $ last es)
where
(e', es') = takeArgs (seTheory env) e es
takeArgs :: SEnv TheorySymbol -> Expr -> [(Expr, a)] -> (Expr, [(Expr, a)])
takeArgs env e es =
case Thy.isSmt2App env e of
Just n -> let (es1, es2) = splitAt n es
in (eApps e (fst <$> es1), es2)
Nothing -> (e, es)
-- 'e1' is the function, 'e2' is the argument, 's' is the OUTPUT TYPE
makeApplication :: Expr -> (Expr, Sort) -> Expr
makeApplication e1 (e2, s) =
ECst (EApp (EApp f e1) e2) s
where
f = {- notracepp ("makeApplication: " ++ showpp (e2, t2)) $ -} applyAt t2 s
t2 = exprSort "makeAppl" e2
applyAt :: Sort -> Sort -> Expr
applyAt s t = ECst (EVar applyName) (FFunc s t)
-- JUST make "toInt" call "makeApplication" also, so they are wrapped in apply
-- MAY CAUSE CRASH (apply-on-apply) so rig `isSmt2App` to treat `apply` as SPECIAL.
-- TODO: proper toInt
toInt :: SymEnv -> Expr -> Sort -> Expr
toInt env e s
| isSmtInt = e
| otherwise = ECst (EApp f (ECst e s)) FInt
where
isSmtInt = isInt env s
f = toIntAt s
isInt :: SymEnv -> Sort -> Bool
isInt env s = case sortSmtSort False (seData env) s of
SInt -> True
SString -> True
SReal -> True
_ -> False
toIntAt :: Sort -> Expr
toIntAt s = ECst (EVar toIntName) (FFunc s FInt)
unElab :: Expr -> Expr
unElab = Vis.stripCasts . unApply
unElabSortedReft :: SortedReft -> SortedReft
unElabSortedReft sr = sr { sr_reft = mapPredReft unElab (sr_reft sr) }
unApplySortedReft :: SortedReft -> SortedReft
unApplySortedReft sr = sr { sr_reft = mapPredReft unApply (sr_reft sr) }
unApply :: Expr -> Expr
unApply = Vis.mapExprOnExpr go
where
go (ECst (EApp (EApp f e1) e2) _)
| Just _ <- unApplyAt f = EApp e1 e2
go (ELam (x,s) e) = ELam (x, Vis.mapSort go' s) e
go e = e
go' (FApp (FApp fs t1) t2) | fs == funcSort
= FFunc t1 t2
go' t = t
unApplyAt :: Expr -> Maybe Sort
unApplyAt (ECst (EVar f) t@FFunc{})
| f == applyName = Just t
unApplyAt _ = Nothing
splitArgs :: Expr -> (Expr, [(Expr, Sort)])
splitArgs = go []
where
go acc (ECst (EApp e1 e) s) = go ((e, s) : acc) e1
go _ e@EApp{} = errorstar $ "UNEXPECTED: splitArgs: EApp without output type: " ++ showpp e
go acc e = (e, acc)
--------------------------------------------------------------------------------
{- | [NOTE:apply-monomorphization]
Because SMTLIB does not support higher-order functions,
all _non-theory_ function applications
EApp e1 e2
are represented, in SMTLIB, as
(EApp (EApp apply e1) e2)
where 'apply' is 'ECst (EVar "apply") t' and
't' is 'FFunc a b'
'a','b' are the sorts of 'e2' and 'e1 e2' respectively.
Note that *all polymorphism* goes through this machinery.
Just before sending to the SMT solver, we use the cast 't'
to generate a special 'apply_at_t' symbol.
To let us do the above, we populate 'SymEnv' with the _set_
of all sorts at which 'apply' is used, computed by 'applySorts'.
-}
{- | [NOTE:coerce-apply] -- related to [NOTE:apply-monomorphism]
Haskell's GADTs cause a peculiar problem illustrated below:
```haskell
data Field a where
FInt :: Field Int
FBool :: Field Bool
{-@ reflect proj @-}
proj :: Field a -> a -> a
proj fld x = case fld of
FInt -> 1 + x
FBool -> not b
```
**The Problem**
The problem is you cannot encode the body of `proj` as a well-sorted refinement:
```haskell
if is$FInt fld
then (1 + (coerce (a ~ Int) x))
else (not (coerce (a ~ Bool) x))
```
The catch is that `x` is being used BOTH as `Int` and as `Bool`
which is not supported in SMTLIB.
**Approach: Uninterpreted Functions**
We encode `coerce` as an explicit **uninterpreted function**:
```haskell
if is$FInt fld
then (1 + (coerce@(a -> int) x))
else (not (coerce@(a -> bool) x))
```
where we define, extra constants in the style of `apply`
```haskell
constant coerce@(a -> int ) :: a -> int
constant coerce@(a -> bool) :: a -> int
```
However, it would not let us verify:
```haskell
{-@ reflect unwrap @-}
unwrap :: Field a -> a -> a
unwrap fld x = proj fld x
{-@ test :: _ -> TT @-}
test = unwrap FInt 4 == 5
&& unwrap FBool True == False
```
because we'd get
```haskell
unwrap FInt 4 :: { if is$FInt FInt then (1 + coerce_int_int 4) else ... }
```
and the UIF nature of `coerce_int_int` renders the VC invalid.
**Solution: Eliminate Trivial Coercions**
HOWEVER, the solution here, may simply be to use UIFs when the
coercion is non-trivial (e.g. `a ~ int`) but to eschew them when
they are trivial. That is we would encode:
| Expr | SMTLIB |
|:-----------------------|:-------------------|
| `coerce (a ~ int) x` | `coerce_a_int x` |
| `coerce (int ~ int) x` | `x` |
which, I imagine is what happens _somewhere_ inside GHC too?
-}
--------------------------------------------------------------------------------
applySorts :: Vis.Visitable t => t -> [Sort]
--------------------------------------------------------------------------------
applySorts = {- notracepp "applySorts" . -} (defs ++) . Vis.fold vis () []
where
defs = [FFunc t1 t2 | t1 <- basicSorts, t2 <- basicSorts]
vis = (Vis.defaultVisitor :: Vis.Visitor [KVar] t) { Vis.accExpr = go }
go _ (EApp (ECst (EVar f) t) _) -- get types needed for [NOTE:apply-monomorphism]
| f == applyName
= [t]
go _ (ECoerc t1 t2 _) -- get types needed for [NOTE:coerce-apply]
= [FFunc t1 t2]
go _ _ = []
--------------------------------------------------------------------------------
-- | Expressions sort ---------------------------------------------------------
--------------------------------------------------------------------------------
exprSort :: String -> Expr -> Sort
exprSort msg e = fromMaybe (panic err') (exprSortMaybe e)
where
err' = printf "exprSort [%s] on unexpected expression %s" msg (show e)
exprSortMaybe :: Expr -> Maybe Sort
exprSortMaybe = go
where
go (ECst _ s) = Just s
go (ELam (_, sx) e) = FFunc sx <$> go e
go (EApp e ex)
| Just (FFunc sx s) <- genSort <$> go e
= maybe s (`apply` s) . (`unifySorts` sx) <$> go ex
go _ = Nothing
genSort :: Sort -> Sort
genSort (FAbs _ t) = genSort t
genSort t = t
unite :: Env -> Expr -> Sort -> Sort -> CheckM (Sort, Sort)
unite f e t1 t2 = do
su <- unifys f (Just e) [t1] [t2]
return (apply su t1, apply su t2)
throwErrorAt :: String -> CheckM a
throwErrorAt ~err' = do -- Lazy pattern needed because we use LANGUAGE Strict in this module
-- See Note [Lazy error messages]
sp <- asks chSpan
liftIO $ throwIO (ChError (\_ -> atLoc sp err'))
-- Note [Lazy error messages]
--
-- We don't want to construct error messages early, or
-- we might trigger some expensive computation of editDistance
-- when no error has actually occurred yet.
-- | Helper for checking symbol occurrences
checkSym :: Env -> Symbol -> CheckM Sort
checkSym f x = case f x of
Found s -> instantiate s
Alts xs -> throwErrorAt (errUnboundAlts x xs)
-- | Helper for checking if-then-else expressions
checkIte :: Env -> Expr -> Expr -> Expr -> CheckM Sort
checkIte f p e1 e2 = do
checkPred f p
t1 <- checkExpr f e1
t2 <- checkExpr f e2
checkIteTy f p e1 e2 t1 t2
getIte :: Env -> Expr -> Expr -> CheckM Sort
getIte f e1 e2 = do
t1 <- checkExpr f e1
t2 <- checkExpr f e2
(`apply` t1) <$> unifys f Nothing [t1] [t2]
checkIteTy :: Env -> Expr -> Expr -> Expr -> Sort -> Sort -> CheckM Sort
checkIteTy f p e1 e2 t1 t2 =
((`apply` t1) <$> unifys f e' [t1] [t2]) `withError` errIte e1 e2 t1 t2
where
e' = Just (EIte p e1 e2)
-- | Helper for checking cast expressions
checkCst :: Env -> Sort -> Expr -> CheckM Sort
checkCst f t (EApp g e)
= checkApp f (Just t) g e
checkCst f t e
= do t' <- checkExpr f e
su <- unifys f (Just e) [t] [t'] `withError` errCast e t' t
pure (apply su t)
checkApp :: Env -> Maybe Sort -> Expr -> Expr -> CheckM Sort
checkApp f to g es
= snd <$> checkApp' f to g es
checkExprAs :: Env -> Sort -> Expr -> CheckM Sort
checkExprAs f t (EApp g e)
= checkApp f (Just t) g e
checkExprAs f t e
= do t' <- checkExpr f e
θ <- unifys f (Just e) [t'] [t]
pure $ apply θ t
-- | Helper for checking uninterpreted function applications
-- | Checking function application should be curried, e.g.
-- | fromJust :: Maybe a -> a, f :: Maybe (b -> b), x: c |- fromJust f x
-- RJ: The above comment makes no sense to me :(
-- DUPLICATION with 'elabAppAs'
checkApp' :: Env -> Maybe Sort -> Expr -> Expr -> CheckM (TVSubst, Sort)
checkApp' f to g e = do
gt <- checkExpr f g
et <- checkExpr f e
(it, ot, isu) <- checkFunSort gt
let ge = Just (EApp g e)
su <- unifyMany f ge isu [it] [et]
let t = apply su ot
case to of
Nothing -> return (su, t)
Just t' -> do θ' <- unifyMany f ge su [t] [t']
let ti = apply θ' et
_ <- checkExprAs f ti e
return (θ', apply θ' t)
-- | Helper for checking binary (numeric) operations
checkNeg :: Env -> Expr -> CheckM Sort
checkNeg f e = do
t <- checkExpr f e
checkNumeric f t >> return t
checkOp :: Env -> Expr -> Bop -> Expr -> CheckM Sort
checkOp f e1 o e2
= do t1 <- checkExpr f e1
t2 <- checkExpr f e2
checkOpTy f (EBin o e1 e2) t1 t2
checkOpTy :: Env -> Expr -> Sort -> Sort -> CheckM Sort
checkOpTy _ _ FInt FInt
= return FInt
checkOpTy _ _ FReal FReal
= return FReal
-- Coercing int to real is somewhat suspicious, but z3 seems
-- to be ok with it
checkOpTy _ _ FInt FReal
= return FReal
checkOpTy _ _ FReal FInt
= return FReal
checkOpTy f e t t'
| Just s <- unify f (Just e) t t'
= checkNumeric f (apply s t) >> return (apply s t)
checkOpTy _ e t t'
= throwErrorAt (errOp e t t')
checkFractional :: Env -> Sort -> CheckM ()
checkFractional f s@(FObj l)
= do t <- checkSym f l
unless (t == FFrac) $ throwErrorAt (errNonFractional s)
checkFractional _ s
= unless (isReal s) $ throwErrorAt (errNonFractional s)
checkNumeric :: Env -> Sort -> CheckM ()
checkNumeric f s@(FObj l)
= do t <- checkSym f l
unless (t `elem` [FNum, FFrac, intSort, FInt]) (throwErrorAt $ errNonNumeric s)
checkNumeric _ s
= unless (isNumeric s) (throwErrorAt $ errNonNumeric s)
checkEqConstr :: Env -> Maybe Expr -> TVSubst -> Symbol -> Sort -> CheckM TVSubst
checkEqConstr _ _ θ a (FObj b)
| a == b
= return θ
checkEqConstr f e θ a t =
case f a of
Found tA -> unify1 f e θ tA t
_ -> throwErrorAt $ errUnifyMsg (Just "ceq2") e (FObj a) t
--------------------------------------------------------------------------------
-- | Checking Predicates -------------------------------------------------------
--------------------------------------------------------------------------------
checkPred :: Env -> Expr -> CheckM ()
checkPred f e = checkExpr f e >>= checkBoolSort e
checkBoolSort :: Expr -> Sort -> CheckM ()
checkBoolSort e s
| s == boolSort = return ()
| otherwise = throwErrorAt (errBoolSort e s)
-- | Checking Relations
checkRel :: HasCallStack => Env -> Brel -> Expr -> Expr -> CheckM ()
checkRel f Eq e1 e2 = do
t1 <- checkExpr f e1
t2 <- checkExpr f e2
su <- unifys f (Just e) [t1] [t2] `withError` errRel e t1 t2
_ <- checkExprAs f (apply su t1) e1
_ <- checkExprAs f (apply su t2) e2
checkRelTy f e Eq t1 t2
where
e = PAtom Eq e1 e2
checkRel f r e1 e2 = do
t1 <- checkExpr f e1
t2 <- checkExpr f e2
checkRelTy f (PAtom r e1 e2) r t1 t2
checkRelTy :: Env -> Expr -> Brel -> Sort -> Sort -> CheckM ()
checkRelTy _ e Ueq s1 s2 = checkURel e s1 s2
checkRelTy _ e Une s1 s2 = checkURel e s1 s2
checkRelTy f _ _ s1@(FObj l) s2@(FObj l') | l /= l'
= (checkNumeric f s1 >> checkNumeric f s2) `withError` errNonNumerics l l'
checkRelTy _ _ _ FReal FReal = return ()
checkRelTy _ _ _ FInt FReal = return ()
checkRelTy _ _ _ FReal FInt = return ()
checkRelTy f _ _ FInt s2 = checkNumeric f s2 `withError` errNonNumeric s2
checkRelTy f _ _ s1 FInt = checkNumeric f s1 `withError` errNonNumeric s1
checkRelTy f _ _ FReal s2 = checkFractional f s2 `withError` errNonFractional s2
checkRelTy f _ _ s1 FReal = checkFractional f s1 `withError` errNonFractional s1
checkRelTy f e Eq t1 t2 = void (unifys f (Just e) [t1] [t2] `withError` errRel e t1 t2)
checkRelTy f e Ne t1 t2 = void (unifys f (Just e) [t1] [t2] `withError` errRel e t1 t2)
checkRelTy _ e _ t1 t2 = unless (t1 == t2) (throwErrorAt $ errRel e t1 t2)
checkURel :: Expr -> Sort -> Sort -> CheckM ()
checkURel e s1 s2 = unless (b1 == b2) (throwErrorAt $ errRel e s1 s2)
where
b1 = s1 == boolSort
b2 = s2 == boolSort
--------------------------------------------------------------------------------
-- | Sort Unification on Expressions
--------------------------------------------------------------------------------
{-# SCC unifyExpr #-}
unifyExpr :: Env -> Expr -> Maybe TVSubst
unifyExpr f (EApp e1 e2) = Just $ mconcat $ catMaybes [θ1, θ2, θ]
where
θ1 = unifyExpr f e1
θ2 = unifyExpr f e2
θ = unifyExprApp f e1 e2
unifyExpr f (ECst e _)
= unifyExpr f e
unifyExpr _ _
= Nothing
unifyExprApp :: Env -> Expr -> Expr -> Maybe TVSubst
unifyExprApp f e1 e2 = do
t1 <- getArg $ exprSortMaybe e1
t2 <- exprSortMaybe e2
unify f (Just $ EApp e1 e2) t1 t2
where
getArg (Just (FFunc t1 _)) = Just t1
getArg _ = Nothing
--------------------------------------------------------------------------------
-- | Sort Unification
--------------------------------------------------------------------------------
{-# SCC unify #-}
unify :: Env -> Maybe Expr -> Sort -> Sort -> Maybe TVSubst
--------------------------------------------------------------------------------
unify f e t1 t2
= case runCM0 dummySpan (unify1 f e emptySubst t1 t2) of
Left _ -> Nothing
Right su -> Just su
--------------------------------------------------------------------------------
unifyTo1 :: Env -> [Sort] -> Maybe Sort
--------------------------------------------------------------------------------
unifyTo1 f ts
= case runCM0 dummySpan (unifyTo1M f ts) of
Left _ -> Nothing
Right t -> Just t
--------------------------------------------------------------------------------
unifyTo1M :: Env -> [Sort] -> CheckM Sort
--------------------------------------------------------------------------------
unifyTo1M _ [] = panic "unifyTo1: empty list"
unifyTo1M f (t0:ts) = snd <$> foldM step (emptySubst, t0) ts
where
step :: (TVSubst, Sort) -> Sort -> CheckM (TVSubst, Sort)
step (su, t) t' = do
su' <- unify1 f Nothing su t t'
return (su', apply su' t)
--------------------------------------------------------------------------------
unifySorts :: Sort -> Sort -> Maybe TVSubst
--------------------------------------------------------------------------------
unifySorts = unifyFast False emptyEnv
where
emptyEnv x = die $ err dummySpan $ "SortCheck: lookup in Empty Env: " <> pprint x
--------------------------------------------------------------------------------
-- | Fast Unification; `unifyFast True` is just equality
--------------------------------------------------------------------------------
unifyFast :: Bool -> Env -> Sort -> Sort -> Maybe TVSubst
--------------------------------------------------------------------------------
unifyFast False f t1 t2 = unify f Nothing t1 t2
unifyFast True _ t1 t2
| t1 == t2 = Just emptySubst
| otherwise = Nothing
{-
eqFast :: Sort -> Sort -> Bool
eqFast = go
where
go FAbs {} _ = False
go (FFunc s1 s2) t = case t of
FFunc t1 t2 -> go s1 t1 && go s2 t2
_ -> False
go (FApp s1 s2) t = case t of
FApp t1 t2 -> go s1 t1 && go s2 t2
_ -> False
go (FTC s1) t = case t of
FTC t1 -> s1 == t1
_ -> False
go FInt FInt = True
go FReal FReal = True
go FNum FNum = True
go FFrac FFrac = True
go (FVar i1) (FVar i2) = i1 == i2
go _ _ = False
-}
--------------------------------------------------------------------------------
unifys :: HasCallStack => Env -> Maybe Expr -> [Sort] -> [Sort] -> CheckM TVSubst
--------------------------------------------------------------------------------
unifys f e = unifyMany f e emptySubst
unifyMany :: HasCallStack => Env -> Maybe Expr -> TVSubst -> [Sort] -> [Sort] -> CheckM TVSubst
unifyMany f e θ ts ts'
| length ts == length ts' = foldM (uncurry . unify1 f e) θ $ zip ts ts'
| otherwise = throwErrorAt (errUnifyMany ts ts')
unify1 :: Env -> Maybe Expr -> TVSubst -> Sort -> Sort -> CheckM TVSubst
unify1 f e !θ (FVar !i) !t
= unifyVar f e θ i t
unify1 f e !θ !t (FVar !i)
= unifyVar f e θ i t
unify1 f e !θ (FApp !t1 !t2) (FApp !t1' !t2')
= unifyMany f e θ [t1, t2] [t1', t2']
unify1 _ _ !θ (FTC !l1) (FTC !l2)
| isListTC l1 && isListTC l2
= return θ
unify1 f e !θ t1@(FAbs _ _) !t2 = do
!t1' <- instantiate t1
unifyMany f e θ [t1'] [t2]
unify1 f e !θ !t1 t2@(FAbs _ _) = do
!t2' <- instantiate t2
unifyMany f e θ [t1] [t2']
unify1 _ _ !θ !s1 !s2
| isString s1, isString s2
= return θ
unify1 _ _ !θ FInt FReal = return θ
unify1 _ _ !θ FReal FInt = return θ
unify1 f e !θ !t FInt = do
checkNumeric f t `withError` errUnify e t FInt
return θ
unify1 f e !θ FInt !t = do
checkNumeric f t `withError` errUnify e FInt t
return θ
unify1 f e !θ (FFunc !t1 !t2) (FFunc !t1' !t2') =
unifyMany f e θ [t1, t2] [t1', t2']
unify1 f e θ (FObj a) !t =
checkEqConstr f e θ a t
unify1 f e θ !t (FObj a) =
checkEqConstr f e θ a t
unify1 _ e θ !t1 !t2
| t1 == t2
= return θ
| otherwise
= throwErrorAt (errUnify e t1 t2)
subst :: Int -> Sort -> Sort -> Sort
subst !j !tj t@(FVar !i)
| i == j = tj
| otherwise = t
subst !j !tj (FApp !t1 !t2) = FApp t1' t2'
where
!t1' = subst j tj t1
!t2' = subst j tj t2
-- subst _ _ !(FTC l) = FTC l
subst !j !tj (FFunc !t1 !t2) = FFunc t1' t2'
where
!t1' = subst j tj $! t1
!t2' = subst j tj $! t2
subst !j !tj (FAbs !i !t)
| i == j = FAbs i t
| otherwise = FAbs i t'
where
!t' = subst j tj t
subst _ _ !s = s
--------------------------------------------------------------------------------
instantiate :: Sort -> CheckM Sort
--------------------------------------------------------------------------------
instantiate !t = go t
where
go (FAbs !i !t') = do
!t'' <- instantiate t'
!v <- fresh
return $ subst i (FVar v) t''
go !t' =
return t'
unifyVar :: Env -> Maybe Expr -> TVSubst -> Int -> Sort -> CheckM TVSubst
unifyVar _ _ θ !i t@(FVar !j)
= case lookupVar i θ of
Just !t' -> if t == t' then return θ else return (updateVar j t' θ)
Nothing -> return (updateVar i t θ)
unifyVar f e θ !i !t
= case lookupVar i θ of
Just (FVar !j) -> return $ updateVar i t $ updateVar j t θ
Just !t' -> if t == t' then return θ else unify1 f e θ t t'
Nothing -> return (updateVar i t θ)
--------------------------------------------------------------------------------
-- | Applying a Type Substitution ----------------------------------------------
--------------------------------------------------------------------------------
apply :: TVSubst -> Sort -> Sort
--------------------------------------------------------------------------------
apply θ = Vis.mapSort f
where
f t@(FVar i) = fromMaybe t (lookupVar i θ)
f t = t
applyExpr :: Maybe TVSubst -> Expr -> Expr
applyExpr Nothing e = e
applyExpr (Just θ) e = Vis.mapExprOnExpr f e
where
f (ECst e' s) = ECst e' (apply θ s)
f e' = e'
--------------------------------------------------------------------------------
_applyCoercion :: Symbol -> Sort -> Sort -> Sort
--------------------------------------------------------------------------------
_applyCoercion a t = Vis.mapSort f
where
f (FObj b)
| a == b = t
f s = s
--------------------------------------------------------------------------------
-- | Deconstruct a function-sort -----------------------------------------------
--------------------------------------------------------------------------------
checkFunSort :: Sort -> CheckM (Sort, Sort, TVSubst)
checkFunSort (FAbs _ t) = checkFunSort t
checkFunSort (FFunc t1 t2) = return (t1, t2, emptySubst)
checkFunSort (FVar i) = do j <- fresh
k <- fresh
return (FVar j, FVar k, updateVar i (FFunc (FVar j) (FVar k)) emptySubst)
checkFunSort t = throwErrorAt (errNonFunction 1 t)
--------------------------------------------------------------------------------
-- | API for manipulating Sort Substitutions -----------------------------------
--------------------------------------------------------------------------------
newtype TVSubst = Th (M.HashMap Int Sort) deriving (Show)
instance Semigroup TVSubst where
(Th s1) <> (Th s2) = Th (s1 <> s2)
instance Monoid TVSubst where
mempty = Th mempty
mappend = (<>)
lookupVar :: Int -> TVSubst -> Maybe Sort
lookupVar i (Th m) = M.lookup i m
{-# SCC lookupVar #-}
updateVar :: Int -> Sort -> TVSubst -> TVSubst
updateVar !i !t (Th m) = Th (M.insert i t m)
emptySubst :: TVSubst
emptySubst = Th M.empty
--------------------------------------------------------------------------------
-- | Error messages ------------------------------------------------------------
--------------------------------------------------------------------------------
errElabExpr :: Expr -> String
errElabExpr e = printf "Elaborate fails on %s" (showpp e)
errUnifyMsg :: Maybe String -> Maybe Expr -> Sort -> Sort -> String
errUnifyMsg msgMb eo t1 t2
= printf "Cannot unify %s with %s %s %s"
(showpp t1) {- (show t1) -} (showpp t2) {-(show t2)-} (errUnifyExpr eo) msgStr
where
msgStr = case msgMb of { Nothing -> ""; Just s -> "<< " ++ s ++ " >>"}
errUnify :: Maybe Expr -> Sort -> Sort -> String
errUnify = errUnifyMsg Nothing
errUnifyExpr :: Maybe Expr -> String
errUnifyExpr Nothing = ""
errUnifyExpr (Just e) = "in expression: " ++ showpp e
errUnifyMany :: [Sort] -> [Sort] -> String
errUnifyMany ts ts' = printf "Cannot unify types with different cardinalities %s and %s"
(showpp ts) (showpp ts')
errRel :: HasCallStack => Expr -> Sort -> Sort -> String
errRel e t1 t2 =
traced $ printf "Invalid Relation %s with operand types %s and %s"
(showpp e) (showpp t1) (showpp t2)
errOp :: Expr -> Sort -> Sort -> String
errOp e t t'
| t == t' = printf "Operands have non-numeric types %s in %s"
(showpp t) (showpp e)
| otherwise = printf "Operands have different types %s and %s in %s"
(showpp t) (showpp t') (showpp e)
errIte :: Expr -> Expr -> Sort -> Sort -> String
errIte e1 e2 t1 t2 = printf "Mismatched branches in Ite: then %s : %s, else %s : %s"
(showpp e1) (showpp t1) (showpp e2) (showpp t2)
errCast :: Expr -> Sort -> Sort -> String
errCast e t' t = printf "Cannot cast %s of sort %s to incompatible sort %s"
(showpp e) (showpp t') (showpp t)
errUnboundAlts :: Symbol -> [Symbol] -> String
errUnboundAlts x xs = printf "Unbound symbol %s --- perhaps you meant: %s ?"
(showpp x) (L.intercalate ", " (showpp <$> xs))
errNonFunction :: Int -> Sort -> String
errNonFunction i t = printf "The sort %s is not a function with at least %s arguments\n" (showpp t) (showpp i)
errNonNumeric :: Sort -> String
errNonNumeric l = printf "The sort %s is not numeric" (showpp l)
errNonNumerics :: Symbol -> Symbol -> String
errNonNumerics l l' = printf "FObj sort %s and %s are different and not numeric" (showpp l) (showpp l')
errNonFractional :: Sort -> String
errNonFractional l = printf "The sort %s is not fractional" (showpp l)
errBoolSort :: Expr -> Sort -> String
errBoolSort e s = printf "Expressions %s should have bool sort, but has %s" (showpp e) (showpp s)