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Diffstat (limited to 'compiler/types/Unify.lhs')
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diff --git a/compiler/types/Unify.lhs b/compiler/types/Unify.lhs new file mode 100644 index 0000000000..f60c7bee61 --- /dev/null +++ b/compiler/types/Unify.lhs @@ -0,0 +1,536 @@ +\begin{code} +module Unify ( + -- Matching and unification + tcMatchTys, tcMatchTyX, ruleMatchTyX, tcMatchPreds, MatchEnv(..), + + tcUnifyTys, + + gadtRefineTys, BindFlag(..), + + coreRefineTys, TypeRefinement, + + -- Re-export + MaybeErr(..) + ) where + +#include "HsVersions.h" + +import Var ( Var, TyVar, tyVarKind ) +import VarEnv +import VarSet +import Kind ( isSubKind ) +import Type ( typeKind, tyVarsOfType, tyVarsOfTypes, tyVarsOfTheta, mkTyVarTys, + TvSubstEnv, emptyTvSubstEnv, TvSubst(..), substTy, tcEqTypeX, + mkOpenTvSubst, tcView ) +import TypeRep ( Type(..), PredType(..), funTyCon ) +import DataCon ( DataCon, dataConInstResTy ) +import Util ( snocView ) +import ErrUtils ( Message ) +import Outputable +import Maybes +\end{code} + + +%************************************************************************ +%* * + Matching +%* * +%************************************************************************ + + +Matching is much tricker than you might think. + +1. The substitution we generate binds the *template type variables* + which are given to us explicitly. + +2. We want to match in the presence of foralls; + e.g (forall a. t1) ~ (forall b. t2) + + That is what the RnEnv2 is for; it does the alpha-renaming + that makes it as if a and b were the same variable. + Initialising the RnEnv2, so that it can generate a fresh + binder when necessary, entails knowing the free variables of + both types. + +3. We must be careful not to bind a template type variable to a + locally bound variable. E.g. + (forall a. x) ~ (forall b. b) + where x is the template type variable. Then we do not want to + bind x to a/b! This is a kind of occurs check. + The necessary locals accumulate in the RnEnv2. + + +\begin{code} +data MatchEnv + = ME { me_tmpls :: VarSet -- Template tyvars + , me_env :: RnEnv2 -- Renaming envt for nested foralls + } -- In-scope set includes template tyvars + +tcMatchTys :: TyVarSet -- Template tyvars + -> [Type] -- Template + -> [Type] -- Target + -> Maybe TvSubst -- One-shot; in principle the template + -- variables could be free in the target + +tcMatchTys tmpls tys1 tys2 + = case match_tys menv emptyTvSubstEnv tys1 tys2 of + Just subst_env -> Just (TvSubst in_scope subst_env) + Nothing -> Nothing + where + menv = ME { me_tmpls = tmpls, me_env = mkRnEnv2 in_scope } + in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfTypes tys2) + -- We're assuming that all the interesting + -- tyvars in tys1 are in tmpls + +-- This is similar, but extends a substitution +tcMatchTyX :: TyVarSet -- Template tyvars + -> TvSubst -- Substitution to extend + -> Type -- Template + -> Type -- Target + -> Maybe TvSubst +tcMatchTyX tmpls (TvSubst in_scope subst_env) ty1 ty2 + = case match menv subst_env ty1 ty2 of + Just subst_env -> Just (TvSubst in_scope subst_env) + Nothing -> Nothing + where + menv = ME {me_tmpls = tmpls, me_env = mkRnEnv2 in_scope} + +tcMatchPreds + :: [TyVar] -- Bind these + -> [PredType] -> [PredType] + -> Maybe TvSubstEnv +tcMatchPreds tmpls ps1 ps2 + = match_list (match_pred menv) emptyTvSubstEnv ps1 ps2 + where + menv = ME { me_tmpls = mkVarSet tmpls, me_env = mkRnEnv2 in_scope_tyvars } + in_scope_tyvars = mkInScopeSet (tyVarsOfTheta ps1 `unionVarSet` tyVarsOfTheta ps2) + +-- This one is called from the expression matcher, which already has a MatchEnv in hand +ruleMatchTyX :: MatchEnv + -> TvSubstEnv -- Substitution to extend + -> Type -- Template + -> Type -- Target + -> Maybe TvSubstEnv + +ruleMatchTyX menv subst ty1 ty2 = match menv subst ty1 ty2 -- Rename for export +\end{code} + +Now the internals of matching + +\begin{code} +match :: MatchEnv -- For the most part this is pushed downwards + -> TvSubstEnv -- Substitution so far: + -- Domain is subset of template tyvars + -- Free vars of range is subset of + -- in-scope set of the RnEnv2 + -> Type -> Type -- Template and target respectively + -> Maybe TvSubstEnv +-- This matcher works on source types; that is, +-- it respects NewTypes and PredType + +match menv subst ty1 ty2 | Just ty1' <- tcView ty1 = match menv subst ty1' ty2 +match menv subst ty1 ty2 | Just ty2' <- tcView ty2 = match menv subst ty1 ty2' + +match menv subst (TyVarTy tv1) ty2 + | tv1 `elemVarSet` me_tmpls menv + = case lookupVarEnv subst tv1' of + Nothing | any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2)) + -> Nothing -- Occurs check + | not (typeKind ty2 `isSubKind` tyVarKind tv1) + -> Nothing -- Kind mis-match + | otherwise + -> Just (extendVarEnv subst tv1 ty2) + + Just ty1' | tcEqTypeX (nukeRnEnvL rn_env) ty1' ty2 + -- ty1 has no locally-bound variables, hence nukeRnEnvL + -- Note tcEqType...we are doing source-type matching here + -> Just subst + + other -> Nothing + + | otherwise -- tv1 is not a template tyvar + = case ty2 of + TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst + other -> Nothing + where + rn_env = me_env menv + tv1' = rnOccL rn_env tv1 + +match menv subst (ForAllTy tv1 ty1) (ForAllTy tv2 ty2) + = match menv' subst ty1 ty2 + where -- Use the magic of rnBndr2 to go under the binders + menv' = menv { me_env = rnBndr2 (me_env menv) tv1 tv2 } + +match menv subst (PredTy p1) (PredTy p2) + = match_pred menv subst p1 p2 +match menv subst (TyConApp tc1 tys1) (TyConApp tc2 tys2) + | tc1 == tc2 = match_tys menv subst tys1 tys2 +match menv subst (FunTy ty1a ty1b) (FunTy ty2a ty2b) + = do { subst' <- match menv subst ty1a ty2a + ; match menv subst' ty1b ty2b } +match menv subst (AppTy ty1a ty1b) ty2 + | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2 + = do { subst' <- match menv subst ty1a ty2a + ; match menv subst' ty1b ty2b } + +match menv subst ty1 ty2 + = Nothing + +-------------- +match_tys menv subst tys1 tys2 = match_list (match menv) subst tys1 tys2 + +-------------- +match_list :: (TvSubstEnv -> a -> a -> Maybe TvSubstEnv) + -> TvSubstEnv -> [a] -> [a] -> Maybe TvSubstEnv +match_list fn subst [] [] = Just subst +match_list fn subst (ty1:tys1) (ty2:tys2) = do { subst' <- fn subst ty1 ty2 + ; match_list fn subst' tys1 tys2 } +match_list fn subst tys1 tys2 = Nothing + +-------------- +match_pred menv subst (ClassP c1 tys1) (ClassP c2 tys2) + | c1 == c2 = match_tys menv subst tys1 tys2 +match_pred menv subst (IParam n1 t1) (IParam n2 t2) + | n1 == n2 = match menv subst t1 t2 +match_pred menv subst p1 p2 = Nothing +\end{code} + + +%************************************************************************ +%* * + Unification +%* * +%************************************************************************ + +\begin{code} +tcUnifyTys :: (TyVar -> BindFlag) + -> [Type] -> [Type] + -> Maybe TvSubst -- A regular one-shot substitution +-- The two types may have common type variables, and indeed do so in the +-- second call to tcUnifyTys in FunDeps.checkClsFD +tcUnifyTys bind_fn tys1 tys2 + = maybeErrToMaybe $ initUM bind_fn $ + do { subst_env <- unify_tys emptyTvSubstEnv tys1 tys2 + + -- Find the fixed point of the resulting non-idempotent substitution + ; let in_scope = mkInScopeSet (tvs1 `unionVarSet` tvs2) + subst = TvSubst in_scope subst_env_fixpt + subst_env_fixpt = mapVarEnv (substTy subst) subst_env + ; return subst } + where + tvs1 = tyVarsOfTypes tys1 + tvs2 = tyVarsOfTypes tys2 + +---------------------------- +coreRefineTys :: DataCon -> [TyVar] -- Case pattern (con tv1 .. tvn ...) + -> Type -- Type of scrutinee + -> Maybe TypeRefinement + +type TypeRefinement = (TvSubstEnv, Bool) + -- The Bool is True iff all the bindings in the + -- env are for the pattern type variables + -- In this case, there is no type refinement + -- for already-in-scope type variables + +-- Used by Core Lint and the simplifier. +coreRefineTys con tvs scrut_ty + = maybeErrToMaybe $ initUM (tryToBind tv_set) $ + do { -- Run the unifier, starting with an empty env + ; subst_env <- unify emptyTvSubstEnv pat_res_ty scrut_ty + + -- Find the fixed point of the resulting non-idempotent substitution + ; let subst = mkOpenTvSubst subst_env_fixpt + subst_env_fixpt = mapVarEnv (substTy subst) subst_env + + ; return (subst_env_fixpt, all_bound_here subst_env) } + where + pat_res_ty = dataConInstResTy con (mkTyVarTys tvs) + + -- 'tvs' are the tyvars bound by the pattern + tv_set = mkVarSet tvs + all_bound_here env = all bound_here (varEnvKeys env) + bound_here uniq = elemVarSetByKey uniq tv_set + +-- This version is used by the type checker +gadtRefineTys :: TvSubst + -> DataCon -> [TyVar] + -> [Type] -> [Type] + -> MaybeErr Message (TvSubst, Bool) +-- The bool is True <=> the only *new* bindings are for pat_tvs + +gadtRefineTys (TvSubst in_scope env1) con pat_tvs pat_tys ctxt_tys + = initUM (tryToBind tv_set) $ + do { -- Run the unifier, starting with an empty env + ; env2 <- unify_tys env1 pat_tys ctxt_tys + + -- Find the fixed point of the resulting non-idempotent substitution + ; let subst2 = TvSubst in_scope subst_env_fixpt + subst_env_fixpt = mapVarEnv (substTy subst2) env2 + + ; return (subst2, all_bound_here env2) } + where + -- 'tvs' are the tyvars bound by the pattern + tv_set = mkVarSet pat_tvs + all_bound_here env = all bound_here (varEnvKeys env) + bound_here uniq = elemVarEnvByKey uniq env1 || elemVarSetByKey uniq tv_set + -- The bool is True <=> the only *new* bindings are for pat_tvs + +---------------------------- +tryToBind :: TyVarSet -> TyVar -> BindFlag +tryToBind tv_set tv | tv `elemVarSet` tv_set = BindMe + | otherwise = AvoidMe +\end{code} + + +%************************************************************************ +%* * + The workhorse +%* * +%************************************************************************ + +\begin{code} +unify :: TvSubstEnv -- An existing substitution to extend + -> Type -> Type -- Types to be unified + -> UM TvSubstEnv -- Just the extended substitution, + -- Nothing if unification failed +-- We do not require the incoming substitution to be idempotent, +-- nor guarantee that the outgoing one is. That's fixed up by +-- the wrappers. + +-- Respects newtypes, PredTypes + +unify subst ty1 ty2 = -- pprTrace "unify" (ppr subst <+> pprParendType ty1 <+> pprParendType ty2) $ + unify_ subst ty1 ty2 + +-- in unify_, any NewTcApps/Preds should be taken at face value +unify_ subst (TyVarTy tv1) ty2 = uVar False subst tv1 ty2 +unify_ subst ty1 (TyVarTy tv2) = uVar True subst tv2 ty1 + +unify_ subst ty1 ty2 | Just ty1' <- tcView ty1 = unify subst ty1' ty2 +unify_ subst ty1 ty2 | Just ty2' <- tcView ty2 = unify subst ty1 ty2' + +unify_ subst (PredTy p1) (PredTy p2) = unify_pred subst p1 p2 + +unify_ subst t1@(TyConApp tyc1 tys1) t2@(TyConApp tyc2 tys2) + | tyc1 == tyc2 = unify_tys subst tys1 tys2 + +unify_ subst (FunTy ty1a ty1b) (FunTy ty2a ty2b) + = do { subst' <- unify subst ty1a ty2a + ; unify subst' ty1b ty2b } + + -- Applications need a bit of care! + -- They can match FunTy and TyConApp, so use splitAppTy_maybe + -- NB: we've already dealt with type variables and Notes, + -- so if one type is an App the other one jolly well better be too +unify_ subst (AppTy ty1a ty1b) ty2 + | Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2 + = do { subst' <- unify subst ty1a ty2a + ; unify subst' ty1b ty2b } + +unify_ subst ty1 (AppTy ty2a ty2b) + | Just (ty1a, ty1b) <- repSplitAppTy_maybe ty1 + = do { subst' <- unify subst ty1a ty2a + ; unify subst' ty1b ty2b } + +unify_ subst ty1 ty2 = failWith (misMatch ty1 ty2) + +------------------------------ +unify_pred subst (ClassP c1 tys1) (ClassP c2 tys2) + | c1 == c2 = unify_tys subst tys1 tys2 +unify_pred subst (IParam n1 t1) (IParam n2 t2) + | n1 == n2 = unify subst t1 t2 +unify_pred subst p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2)) + +------------------------------ +unify_tys = unifyList unify + +unifyList :: Outputable a + => (TvSubstEnv -> a -> a -> UM TvSubstEnv) + -> TvSubstEnv -> [a] -> [a] -> UM TvSubstEnv +unifyList unifier subst orig_xs orig_ys + = go subst orig_xs orig_ys + where + go subst [] [] = return subst + go subst (x:xs) (y:ys) = do { subst' <- unifier subst x y + ; go subst' xs ys } + go subst _ _ = failWith (lengthMisMatch orig_xs orig_ys) + +------------------------------ +uVar :: Bool -- Swapped + -> TvSubstEnv -- An existing substitution to extend + -> TyVar -- Type variable to be unified + -> Type -- with this type + -> UM TvSubstEnv + +uVar swap subst tv1 ty + = -- Check to see whether tv1 is refined by the substitution + case (lookupVarEnv subst tv1) of + -- Yes, call back into unify' + Just ty' | swap -> unify subst ty ty' + | otherwise -> unify subst ty' ty + -- No, continue + Nothing -> uUnrefined subst tv1 ty ty + + +uUnrefined :: TvSubstEnv -- An existing substitution to extend + -> TyVar -- Type variable to be unified + -> Type -- with this type + -> Type -- (de-noted version) + -> UM TvSubstEnv + +-- We know that tv1 isn't refined + +uUnrefined subst tv1 ty2 ty2' + | Just ty2'' <- tcView ty2' + = uUnrefined subst tv1 ty2 ty2'' -- Unwrap synonyms + -- This is essential, in case we have + -- type Foo a = a + -- and then unify a :=: Foo a + +uUnrefined subst tv1 ty2 (TyVarTy tv2) + | tv1 == tv2 -- Same type variable + = return subst + + -- Check to see whether tv2 is refined + | Just ty' <- lookupVarEnv subst tv2 + = uUnrefined subst tv1 ty' ty' + + -- So both are unrefined; next, see if the kinds force the direction + | k1 == k2 -- Can update either; so check the bind-flags + = do { b1 <- tvBindFlag tv1 + ; b2 <- tvBindFlag tv2 + ; case (b1,b2) of + (BindMe, _) -> bind tv1 ty2 + + (AvoidMe, BindMe) -> bind tv2 ty1 + (AvoidMe, _) -> bind tv1 ty2 + + (WildCard, WildCard) -> return subst + (WildCard, Skolem) -> return subst + (WildCard, _) -> bind tv2 ty1 + + (Skolem, WildCard) -> return subst + (Skolem, Skolem) -> failWith (misMatch ty1 ty2) + (Skolem, _) -> bind tv2 ty1 + } + + | k1 `isSubKind` k2 = bindTv subst tv2 ty1 -- Must update tv2 + | k2 `isSubKind` k1 = bindTv subst tv1 ty2 -- Must update tv1 + + | otherwise = failWith (kindMisMatch tv1 ty2) + where + ty1 = TyVarTy tv1 + k1 = tyVarKind tv1 + k2 = tyVarKind tv2 + bind tv ty = return (extendVarEnv subst tv ty) + +uUnrefined subst tv1 ty2 ty2' -- ty2 is not a type variable + | tv1 `elemVarSet` substTvSet subst (tyVarsOfType ty2') + = failWith (occursCheck tv1 ty2) -- Occurs check + | not (k2 `isSubKind` k1) + = failWith (kindMisMatch tv1 ty2) -- Kind check + | otherwise + = bindTv subst tv1 ty2 -- Bind tyvar to the synonym if poss + where + k1 = tyVarKind tv1 + k2 = typeKind ty2' + +substTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet +-- Apply the non-idempotent substitution to a set of type variables, +-- remembering that the substitution isn't necessarily idempotent +substTvSet subst tvs + = foldVarSet (unionVarSet . get) emptyVarSet tvs + where + get tv = case lookupVarEnv subst tv of + Nothing -> unitVarSet tv + Just ty -> substTvSet subst (tyVarsOfType ty) + +bindTv subst tv ty -- ty is not a type variable + = do { b <- tvBindFlag tv + ; case b of + Skolem -> failWith (misMatch (TyVarTy tv) ty) + WildCard -> return subst + other -> return (extendVarEnv subst tv ty) + } +\end{code} + +%************************************************************************ +%* * + Unification monad +%* * +%************************************************************************ + +\begin{code} +data BindFlag + = BindMe -- A regular type variable + | AvoidMe -- Like BindMe but, given the choice, avoid binding it + + | Skolem -- This type variable is a skolem constant + -- Don't bind it; it only matches itself + + | WildCard -- This type variable matches anything, + -- and does not affect the substitution + +newtype UM a = UM { unUM :: (TyVar -> BindFlag) + -> MaybeErr Message a } + +instance Monad UM where + return a = UM (\tvs -> Succeeded a) + fail s = UM (\tvs -> Failed (text s)) + m >>= k = UM (\tvs -> case unUM m tvs of + Failed err -> Failed err + Succeeded v -> unUM (k v) tvs) + +initUM :: (TyVar -> BindFlag) -> UM a -> MaybeErr Message a +initUM badtvs um = unUM um badtvs + +tvBindFlag :: TyVar -> UM BindFlag +tvBindFlag tv = UM (\tv_fn -> Succeeded (tv_fn tv)) + +failWith :: Message -> UM a +failWith msg = UM (\tv_fn -> Failed msg) + +maybeErrToMaybe :: MaybeErr fail succ -> Maybe succ +maybeErrToMaybe (Succeeded a) = Just a +maybeErrToMaybe (Failed m) = Nothing + +------------------------------ +repSplitAppTy_maybe :: Type -> Maybe (Type,Type) +-- Like Type.splitAppTy_maybe, but any coreView stuff is already done +repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2) +repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2) +repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of + Just (tys', ty') -> Just (TyConApp tc tys', ty') + Nothing -> Nothing +repSplitAppTy_maybe other = Nothing +\end{code} + + +%************************************************************************ +%* * + Error reporting + We go to a lot more trouble to tidy the types + in TcUnify. Maybe we'll end up having to do that + here too, but I'll leave it for now. +%* * +%************************************************************************ + +\begin{code} +misMatch t1 t2 + = ptext SLIT("Can't match types") <+> quotes (ppr t1) <+> + ptext SLIT("and") <+> quotes (ppr t2) + +lengthMisMatch tys1 tys2 + = sep [ptext SLIT("Can't match unequal length lists"), + nest 2 (ppr tys1), nest 2 (ppr tys2) ] + +kindMisMatch tv1 t2 + = vcat [ptext SLIT("Can't match kinds") <+> quotes (ppr (tyVarKind tv1)) <+> + ptext SLIT("and") <+> quotes (ppr (typeKind t2)), + ptext SLIT("when matching") <+> quotes (ppr tv1) <+> + ptext SLIT("with") <+> quotes (ppr t2)] + +occursCheck tv ty + = hang (ptext SLIT("Can't construct the infinite type")) + 2 (ppr tv <+> equals <+> ppr ty) +\end{code}
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