+%
+% (c) The University of Glasgow 2006
+%
+
\begin{code}
module Unify (
-- Matching of types:
-- the "tc" prefix indicates that matching always
-- respects newtypes (rather than looking through them)
- tcMatchTys, tcMatchTyX, ruleMatchTyX, tcMatchPreds, MatchEnv(..)
+ tcMatchTy, tcMatchTys, tcMatchTyX,
+ ruleMatchTyX, tcMatchPreds,
+
+ MatchEnv(..), matchList,
+
+ typesCantMatch,
+
+ -- Side-effect free unification
+ tcUnifyTys, BindFlag(..),
+ niFixTvSubst, niSubstTvSet
+
) where
#include "HsVersions.h"
-import Var ( Var, TyVar, tyVarKind )
+import Var
import VarEnv
import VarSet
-import Type ( typeKind, tyVarsOfType, tyVarsOfTypes, tyVarsOfTheta, mkTyVarTys,
- TvSubstEnv, emptyTvSubstEnv, TvSubst(..), substTy, tcEqTypeX,
- mkOpenTvSubst, tcView, isSubKind, eqKind, repSplitAppTy_maybe )
-import TypeRep ( Type(..), PredType(..), funTyCon )
-import DataCon ( DataCon, dataConResTys )
-import Util ( snocView )
-import ErrUtils ( Message )
+import Kind
+import Type
+import TyCon
+import TypeRep
import Outputable
+import ErrUtils
+import Util
import Maybes
+import FastString
+
+import Control.Monad (guard)
\end{code}
\begin{code}
data MatchEnv
- = ME { me_tmpls :: VarSet -- Template tyvars
+ = ME { me_tmpls :: VarSet -- Template variables
, me_env :: RnEnv2 -- Renaming envt for nested foralls
- } -- In-scope set includes template tyvars
+ } -- In-scope set includes template variables
+ -- Nota Bene: MatchEnv isn't specific to Types. It is used
+ -- for matching terms and coercions as well as types
+
+tcMatchTy :: TyVarSet -- Template tyvars
+ -> Type -- Template
+ -> Type -- Target
+ -> Maybe TvSubst -- One-shot; in principle the template
+ -- variables could be free in the target
+
+tcMatchTy tmpls ty1 ty2
+ = case match menv emptyTvSubstEnv 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 }
+ in_scope = mkInScopeSet (tmpls `unionVarSet` tyVarsOfType ty2)
+ -- We're assuming that all the interesting
+ -- tyvars in tys1 are in tmpls
tcMatchTys :: TyVarSet -- Template tyvars
- -> [Type] -- Template
- -> [Type] -- Target
- -> Maybe TvSubst -- One-shot; in principle the template
+ -> [Type] -- Template
+ -> [Type] -- Target
+ -> Maybe TvSubst -- One-shot; in principle the template
-- variables could be free in the target
tcMatchTys tmpls tys1 tys2
-> [PredType] -> [PredType]
-> Maybe TvSubstEnv
tcMatchPreds tmpls ps1 ps2
- = match_list (match_pred menv) emptyTvSubstEnv ps1 ps2
+ = matchList (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)
-- 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
+-- This matcher works on core types; that is, it ignores PredTypes
+-- Watch out if newtypes become transparent agin!
+-- this matcher must respect newtypes
-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 ty1 ty2 | Just ty1' <- coreView ty1 = match menv subst ty1' ty2
+ | Just ty2' <- coreView 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
+ | Just ty1' <- lookupVarEnv subst tv1' -- tv1' is already bound
+ = if eqTypeX (nukeRnEnvL rn_env) ty1' ty2
+ -- ty1 has no locally-bound variables, hence nukeRnEnvL
+ then Just subst
+ else Nothing -- ty2 doesn't match
+
+ | tv1' `elemVarSet` me_tmpls menv
+ = if any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2))
+ then Nothing -- Occurs check
+ else do { subst1 <- match_kind menv subst tv1 ty2
+ -- Note [Matching kinds]
+ ; return (extendVarEnv subst1 tv1' ty2) }
| otherwise -- tv1 is not a template tyvar
= case ty2 of
TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst
- other -> Nothing
+ _ -> Nothing
where
rn_env = me_env menv
tv1' = rnOccL rn_env tv1
; match menv subst' ty1b ty2b }
match menv subst (AppTy ty1a ty1b) ty2
| Just (ty2a, ty2b) <- repSplitAppTy_maybe ty2
+ -- 'repSplit' used because the tcView stuff is done above
= do { subst' <- match menv subst ty1a ty2a
; match menv subst' ty1b ty2b }
-match menv subst ty1 ty2
+match _ _ _ _
= Nothing
--------------
-match_tys menv subst tys1 tys2 = match_list (match menv) subst tys1 tys2
+match_kind :: MatchEnv -> TvSubstEnv -> TyVar -> Type -> Maybe TvSubstEnv
+-- Match the kind of the template tyvar with the kind of Type
+-- Note [Matching kinds]
+match_kind _ subst tv ty
+ = guard (typeKind ty `isSubKind` tyVarKind tv) >> return subst
+
+-- Note [Matching kinds]
+-- ~~~~~~~~~~~~~~~~~~~~~
+-- For ordinary type variables, we don't want (m a) to match (n b)
+-- if say (a::*) and (b::*->*). This is just a yes/no issue.
+--
+-- For coercion kinds matters are more complicated. If we have a
+-- coercion template variable co::a~[b], where a,b are presumably also
+-- template type variables, then we must match co's kind against the
+-- kind of the actual argument, so as to give bindings to a,b.
+--
+-- In fact I have no example in mind that *requires* this kind-matching
+-- to instantiate template type variables, but it seems like the right
+-- thing to do. C.f. Note [Matching variable types] in Rules.lhs
--------------
-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_tys :: MatchEnv -> TvSubstEnv -> [Type] -> [Type] -> Maybe TvSubstEnv
+match_tys menv subst tys1 tys2 = matchList (match menv) subst tys1 tys2
--------------
+matchList :: (env -> a -> b -> Maybe env)
+ -> env -> [a] -> [b] -> Maybe env
+matchList _ subst [] [] = Just subst
+matchList fn subst (a:as) (b:bs) = do { subst' <- fn subst a b
+ ; matchList fn subst' as bs }
+matchList _ _ _ _ = Nothing
+
+--------------
+match_pred :: MatchEnv -> TvSubstEnv -> PredType -> PredType -> Maybe TvSubstEnv
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
+match_pred _ _ _ _ = Nothing
+\end{code}
+
+
+%************************************************************************
+%* *
+ GADTs
+%* *
+%************************************************************************
+
+Note [Pruning dead case alternatives]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+Consider data T a where
+ T1 :: T Int
+ T2 :: T a
+
+ newtype X = MkX Int
+ newtype Y = MkY Char
+
+ type family F a
+ type instance F Bool = Int
+
+Now consider case x of { T1 -> e1; T2 -> e2 }
+
+The question before the house is this: if I know something about the type
+of x, can I prune away the T1 alternative?
+
+Suppose x::T Char. It's impossible to construct a (T Char) using T1,
+ Answer = YES (clearly)
+
+Suppose x::T (F a), where 'a' is in scope. Then 'a' might be instantiated
+to 'Bool', in which case x::T Int, so
+ ANSWER = NO (clearly)
+
+Suppose x::T X. Then *in Haskell* it's impossible to construct a (non-bottom)
+value of type (T X) using T1. But *in FC* it's quite possible. The newtype
+gives a coercion
+ CoX :: X ~ Int
+So (T CoX) :: T X ~ T Int; hence (T1 `cast` sym (T CoX)) is a non-bottom value
+of type (T X) constructed with T1. Hence
+ ANSWER = NO (surprisingly)
+
+Furthermore, this can even happen; see Trac #1251. GHC's newtype-deriving
+mechanism uses a cast, just as above, to move from one dictionary to another,
+in effect giving the programmer access to CoX.
+
+Finally, suppose x::T Y. Then *even in FC* we can't construct a
+non-bottom value of type (T Y) using T1. That's because we can get
+from Y to Char, but not to Int.
+
+
+Here's a related question. data Eq a b where EQ :: Eq a a
+Consider
+ case x of { EQ -> ... }
+
+Suppose x::Eq Int Char. Is the alternative dead? Clearly yes.
+
+What about x::Eq Int a, in a context where we have evidence that a~Char.
+Then again the alternative is dead.
+
+
+ Summary
+
+We are really doing a test for unsatisfiability of the type
+constraints implied by the match. And that is clearly, in general, a
+hard thing to do.
+
+However, since we are simply dropping dead code, a conservative test
+suffices. There is a continuum of tests, ranging from easy to hard, that
+drop more and more dead code.
+
+For now we implement a very simple test: type variables match
+anything, type functions (incl newtypes) match anything, and only
+distinct data types fail to match. We can elaborate later.
+
+\begin{code}
+typesCantMatch :: [(Type,Type)] -> Bool
+typesCantMatch prs = any (\(s,t) -> cant_match s t) prs
+ where
+ cant_match :: Type -> Type -> Bool
+ cant_match t1 t2
+ | Just t1' <- coreView t1 = cant_match t1' t2
+ | Just t2' <- coreView t2 = cant_match t1 t2'
+
+ cant_match (FunTy a1 r1) (FunTy a2 r2)
+ = cant_match a1 a2 || cant_match r1 r2
+
+ cant_match (TyConApp tc1 tys1) (TyConApp tc2 tys2)
+ | isDataTyCon tc1 && isDataTyCon tc2
+ = tc1 /= tc2 || typesCantMatch (zipEqual "typesCantMatch" tys1 tys2)
+
+ cant_match (FunTy {}) (TyConApp tc _) = isDataTyCon tc
+ cant_match (TyConApp tc _) (FunTy {}) = isDataTyCon tc
+ -- tc can't be FunTyCon by invariant
+
+ cant_match (AppTy f1 a1) ty2
+ | Just (f2, a2) <- repSplitAppTy_maybe ty2
+ = cant_match f1 f2 || cant_match a1 a2
+ cant_match ty1 (AppTy f2 a2)
+ | Just (f1, a1) <- repSplitAppTy_maybe ty1
+ = cant_match f1 f2 || cant_match a1 a2
+
+ cant_match _ _ = False -- Safe!
+
+-- Things we could add;
+-- foralls
+-- look through newtypes
+-- take account of tyvar bindings (EQ example above)
+\end{code}
+
+
+%************************************************************************
+%* *
+ Unification
+%* *
+%************************************************************************
+
+\begin{code}
+tcUnifyTys :: (TyVar -> BindFlag)
+ -> [Type] -> [Type]
+ -> Maybe TvSubst -- A regular one-shot (idempotent) 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 <- unifyList emptyTvSubstEnv tys1 tys2
+
+ -- Find the fixed point of the resulting non-idempotent substitution
+ ; return (niFixTvSubst subst) }
+\end{code}
+
+
+%************************************************************************
+%* *
+ Non-idempotent substitution
+%* *
+%************************************************************************
+
+Note [Non-idempotent substitution]
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+During unification we use a TvSubstEnv that is
+ (a) non-idempotent
+ (b) loop-free; ie repeatedly applying it yields a fixed point
+
+\begin{code}
+niFixTvSubst :: TvSubstEnv -> TvSubst
+-- Find the idempotent fixed point of the non-idempotent substitution
+-- ToDo: use laziness instead of iteration?
+niFixTvSubst env = f env
+ where
+ f e | not_fixpoint = f (mapVarEnv (substTy subst) e)
+ | otherwise = subst
+ where
+ range_tvs = foldVarEnv (unionVarSet . tyVarsOfType) emptyVarSet e
+ subst = mkTvSubst (mkInScopeSet range_tvs) e
+ not_fixpoint = foldVarSet ((||) . in_domain) False range_tvs
+ in_domain tv = tv `elemVarEnv` e
+
+niSubstTvSet :: TvSubstEnv -> TyVarSet -> TyVarSet
+-- Apply the non-idempotent substitution to a set of type variables,
+-- remembering that the substitution isn't necessarily idempotent
+-- This is used in the occurs check, before extending the substitution
+niSubstTvSet subst tvs
+ = foldVarSet (unionVarSet . get) emptyVarSet tvs
+ where
+ get tv = case lookupVarEnv subst tv of
+ Nothing -> unitVarSet tv
+ Just ty -> niSubstTvSet subst (tyVarsOfType ty)
\end{code}
+%************************************************************************
+%* *
+ The workhorse
+%* *
+%************************************************************************
+
+\begin{code}
+unify :: TvSubstEnv -- An existing substitution to extend
+ -> Type -> Type -- Types to be unified, and witness of their equality
+ -> 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
+-- in unify, any NewTcApps/Preds should be taken at face value
+unify subst (TyVarTy tv1) ty2 = uVar subst tv1 ty2
+unify subst ty1 (TyVarTy tv2) = uVar 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 (TyConApp tyc1 tys1) (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 _ ty1 ty2 = failWith (misMatch ty1 ty2)
+ -- ForAlls??
+
+------------------------------
+unify_pred :: TvSubstEnv -> PredType -> PredType -> UM TvSubstEnv
+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 _ p1 p2 = failWith (misMatch (PredTy p1) (PredTy p2))
+
+------------------------------
+unify_tys :: TvSubstEnv -> [Type] -> [Type] -> UM TvSubstEnv
+unify_tys subst xs ys = unifyList subst xs ys
+
+unifyList :: TvSubstEnv -> [Type] -> [Type] -> UM TvSubstEnv
+unifyList subst orig_xs orig_ys
+ = go subst orig_xs orig_ys
+ where
+ go subst [] [] = return subst
+ go subst (x:xs) (y:ys) = do { subst' <- unify subst x y
+ ; go subst' xs ys }
+ go _ _ _ = failWith (lengthMisMatch orig_xs orig_ys)
+
+---------------------------------
+uVar :: TvSubstEnv -- An existing substitution to extend
+ -> TyVar -- Type variable to be unified
+ -> Type -- with this type
+ -> UM TvSubstEnv
+
+-- PRE-CONDITION: in the call (uVar swap r tv1 ty), we know that
+-- if swap=False (tv1~ty)
+-- if swap=True (ty~tv1)
+
+uVar subst tv1 ty
+ = -- Check to see whether tv1 is refined by the substitution
+ case (lookupVarEnv subst tv1) of
+ Just ty' -> unify subst ty' ty -- Yes, call back into unify'
+ Nothing -> uUnrefined subst -- No, continue
+ tv1 ty ty
+
+uUnrefined :: TvSubstEnv -- An existing substitution to extend
+ -> TyVar -- Type variable to be unified
+ -> Type -- with this type
+ -> Type -- (version w/ expanded synonyms)
+ -> 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
+ | eqKind 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
+ (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` niSubstTvSet 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'
+
+bindTv :: TvSubstEnv -> TyVar -> Type -> UM TvSubstEnv
+bindTv subst tv ty -- ty is not a type variable
+ = do { b <- tvBindFlag tv
+ ; case b of
+ Skolem -> failWith (misMatch (TyVarTy tv) ty)
+ BindMe -> return $ extendVarEnv subst tv ty
+ }
+\end{code}
+
+%************************************************************************
+%* *
+ Binding decisions
+%* *
+%************************************************************************
+
+\begin{code}
+data BindFlag
+ = BindMe -- A regular type variable
+
+ | Skolem -- This type variable is a skolem constant
+ -- Don't bind it; it only matches itself
+\end{code}
+
+
+%************************************************************************
+%* *
+ Unification monad
+%* *
+%************************************************************************
+
+\begin{code}
+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 _) = 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 :: Type -> Type -> SDoc
+misMatch t1 t2
+ = ptext (sLit "Can't match types") <+> quotes (ppr t1) <+>
+ ptext (sLit "and") <+> quotes (ppr t2)
+
+lengthMisMatch :: [Type] -> [Type] -> SDoc
+lengthMisMatch tys1 tys2
+ = sep [ptext (sLit "Can't match unequal length lists"),
+ nest 2 (ppr tys1), nest 2 (ppr tys2) ]
+
+kindMisMatch :: TyVar -> Type -> SDoc
+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 :: TyVar -> Type -> SDoc
+occursCheck tv ty
+ = hang (ptext (sLit "Can't construct the infinite type"))
+ 2 (ppr tv <+> equals <+> ppr ty)
+\end{code}
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