%
% (c) The University of Glasgow 2006
%
\begin{code}
module Unify (
tcMatchTy, tcMatchTys, tcMatchTyX,
ruleMatchTyX, tcMatchPreds, MatchEnv(..),
dataConCannotMatch,
tcUnifyTys, BindFlag(..),
niFixTvSubst, niSubstTvSet
) where
#include "HsVersions.h"
import Var
import VarEnv
import VarSet
import Type
import Coercion
import TyCon
import DataCon
import TypeRep
import Outputable
import ErrUtils
import Util
import Maybes
import FastString
\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
, me_env :: RnEnv2
}
tcMatchTy :: TyVarSet
-> Type
-> Type
-> Maybe TvSubst
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)
tcMatchTys :: TyVarSet
-> [Type]
-> [Type]
-> Maybe TvSubst
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)
tcMatchTyX :: TyVarSet
-> TvSubst
-> Type
-> Type
-> 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]
-> [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)
ruleMatchTyX :: MatchEnv
-> TvSubstEnv
-> Type
-> Type
-> Maybe TvSubstEnv
ruleMatchTyX menv subst ty1 ty2 = match menv subst ty1 ty2
\end{code}
Now the internals of matching
\begin{code}
match :: MatchEnv
-> TvSubstEnv
-> Type -> Type
-> Maybe TvSubstEnv
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
| Just ty1' <- lookupVarEnv subst tv1'
= if tcEqTypeX (nukeRnEnvL rn_env) ty1' ty2
then Just subst
else Nothing
| tv1' `elemVarSet` me_tmpls menv
= if any (inRnEnvR rn_env) (varSetElems (tyVarsOfType ty2))
then Nothing
else do { subst1 <- match_kind menv subst tv1 ty2
; return (extendVarEnv subst1 tv1' ty2) }
| otherwise
= case ty2 of
TyVarTy tv2 | tv1' == rnOccR rn_env tv2 -> Just subst
_ -> 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
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 _ _ _ _
= Nothing
match_kind :: MatchEnv -> TvSubstEnv -> TyVar -> Type -> Maybe TvSubstEnv
match_kind menv subst tv ty
| isCoVar tv = do { let (ty1,ty2) = coVarKind tv
(ty3,ty4) = coercionKind ty
; subst1 <- match menv subst ty1 ty3
; match menv subst1 ty2 ty4 }
| otherwise = if typeKind ty `isSubKind` tyVarKind tv
then Just subst
else Nothing
match_tys :: MatchEnv -> TvSubstEnv -> [Type] -> [Type] -> Maybe TvSubstEnv
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 _ 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 _ _ _ _ = 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 _ _ _ _ = 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}
dataConCannotMatch :: [Type] -> DataCon -> Bool
dataConCannotMatch tys con
| null eq_spec = False
| all isTyVarTy tys = False
| otherwise
= cant_match_s (map (substTyVar subst . fst) eq_spec)
(map snd eq_spec)
where
dc_tvs = dataConUnivTyVars con
eq_spec = dataConEqSpec con
subst = zipTopTvSubst dc_tvs tys
cant_match_s :: [Type] -> [Type] -> Bool
cant_match_s tys1 tys2 = ASSERT( equalLength tys1 tys2 )
or (zipWith cant_match tys1 tys2)
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 || cant_match_s tys1 tys2
cant_match (FunTy {}) (TyConApp tc _) = isDataTyCon tc
cant_match (TyConApp tc _) (FunTy {}) = isDataTyCon tc
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
\end{code}
%************************************************************************
%* *
Unification
%* *
%************************************************************************
\begin{code}
tcUnifyTys :: (TyVar -> BindFlag)
-> [Type] -> [Type]
-> Maybe TvSubst
tcUnifyTys bind_fn tys1 tys2
= maybeErrToMaybe $ initUM bind_fn $
do { subst <- unifyList emptyTvSubstEnv tys1 tys2
; 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
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
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
-> Type -> Type
-> UM TvSubstEnv
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 }
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)
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
-> TyVar
-> Type
-> UM TvSubstEnv
uVar subst tv1 ty
=
case (lookupVarEnv subst tv1) of
Just ty' -> unify subst ty' ty
Nothing -> uUnrefined subst
tv1 ty ty
uUnrefined :: TvSubstEnv
-> TyVar
-> Type
-> Type
-> UM TvSubstEnv
uUnrefined subst tv1 ty2 ty2'
| Just ty2'' <- tcView ty2'
= uUnrefined subst tv1 ty2 ty2''
uUnrefined subst tv1 ty2 (TyVarTy tv2)
| tv1 == tv2
= return subst
| Just ty' <- lookupVarEnv subst tv2
= uUnrefined subst tv1 ty' ty'
| eqKind k1 k2
= 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
| k2 `isSubKind` k1 = bindTv subst tv1 ty2
| 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'
| tv1 `elemVarSet` niSubstTvSet subst (tyVarsOfType ty2')
= failWith (occursCheck tv1 ty2)
| not (k2 `isSubKind` k1)
= failWith (kindMisMatch tv1 ty2)
| otherwise
= bindTv subst tv1 ty2
where
k1 = tyVarKind tv1
k2 = typeKind ty2'
bindTv :: TvSubstEnv -> TyVar -> Type -> UM TvSubstEnv
bindTv subst tv ty
= 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
| Skolem
\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}