+-- 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}