import Data.List (nub)
import Control.Monad.Error
--- TO DO: propagate occurs-check errors through the Unifier instead of using Prelude.error
-
-- | a unification variable
newtype UVar = UVar Int
deriving (Ord, Eq)
-- /values/ of type @t@. Invariant: values of the map are always
-- fully resolved with respect to the map.
data Unifier t = Unifier (Map UVar t)
+ | UnifierError String
-- | Resolves a unification variable according to a Unifier.
getU :: Unifier t -> UVar -> Maybe t
-getU (Unifier u) v = lookup v u
+getU (Unifier u) v = lookup v u
+getU (UnifierError e) v = error e
-- | An infinite supply of distinct unification variables.
uvarSupply :: [UVar]
-- | Returns a copy of the @t@ argument in which all @UVar@
-- occurrences have been replaced by fully-resolved @t@ values.
resolve :: Unifiable t => Unifier t -> t -> t
-resolve (Unifier m) t = resolve' (toList m) t
+resolve (UnifierError e) _ = error e
+resolve (Unifier m) t = resolve' (toList m) t
where
resolve' [] t = t
resolve' ((uv,v):rest) t | Just uvt <- project t = if uvt == uv
-- | Given two unifiables, find their most general unifier.
unify :: Unifiable t => t -> t -> Unifier t
-unify v1 v2 | (Just v1') <- project v1, (Just v2') <- project v2, v1'==v2' = emptyUnifier
-unify v1 v2 | (Just v1') <- project v1 = if elem v1' (occurrences v2)
- then error "occurs check failed in Unify.unify"
- else Unifier $ insert v1' v2 empty
-unify v1 v2 | (Just v2') <- project v2 = unify v2 v1
-unify v1 v2 | _ <- project v1, _ <- project v2 = unify' v1 v2
+unify v1 v2 | (Just v1') <- project v1, (Just v2') <- project v2, v1'==v2' = emptyUnifier
+unify v1 v2 | (Just v1') <- project v1 = if elem v1' (occurrences v2)
+ then UnifierError "occurs check failed in Unify.unify"
+ else Unifier $ insert v1' v2 empty
+unify v1 v2 | (Just v2') <- project v2 = unify v2 v1
+unify v1 v2 | _ <- project v1, _ <- project v2 = unify' v1 v2
-- | Merge two unifiers into a single unifier.
mergeU :: Unifiable t => Unifier t -> Unifier t -> Unifier t
-mergeU (Unifier u) u' = foldr (\(k,v) -> \uacc -> mergeU' uacc k (resolve uacc v)) u' (toList u)
+mergeU ue@(UnifierError _) _ = ue
+mergeU (Unifier u) u' = foldr (\(k,v) -> \uacc -> mergeU' uacc k (resolve uacc v)) u' (toList u)
where
- mergeU' u@(Unifier m) v1 v2 | member v1 m = mergeU u $ unify (m ! v1) v2
- | Just v2' <- project (resolve u v2), v2' == v1 = u
- | elem v1 (occurrences v2) = error "occurs check failed in Unify.mergeU"
- | otherwise = Unifier $ insert v1 v2 m
+ mergeU' ue@(UnifierError _) _ _ = ue
+ mergeU' u@(Unifier m) v1 v2 | member v1 m = mergeU u $ unify (m ! v1) v2
+ | Just v2' <- project (resolve u v2), v2' == v1 = u
+ | elem v1 (occurrences v2) = UnifierError "occurs check failed in Unify.mergeU"
+ | otherwise = Unifier $ insert v1 v2 m
-- | Enumerates the unification variables, sorted by occurs-check.
sortU :: (Unifiable t, Eq t) => Unifier t -> [UVar]
-sortU u@(Unifier um) = reverse $ nub $ concatMap (\k -> occurrences (um!k)) (keys um)
+sortU u@(Unifier um) = reverse $ nub $ concatMap (\k -> occurrences (um!k)) (keys um)
+sortU (UnifierError ue) = error ue