@@ -46,17 +46,17 @@ type family Combine (a :: v) (b :: v) :: v
4646
4747{-| Delete elements from a map by key -}
4848type family (m :: [Mapping k v]) :\ (c :: k) :: [Mapping k v] where
49− '[] :\ k = '[]
50− ((k :-> v) ': m) :\ k = m :\ k
51− (kvp ': m) :\ k = kvp ': (m :\ k)
49+ '[] :\ k = '[]
50+ ((k :-> v) ': m) :\ k = m :\ k
51+ (kvp ': m) :\ k = kvp ': (m :\ k)
5252
53−{-| Lookup elements from a map -}
53+{-| Type-level lookup of elements from a map -}
5454type family Lookup (m :: [Mapping k v]) (c :: k) :: Maybe v where
5555 Lookup '[] k = Nothing
5656 Lookup ((k :-> v) ': m) k = Just v
5757 Lookup (kvp ': m) k = Lookup m k
5858
59−{-| Membership test -}
59+{-| Membership test as type function -}
6060type family Member (c :: k) (m :: [Mapping k v]) :: Bool where
6161 Member k '[] = False
6262 Member k ((k :-> v) ': m) = True
@@ -84,7 +84,7 @@ class IsMember v t m where
8484instance {-# OVERLAPS #-} IsMember v t ((v ':-> t) ': m) where
8585 lookp _ (Ext _ x _) = x
8686
87−instance IsMember v t m => IsMember v t (x ': m) where
87+instance {-# OVERLAPPABLE #-} IsMember v t m => IsMember v t (x ': m) where
8888 lookp v (Ext _ _ m) = lookp v m
8989
9090
@@ -100,8 +100,12 @@ instance {-# OVERLAPS #-} Updatable v t ((v ':-> s) ': m) ((v ':-> t) ': m) wher
100100instance Updatable v t m n => Updatable v t ((w ':-> y) ': m) ((w ':-> y) ': n) where
101101 update (Ext w y m) v x = Ext w y (update m v x)
102102
103−instance Updatable v t '[] '[v ':-> t] where
104− update Empty v x = Ext v x Empty
103+-- instance Updatable v t '[] '[v ':-> t] where
104+-- update Empty v x = Ext v x Empty
105+
106+instance Updatable v t s ((v ':-> t) ': s) where
107+ update xs v x = Ext v x xs
108+
105109
106110{-| Predicate to check if in normalised map form -}
107111type IsMap s = (s ~ Nub (Sort s))
@@ -117,7 +121,7 @@ instance Show (Map '[]) where
117121 show Empty = "{}"
118122
119123instance (KnownSymbol k, Show v, Show' (Map s)) => Show (Map ((k :-> v) ': s)) where
120− show (Ext k v s) = "{" ++ show k ++ " :-> " ++ show v ++ (show' s) ++ "}"
124+ show (Ext k v s) = "{" ++ show k ++ " :-> " ++ show v ++ show' s ++ "}"
121125
122126class Show' t where
123127 show' :: t -> String
@@ -129,15 +133,22 @@ instance (KnownSymbol k, Show v, Show' (Map s)) => Show' (Map ((k :-> v) ': s))
129133instance Eq (Map '[]) where
130134 Empty == Empty = True
131135
132−instance (KnownSymbol k, Eq (Var k), Eq v, Eq (Map s)) => Eq (Map ((k :-> v) ': s)) where
133− (Ext k v m) == (Ext k' v' m') = k == k' && v == v' && m == m'
136+instance (Eq v, Eq (Map s)) => Eq (Map ((k :-> v) ': s)) where
137+ (Ext Var v m) == (Ext Var v' m') = v == v' && m == m'
134138
135−{-| Union of two finite maps -}
139+instance Ord (Map '[]) where
140+ compare Empty Empty = EQ
141+
142+instance (Ord v, Ord (Map s)) => Ord (Map ((k :-> v) ': s)) where
143+ compare (Ext Var v m) (Ext Var v' m') = compare v v' `mappend` compare m m'
144+
145+{-| Union of two finite maps (normalising) -}
136146union :: (Unionable s t) => Map s -> Map t -> Map (Union s t)
137147union s t = nub (quicksort (append s t))
138148
139149type Unionable s t = (Nubable (Sort (s :++ t)), Sortable (s :++ t))
140150
151+{-| Append of two finite maps (non normalising) -}
141152append :: Map s -> Map t -> Map (s :++ t)
142153append Empty x = x
143154append (Ext k v xs) ys = Ext k v (append xs ys)
@@ -152,11 +163,15 @@ class Sortable xs where
152163instance Sortable '[] where
153164 quicksort Empty = Empty
154165
155−instance (Sortable (Filter FMin (k :-> v) xs),
156− Sortable (Filter FMax (k :-> v) xs), FilterV FMin k v xs, FilterV FMax k v xs) => Sortable ((k :-> v) ': xs) where
157− quicksort (Ext k v xs) = ((quicksort (less k v xs)) `append` (Ext k v Empty)) `append` (quicksort (more k v xs))
158− where less = filterV (Proxy::(Proxy FMin))
159− more = filterV (Proxy::(Proxy FMax))
166+instance (Sortable (Filter FMin (k :-> v) xs)
167+ , Sortable (Filter FMax (k :-> v) xs)
168+ , FilterV FMin k v xs
169+ , FilterV FMax k v xs) => Sortable ((k :-> v) ': xs) where
170+ quicksort (Ext k v xs) =
171+ quicksort (less k v xs) `append` Ext k v Empty `append` quicksort (more k v xs)
172+ where
173+ less = filterV (Proxy::(Proxy FMin))
174+ more = filterV (Proxy::(Proxy FMax))
160175
161176{- Filter out the elements less-than or greater-than-or-equal to the pivot -}
162177class FilterV (f::Flag) k v xs where
@@ -165,13 +180,19 @@ class FilterV (f::Flag) k v xs where
165180instance FilterV f k v '[] where
166181 filterV _ k v Empty = Empty
167182
168−instance (Conder ((Cmp x (k :-> v)) == LT), FilterV FMin k v xs) => FilterV FMin k v (x ': xs) where
169− filterV f@Proxy k v (Ext k' v' xs) = cond (Proxy::(Proxy ((Cmp x (k :-> v)) == LT)))
170− (Ext k' v' (filterV f k v xs)) (filterV f k v xs)
183+instance (Conder (Cmp x (k :-> v) == LT), FilterV FMin k v xs) => FilterV FMin k v (x ': xs) where
184+ filterV f@Proxy k v (Ext k' v' xs) =
185+ cond (Proxy::(Proxy (Cmp x (k :-> v) == LT)))
186+ (Ext k' v' (filterV f k v xs))
187+ (filterV f k v xs)
171188
172−instance (Conder (((Cmp x (k :-> v)) == GT) || ((Cmp x (k :-> v)) == EQ)), FilterV FMax k v xs) => FilterV FMax k v (x ': xs) where
173− filterV f@Proxy k v (Ext k' v' xs) = cond (Proxy::(Proxy (((Cmp x (k :-> v)) == GT) || ((Cmp x (k :-> v)) == EQ))))
174− (Ext k' v' (filterV f k v xs)) (filterV f k v xs)
189+instance
190+ (Conder ((Cmp x (k :-> v) == GT) || (Cmp x (k :-> v) == EQ)), FilterV FMax k v xs)
191+ => FilterV FMax k v (x ': xs) where
192+ filterV f@Proxy k v (Ext k' v' xs) =
193+ cond (Proxy::(Proxy ((Cmp x (k :-> v) == GT) || (Cmp x (k :-> v) == EQ))))
194+ (Ext k' v' (filterV f k v xs))
195+ (filterV f k v xs)
175196
176197class Combinable t t' where
177198 combine :: t -> t' -> Combine t t'
@@ -191,7 +212,8 @@ instance {-# OVERLAPPABLE #-}
191212 nub (Ext k v (Ext k' v' s)) = Ext k v (nub (Ext k' v' s))
192213
193214instance {-# OVERLAPS #-}
194− (Combinable v v', Nubable ((k :-> Combine v v') ': s)) => Nubable ((k :-> v) ': (k :-> v') ': s) where
215+ (Combinable v v', Nubable ((k :-> Combine v v') ': s))
216+ => Nubable ((k :-> v) ': (k :-> v') ': s) where
195217 nub (Ext k v (Ext k' v' s)) = nub (Ext k (combine v v') s)
196218
197219