@@ -5,14 +5,13 @@ The implementation is similar to that shown in the paper.
55{-# LANGUAGE TypeOperators, PolyKinds, DataKinds, KindSignatures,
66 TypeFamilies, UndecidableInstances, MultiParamTypeClasses,
77 FlexibleInstances, GADTs, FlexibleContexts, ScopedTypeVariables,
8− ConstraintKinds, IncoherentInstances #-}
8+ ConstraintKinds #-}
99
1010module Data.Type.Map (Mapping(..), Union, Unionable, union, Var(..), Map(..),
1111 Combine, Combinable(..), Cmp,
1212 Nubable, nub,
1313 Lookup, Member, (:\), Split, split,
14− IsMember, lookp, Updatable, update,
15− IsMap, AsMap, asMap,
14+ IsMap, AsMap, asMap,
1615 Submap, submap) where
1716
1817import GHC.TypeLits
@@ -46,17 +45,17 @@ type family Combine (a :: v) (b :: v) :: v
4645
4746{-| Delete elements from a map by key -}
4847type 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)
48+ '[] :\ k = '[]
49+ ((k :-> v) ': m) :\ k = m :\ k
50+ (kvp ': m) :\ k = kvp ': (m :\ k)
5251
53−{-| Type-level lookup of elements from a map -}
52+{-| Lookup elements from a map -}
5453type family Lookup (m :: [Mapping k v]) (c :: k) :: Maybe v where
5554 Lookup '[] k = Nothing
5655 Lookup ((k :-> v) ': m) k = Just v
5756 Lookup (kvp ': m) k = Lookup m k
5857
59−{-| Membership test as type function -}
58+{-| Membership test -}
6059type family Member (c :: k) (m :: [Mapping k v]) :: Bool where
6160 Member k '[] = False
6261 Member k ((k :-> v) ': m) = True
@@ -76,37 +75,6 @@ data Map (n :: [Mapping Symbol *]) where
7675 Empty :: Map '[]
7776 Ext :: Var k -> v -> Map m -> Map ((k :-> v) ': m)
7877
79−{-| Membership test a type class (predicate) -}
80−class IsMember v t m where
81− {-| Value-level lookup of elements from a map, via type class predicate -}
82− lookp :: Var v -> Map m -> t
83−
84−instance {-# OVERLAPS #-} IsMember v t ((v ':-> t) ': m) where
85− lookp _ (Ext _ x _) = x
86−
87−instance {-# OVERLAPPABLE #-} IsMember v t m => IsMember v t (x ': m) where
88− lookp v (Ext _ _ m) = lookp v m
89−
90−
91−{-| Updatability as a type class -}
92−class Updatable v t m n where
93− {-| Update a map with `m` at variable `v` with a value of type `t`
94− to produce a map of type `n` -}
95− update :: Map m -> Var v -> t -> Map n
96−
97−instance {-# OVERLAPS #-} Updatable v t ((v ':-> s) ': m) ((v ':-> t) ': m) where
98− update (Ext v _ m) _ x = Ext v x m
99−
100−instance Updatable v t m n => Updatable v t ((w ':-> y) ': m) ((w ':-> y) ': n) where
101− update (Ext w y m) v x = Ext w y (update m v x)
102−
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−
109−
11078{-| Predicate to check if in normalised map form -}
11179type IsMap s = (s ~ Nub (Sort s))
11280
@@ -121,7 +89,7 @@ instance Show (Map '[]) where
12189 show Empty = "{}"
12290
12391instance (KnownSymbol k, Show v, Show' (Map s)) => Show (Map ((k :-> v) ': s)) where
124− show (Ext k v s) = "{" ++ show k ++ " :-> " ++ show v ++ show' s ++ "}"
92+ show (Ext k v s) = "{" ++ show k ++ " :-> " ++ show v ++ (show' s) ++ "}"
12593
12694class Show' t where
12795 show' :: t -> String
@@ -130,25 +98,12 @@ instance Show' (Map '[]) where
13098instance (KnownSymbol k, Show v, Show' (Map s)) => Show' (Map ((k :-> v) ': s)) where
13199 show' (Ext k v s) = ", " ++ show k ++ " :-> " ++ show v ++ (show' s)
132100
133−instance Eq (Map '[]) where
134− Empty == Empty = True
135−
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'
138−
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) -}
101+{-| Union of two finite maps -}
146102union :: (Unionable s t) => Map s -> Map t -> Map (Union s t)
147103union s t = nub (quicksort (append s t))
148104
149105type Unionable s t = (Nubable (Sort (s :++ t)), Sortable (s :++ t))
150106
151−{-| Append of two finite maps (non normalising) -}
152107append :: Map s -> Map t -> Map (s :++ t)
153108append Empty x = x
154109append (Ext k v xs) ys = Ext k v (append xs ys)
@@ -163,15 +118,11 @@ class Sortable xs where
163118instance Sortable '[] where
164119 quicksort Empty = Empty
165120
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))
121+instance (Sortable (Filter FMin (k :-> v) xs),
122+ Sortable (Filter FMax (k :-> v) xs), FilterV FMin k v xs, FilterV FMax k v xs) => Sortable ((k :-> v) ': xs) where
123+ quicksort (Ext k v xs) = ((quicksort (less k v xs)) `append` (Ext k v Empty)) `append` (quicksort (more k v xs))
124+ where less = filterV (Proxy::(Proxy FMin))
125+ more = filterV (Proxy::(Proxy FMax))
175126
176127{- Filter out the elements less-than or greater-than-or-equal to the pivot -}
177128class FilterV (f::Flag) k v xs where
@@ -180,19 +131,13 @@ class FilterV (f::Flag) k v xs where
180131instance FilterV f k v '[] where
181132 filterV _ k v Empty = Empty
182133
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)
134+instance (Conder ((Cmp x (k :-> v)) == LT), FilterV FMin k v xs) => FilterV FMin k v (x ': xs) where
135+ filterV f@Proxy k v (Ext k' v' xs) = cond (Proxy::(Proxy ((Cmp x (k :-> v)) == LT)))
136+ (Ext k' v' (filterV f k v xs)) (filterV f k v xs)
188137
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)
138+instance (Conder (((Cmp x (k :-> v)) == GT) || ((Cmp x (k :-> v)) == EQ)), FilterV FMax k v xs) => FilterV FMax k v (x ': xs) where
139+ filterV f@Proxy k v (Ext k' v' xs) = cond (Proxy::(Proxy (((Cmp x (k :-> v)) == GT) || ((Cmp x (k :-> v)) == EQ))))
140+ (Ext k' v' (filterV f k v xs)) (filterV f k v xs)
196141
197142class Combinable t t' where
198143 combine :: t -> t' -> Combine t t'
@@ -206,14 +151,13 @@ instance Nubable '[] where
206151instance Nubable '[e] where
207152 nub (Ext k v Empty) = Ext k v Empty
208153
209−instance {-# OVERLAPPABLE #-}
154+instance {-# OVERLAPABLE #-}
210155 (Nub (e ': f ': s) ~ (e ': Nub (f ': s)),
211156 Nubable (f ': s)) => Nubable (e ': f ': s) where
212157 nub (Ext k v (Ext k' v' s)) = Ext k v (nub (Ext k' v' s))
213158
214159instance {-# OVERLAPS #-}
215− (Combinable v v', Nubable ((k :-> Combine v v') ': s))
216− => Nubable ((k :-> v) ': (k :-> v') ': s) where
160+ (Combinable v v', Nubable ((k :-> Combine v v') ': s)) => Nubable ((k :-> v) ': (k :-> v') ': s) where
217161 nub (Ext k v (Ext k' v' s)) = nub (Ext k (combine v v') s)
218162
219163