2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1996
4 \section[Bags]{@Bag@: an unordered collection with duplicates}
10 emptyBag, unitBag, unionBags, unionManyBags,
14 filterBag, partitionBag, concatBag, foldBag,
15 isEmptyBag, consBag, snocBag,
19 import List(partition)
24 | TwoBags (Bag a) (Bag a) -- The ADT guarantees that at least
25 -- one branch is non-empty
26 | ListBag [a] -- The list is non-empty
27 | ListOfBags [Bag a] -- The list is non-empty
32 elemBag :: Eq a => a -> Bag a -> Bool
34 elemBag x EmptyBag = False
35 elemBag x (UnitBag y) = x==y
36 elemBag x (TwoBags b1 b2) = x `elemBag` b1 || x `elemBag` b2
37 elemBag x (ListBag ys) = any (x ==) ys
38 elemBag x (ListOfBags bs) = any (x `elemBag`) bs
40 unionManyBags [] = EmptyBag
41 unionManyBags xs = ListOfBags xs
43 -- This one is a bit stricter! The bag will get completely evaluated.
45 unionBags EmptyBag b = b
46 unionBags b EmptyBag = b
47 unionBags b1 b2 = TwoBags b1 b2
49 consBag :: a -> Bag a -> Bag a
50 snocBag :: Bag a -> a -> Bag a
52 consBag elt bag = (unitBag elt) `unionBags` bag
53 snocBag bag elt = bag `unionBags` (unitBag elt)
55 isEmptyBag EmptyBag = True
56 isEmptyBag (UnitBag x) = False
57 isEmptyBag (TwoBags b1 b2) = isEmptyBag b1 && isEmptyBag b2 -- Paranoid, but safe
58 isEmptyBag (ListBag xs) = null xs -- Paranoid, but safe
59 isEmptyBag (ListOfBags bs) = all isEmptyBag bs
61 filterBag :: (a -> Bool) -> Bag a -> Bag a
62 filterBag pred EmptyBag = EmptyBag
63 filterBag pred b@(UnitBag val) = if pred val then b else EmptyBag
64 filterBag pred (TwoBags b1 b2) = sat1 `unionBags` sat2
66 sat1 = filterBag pred b1
67 sat2 = filterBag pred b2
68 filterBag pred (ListBag vs) = listToBag (filter pred vs)
69 filterBag pred (ListOfBags bs) = ListOfBags sats
71 sats = [filterBag pred b | b <- bs]
73 concatBag :: Bag (Bag a) -> Bag a
75 concatBag EmptyBag = EmptyBag
76 concatBag (UnitBag b) = b
77 concatBag (TwoBags b1 b2) = concatBag b1 `TwoBags` concatBag b2
78 concatBag (ListBag bs) = ListOfBags bs
79 concatBag (ListOfBags bbs) = ListOfBags (map concatBag bbs)
81 partitionBag :: (a -> Bool) -> Bag a -> (Bag a {- Satisfy predictate -},
83 partitionBag pred EmptyBag = (EmptyBag, EmptyBag)
84 partitionBag pred b@(UnitBag val) = if pred val then (b, EmptyBag) else (EmptyBag, b)
85 partitionBag pred (TwoBags b1 b2) = (sat1 `unionBags` sat2, fail1 `unionBags` fail2)
87 (sat1,fail1) = partitionBag pred b1
88 (sat2,fail2) = partitionBag pred b2
89 partitionBag pred (ListBag vs) = (listToBag sats, listToBag fails)
91 (sats,fails) = partition pred vs
92 partitionBag pred (ListOfBags bs) = (ListOfBags sats, ListOfBags fails)
94 (sats, fails) = unzip [partitionBag pred b | b <- bs]
97 foldBag :: (r -> r -> r) -- Replace TwoBags with this; should be associative
98 -> (a -> r) -- Replace UnitBag with this
99 -> r -- Replace EmptyBag with this
103 {- Standard definition
104 foldBag t u e EmptyBag = e
105 foldBag t u e (UnitBag x) = u x
106 foldBag t u e (TwoBags b1 b2) = (foldBag t u e b1) `t` (foldBag t u e b2)
107 foldBag t u e (ListBag xs) = foldr (t.u) e xs
108 foldBag t u e (ListOfBags bs) = foldr (\b r -> foldBag e u t b `t` r) e bs
111 -- More tail-recursive definition, exploiting associativity of "t"
112 foldBag t u e EmptyBag = e
113 foldBag t u e (UnitBag x) = u x `t` e
114 foldBag t u e (TwoBags b1 b2) = foldBag t u (foldBag t u e b2) b1
115 foldBag t u e (ListBag xs) = foldr (t.u) e xs
116 foldBag t u e (ListOfBags bs) = foldr (\b r -> foldBag t u r b) e bs
119 mapBag :: (a -> b) -> Bag a -> Bag b
120 mapBag f EmptyBag = EmptyBag
121 mapBag f (UnitBag x) = UnitBag (f x)
122 mapBag f (TwoBags b1 b2) = TwoBags (mapBag f b1) (mapBag f b2)
123 mapBag f (ListBag xs) = ListBag (map f xs)
124 mapBag f (ListOfBags bs) = ListOfBags (map (mapBag f) bs)
127 listToBag :: [a] -> Bag a
128 listToBag [] = EmptyBag
129 listToBag vs = ListBag vs
131 bagToList :: Bag a -> [a]
132 bagToList EmptyBag = []
133 bagToList (ListBag vs) = vs
134 bagToList b = bagToList_append b []
136 -- (bagToList_append b xs) flattens b and puts xs on the end.
138 bagToList_append EmptyBag xs = xs
139 bagToList_append (UnitBag x) xs = x:xs
140 bagToList_append (TwoBags b1 b2) xs = bagToList_append b1 (bagToList_append b2 xs)
141 bagToList_append (ListBag xx) xs = xx++xs
142 bagToList_append (ListOfBags bs) xs = foldr bagToList_append xs bs