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
35 elemBag :: Eq a => a -> Bag a -> Bool
36 elemBag _ EmptyBag = False
37 elemBag x (UnitBag y) = x==y
38 elemBag x (TwoBags b1 b2) = x `elemBag` b1 || x `elemBag` b2
39 elemBag x (ListBag ys) = any (x ==) ys
40 elemBag x (ListOfBags bs) = any (x `elemBag`) bs
42 unionManyBags :: [Bag a] -> Bag a
43 unionManyBags [] = EmptyBag
44 unionManyBags xs = ListOfBags xs
46 -- This one is a bit stricter! The bag will get completely evaluated.
48 unionBags :: Bag a -> Bag a -> Bag a
49 unionBags EmptyBag b = b
50 unionBags b EmptyBag = b
51 unionBags b1 b2 = TwoBags b1 b2
53 consBag :: a -> Bag a -> Bag a
54 snocBag :: Bag a -> a -> Bag a
56 consBag elt bag = (unitBag elt) `unionBags` bag
57 snocBag bag elt = bag `unionBags` (unitBag elt)
59 isEmptyBag :: Bag a -> Bool
60 isEmptyBag EmptyBag = True
61 isEmptyBag (UnitBag _) = False
62 isEmptyBag (TwoBags b1 b2) = isEmptyBag b1 && isEmptyBag b2 -- Paranoid, but safe
63 isEmptyBag (ListBag xs) = null xs -- Paranoid, but safe
64 isEmptyBag (ListOfBags bs) = all isEmptyBag bs
66 filterBag :: (a -> Bool) -> Bag a -> Bag a
67 filterBag _ EmptyBag = EmptyBag
68 filterBag pred b@(UnitBag val) = if pred val then b else EmptyBag
69 filterBag pred (TwoBags b1 b2) = sat1 `unionBags` sat2
71 sat1 = filterBag pred b1
72 sat2 = filterBag pred b2
73 filterBag pred (ListBag vs) = listToBag (filter pred vs)
74 filterBag pred (ListOfBags bs) = ListOfBags sats
76 sats = [filterBag pred b | b <- bs]
78 concatBag :: Bag (Bag a) -> Bag a
80 concatBag EmptyBag = EmptyBag
81 concatBag (UnitBag b) = b
82 concatBag (TwoBags b1 b2) = concatBag b1 `TwoBags` concatBag b2
83 concatBag (ListBag bs) = ListOfBags bs
84 concatBag (ListOfBags bbs) = ListOfBags (map concatBag bbs)
86 partitionBag :: (a -> Bool) -> Bag a -> (Bag a {- Satisfy predictate -},
88 partitionBag _ EmptyBag = (EmptyBag, EmptyBag)
89 partitionBag pred b@(UnitBag val) = if pred val then (b, EmptyBag) else (EmptyBag, b)
90 partitionBag pred (TwoBags b1 b2) = (sat1 `unionBags` sat2, fail1 `unionBags` fail2)
92 (sat1,fail1) = partitionBag pred b1
93 (sat2,fail2) = partitionBag pred b2
94 partitionBag pred (ListBag vs) = (listToBag sats, listToBag fails)
96 (sats,fails) = partition pred vs
97 partitionBag pred (ListOfBags bs) = (ListOfBags sats, ListOfBags fails)
99 (sats, fails) = unzip [partitionBag pred b | b <- bs]
102 foldBag :: (r -> r -> r) -- Replace TwoBags with this; should be associative
103 -> (a -> r) -- Replace UnitBag with this
104 -> r -- Replace EmptyBag with this
108 {- Standard definition
109 foldBag _ _ e EmptyBag = e
110 foldBag t u e (UnitBag x) = u x
111 foldBag t u e (TwoBags b1 b2) = (foldBag t u e b1) `t` (foldBag t u e b2)
112 foldBag t u e (ListBag xs) = foldr (t.u) e xs
113 foldBag t u e (ListOfBags bs) = foldr (\b r -> foldBag e u t b `t` r) e bs
116 -- More tail-recursive definition, exploiting associativity of "t"
117 foldBag _ _ e EmptyBag = e
118 foldBag t u e (UnitBag x) = u x `t` e
119 foldBag t u e (TwoBags b1 b2) = foldBag t u (foldBag t u e b2) b1
120 foldBag t u e (ListBag xs) = foldr (t.u) e xs
121 foldBag t u e (ListOfBags bs) = foldr (\b r -> foldBag t u r b) e bs
124 mapBag :: (a -> b) -> Bag a -> Bag b
125 mapBag _ EmptyBag = EmptyBag
126 mapBag f (UnitBag x) = UnitBag (f x)
127 mapBag f (TwoBags b1 b2) = TwoBags (mapBag f b1) (mapBag f b2)
128 mapBag f (ListBag xs) = ListBag (map f xs)
129 mapBag f (ListOfBags bs) = ListOfBags (map (mapBag f) bs)
132 listToBag :: [a] -> Bag a
133 listToBag [] = EmptyBag
134 listToBag vs = ListBag vs
136 bagToList :: Bag a -> [a]
137 bagToList EmptyBag = []
138 bagToList (ListBag vs) = vs
139 bagToList b = bagToList_append b []
141 -- (bagToList_append b xs) flattens b and puts xs on the end.
143 bagToList_append :: Bag a -> [a] -> [a]
144 bagToList_append EmptyBag xs = xs
145 bagToList_append (UnitBag x) xs = x:xs
146 bagToList_append (TwoBags b1 b2) xs = bagToList_append b1 (bagToList_append b2 xs)
147 bagToList_append (ListBag xx) xs = xx++xs
148 bagToList_append (ListOfBags bs) xs = foldr bagToList_append xs bs