2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1996
4 \section[Bags]{@Bag@: an unordered collection with duplicates}
10 emptyBag, unitBag, unionBags, unionManyBags,
13 filterBag, partitionBag, concatBag, foldBag, foldrBag,
14 isEmptyBag, consBag, snocBag,
18 #include "HsVersions.h"
21 import List ( partition )
29 | TwoBags (Bag a) (Bag a) -- The ADT guarantees that at least
30 -- one branch is non-empty
31 | ListBag [a] -- The list is non-empty
32 | ListOfBags [Bag a] -- The list is non-empty
37 elemBag :: Eq a => a -> Bag a -> Bool
39 elemBag x EmptyBag = False
40 elemBag x (UnitBag y) = x==y
41 elemBag x (TwoBags b1 b2) = x `elemBag` b1 || x `elemBag` b2
42 elemBag x (ListBag ys) = any (x ==) ys
43 elemBag x (ListOfBags bs) = any (x `elemBag`) bs
45 unionManyBags [] = EmptyBag
46 unionManyBags xs = ListOfBags xs
48 -- This one is a bit stricter! The bag will get completely evaluated.
50 unionBags EmptyBag b = b
51 unionBags b EmptyBag = b
52 unionBags b1 b2 = TwoBags b1 b2
54 consBag :: a -> Bag a -> Bag a
55 snocBag :: Bag a -> a -> Bag a
57 consBag elt bag = (unitBag elt) `unionBags` bag
58 snocBag bag elt = bag `unionBags` (unitBag elt)
60 isEmptyBag EmptyBag = True
61 isEmptyBag (UnitBag x) = 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 pred 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 pred 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 t u 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 t u 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
123 foldrBag :: (a -> r -> r) -> r
127 foldrBag k z EmptyBag = z
128 foldrBag k z (UnitBag x) = k x z
129 foldrBag k z (TwoBags b1 b2) = foldrBag k (foldrBag k z b2) b1
130 foldrBag k z (ListBag xs) = foldr k z xs
131 foldrBag k z (ListOfBags bs) = foldr (\b r -> foldrBag k r b) z bs
134 mapBag :: (a -> b) -> Bag a -> Bag b
135 mapBag f EmptyBag = EmptyBag
136 mapBag f (UnitBag x) = UnitBag (f x)
137 mapBag f (TwoBags b1 b2) = TwoBags (mapBag f b1) (mapBag f b2)
138 mapBag f (ListBag xs) = ListBag (map f xs)
139 mapBag f (ListOfBags bs) = ListOfBags (map (mapBag f) bs)
142 listToBag :: [a] -> Bag a
143 listToBag [] = EmptyBag
144 listToBag vs = ListBag vs
146 bagToList :: Bag a -> [a]
147 bagToList b = foldrBag (:) [] b
151 instance (Outputable a) => Outputable (Bag a) where
152 ppr EmptyBag = ptext SLIT("emptyBag")
153 ppr (UnitBag a) = ppr a
154 ppr (TwoBags b1 b2) = hsep [ppr b1 <> comma, ppr b2]
155 ppr (ListBag as) = interpp'SP as
156 ppr (ListOfBags bs) = brackets (interpp'SP bs)