2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
4 \section[Bags]{@Bag@: an unordered collection with duplicates}
10 emptyBag, unitBag, unionBags, unionManyBags,
13 filterBag, partitionBag, concatBag, foldBag, foldrBag, foldlBag,
14 isEmptyBag, isSingletonBag, consBag, snocBag,
16 mapBagM, mapAndUnzipBagM
19 #include "HsVersions.h"
22 import Util ( isSingleton )
23 import List ( partition )
31 | TwoBags (Bag a) (Bag a) -- INVARIANT: neither branch is empty
32 | ListBag [a] -- INVARIANT: 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
44 unionManyBags :: [Bag a] -> Bag a
45 unionManyBags xs = foldr unionBags EmptyBag xs
47 -- This one is a bit stricter! The bag will get completely evaluated.
49 unionBags :: Bag a -> Bag a -> Bag a
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 other = False -- NB invariants
63 isSingletonBag :: Bag a -> Bool
64 isSingletonBag EmptyBag = False
65 isSingletonBag (UnitBag x) = True
66 isSingletonBag (TwoBags b1 b2) = False -- Neither is empty
67 isSingletonBag (ListBag xs) = isSingleton xs
69 filterBag :: (a -> Bool) -> Bag a -> Bag a
70 filterBag pred EmptyBag = EmptyBag
71 filterBag pred b@(UnitBag val) = if pred val then b else EmptyBag
72 filterBag pred (TwoBags b1 b2) = sat1 `unionBags` sat2
74 sat1 = filterBag pred b1
75 sat2 = filterBag pred b2
76 filterBag pred (ListBag vs) = listToBag (filter pred vs)
78 concatBag :: Bag (Bag a) -> Bag a
79 concatBag EmptyBag = EmptyBag
80 concatBag (UnitBag b) = b
81 concatBag (TwoBags b1 b2) = concatBag b1 `unionBags` concatBag b2
82 concatBag (ListBag bs) = unionManyBags bs
84 partitionBag :: (a -> Bool) -> Bag a -> (Bag a {- Satisfy predictate -},
86 partitionBag pred EmptyBag = (EmptyBag, EmptyBag)
87 partitionBag pred b@(UnitBag val) = if pred val then (b, EmptyBag) else (EmptyBag, b)
88 partitionBag pred (TwoBags b1 b2) = (sat1 `unionBags` sat2, fail1 `unionBags` fail2)
90 (sat1,fail1) = partitionBag pred b1
91 (sat2,fail2) = partitionBag pred b2
92 partitionBag pred (ListBag vs) = (listToBag sats, listToBag fails)
94 (sats,fails) = partition pred vs
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
110 -- More tail-recursive definition, exploiting associativity of "t"
111 foldBag t u e EmptyBag = e
112 foldBag t u e (UnitBag x) = u x `t` e
113 foldBag t u e (TwoBags b1 b2) = foldBag t u (foldBag t u e b2) b1
114 foldBag t u e (ListBag xs) = foldr (t.u) e xs
116 foldrBag :: (a -> r -> r) -> r
120 foldrBag k z EmptyBag = z
121 foldrBag k z (UnitBag x) = k x z
122 foldrBag k z (TwoBags b1 b2) = foldrBag k (foldrBag k z b2) b1
123 foldrBag k z (ListBag xs) = foldr k z xs
125 foldlBag :: (r -> a -> r) -> r
129 foldlBag k z EmptyBag = z
130 foldlBag k z (UnitBag x) = k z x
131 foldlBag k z (TwoBags b1 b2) = foldlBag k (foldlBag k z b1) b2
132 foldlBag k z (ListBag xs) = foldl k z xs
135 mapBag :: (a -> b) -> Bag a -> Bag b
136 mapBag f EmptyBag = EmptyBag
137 mapBag f (UnitBag x) = UnitBag (f x)
138 mapBag f (TwoBags b1 b2) = TwoBags (mapBag f b1) (mapBag f b2)
139 mapBag f (ListBag xs) = ListBag (map f xs)
141 mapBagM :: Monad m => (a -> m b) -> Bag a -> m (Bag b)
142 mapBagM f EmptyBag = return EmptyBag
143 mapBagM f (UnitBag x) = do { r <- f x; return (UnitBag r) }
144 mapBagM f (TwoBags b1 b2) = do { r1 <- mapBagM f b1; r2 <- mapBagM f b2; return (TwoBags r1 r2) }
145 mapBagM f (ListBag xs) = do { rs <- mapM f xs; return (ListBag rs) }
147 mapAndUnzipBagM :: Monad m => (a -> m (b,c)) -> Bag a -> m (Bag b, Bag c)
148 mapAndUnzipBagM f EmptyBag = return (EmptyBag, EmptyBag)
149 mapAndUnzipBagM f (UnitBag x) = do { (r,s) <- f x; return (UnitBag r, UnitBag s) }
150 mapAndUnzipBagM f (TwoBags b1 b2) = do { (r1,s1) <- mapAndUnzipBagM f b1
151 ; (r2,s2) <- mapAndUnzipBagM f b2
152 ; return (TwoBags r1 r2, TwoBags s1 s2) }
153 mapAndUnzipBagM f (ListBag xs) = do { ts <- mapM f xs
154 ; let (rs,ss) = unzip ts
155 ; return (ListBag rs, ListBag ss) }
157 listToBag :: [a] -> Bag a
158 listToBag [] = EmptyBag
159 listToBag vs = ListBag vs
161 bagToList :: Bag a -> [a]
162 bagToList b = foldrBag (:) [] b
166 instance (Outputable a) => Outputable (Bag a) where
167 ppr EmptyBag = ptext SLIT("emptyBag")
168 ppr (UnitBag a) = ppr a
169 ppr (TwoBags b1 b2) = hsep [ppr b1 <> comma, ppr b2]
170 ppr (ListBag as) = interpp'SP as