Bag: an unordered collection with duplicates
\begin{code}
-{-# OPTIONS -w #-}
--- The above warning supression flag is a temporary kludge.
--- While working on this module you are encouraged to remove it and fix
--- any warnings in the module. See
--- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
--- for details
-
module Bag (
- Bag, -- abstract type
-
- emptyBag, unitBag, unionBags, unionManyBags,
- mapBag,
- elemBag,
- filterBag, partitionBag, concatBag, foldBag, foldrBag, foldlBag,
- isEmptyBag, isSingletonBag, consBag, snocBag, anyBag,
- listToBag, bagToList,
- mapBagM, mapAndUnzipBagM
+ Bag, -- abstract type
+
+ emptyBag, unitBag, unionBags, unionManyBags,
+ mapBag,
+ elemBag,
+ filterBag, partitionBag, concatBag, foldBag, foldrBag, foldlBag,
+ isEmptyBag, isSingletonBag, consBag, snocBag, anyBag,
+ listToBag, bagToList,
+ mapBagM, mapAndUnzipBagM
) where
-#include "HsVersions.h"
-
import Outputable
-import Util ( isSingleton )
+import Util ( isSingleton )
-import Data.List ( partition )
+import Data.List ( partition )
\end{code}
\begin{code}
data Bag a
= EmptyBag
- | UnitBag a
- | TwoBags (Bag a) (Bag a) -- INVARIANT: neither branch is empty
- | ListBag [a] -- INVARIANT: the list is non-empty
+ | UnitBag a
+ | TwoBags (Bag a) (Bag a) -- INVARIANT: neither branch is empty
+ | ListBag [a] -- INVARIANT: the list is non-empty
+emptyBag :: Bag a
emptyBag = EmptyBag
+
+unitBag :: a -> Bag a
unitBag = UnitBag
elemBag :: Eq a => a -> Bag a -> Bool
-
-elemBag x EmptyBag = False
-elemBag x (UnitBag y) = x==y
+elemBag _ EmptyBag = False
+elemBag x (UnitBag y) = x == y
elemBag x (TwoBags b1 b2) = x `elemBag` b1 || x `elemBag` b2
elemBag x (ListBag ys) = any (x ==) ys
consBag elt bag = (unitBag elt) `unionBags` bag
snocBag bag elt = bag `unionBags` (unitBag elt)
+isEmptyBag :: Bag a -> Bool
isEmptyBag EmptyBag = True
-isEmptyBag other = False -- NB invariants
+isEmptyBag _ = False -- NB invariants
isSingletonBag :: Bag a -> Bool
-isSingletonBag EmptyBag = False
-isSingletonBag (UnitBag x) = True
-isSingletonBag (TwoBags b1 b2) = False -- Neither is empty
-isSingletonBag (ListBag xs) = isSingleton xs
+isSingletonBag EmptyBag = False
+isSingletonBag (UnitBag _) = True
+isSingletonBag (TwoBags _ _) = False -- Neither is empty
+isSingletonBag (ListBag xs) = isSingleton xs
filterBag :: (a -> Bool) -> Bag a -> Bag a
-filterBag pred EmptyBag = EmptyBag
+filterBag _ EmptyBag = EmptyBag
filterBag pred b@(UnitBag val) = if pred val then b else EmptyBag
filterBag pred (TwoBags b1 b2) = sat1 `unionBags` sat2
- where
- sat1 = filterBag pred b1
- sat2 = filterBag pred b2
+ where sat1 = filterBag pred b1
+ sat2 = filterBag pred b2
filterBag pred (ListBag vs) = listToBag (filter pred vs)
anyBag :: (a -> Bool) -> Bag a -> Bool
-anyBag p EmptyBag = False
+anyBag _ EmptyBag = False
anyBag p (UnitBag v) = p v
anyBag p (TwoBags b1 b2) = anyBag p b1 || anyBag p b2
anyBag p (ListBag xs) = any p xs
concatBag :: Bag (Bag a) -> Bag a
-concatBag EmptyBag = EmptyBag
-concatBag (UnitBag b) = b
-concatBag (TwoBags b1 b2) = concatBag b1 `unionBags` concatBag b2
-concatBag (ListBag bs) = unionManyBags bs
+concatBag EmptyBag = EmptyBag
+concatBag (UnitBag b) = b
+concatBag (TwoBags b1 b2) = concatBag b1 `unionBags` concatBag b2
+concatBag (ListBag bs) = unionManyBags bs
partitionBag :: (a -> Bool) -> Bag a -> (Bag a {- Satisfy predictate -},
- Bag a {- Don't -})
-partitionBag pred EmptyBag = (EmptyBag, EmptyBag)
-partitionBag pred b@(UnitBag val) = if pred val then (b, EmptyBag) else (EmptyBag, b)
-partitionBag pred (TwoBags b1 b2) = (sat1 `unionBags` sat2, fail1 `unionBags` fail2)
- where
- (sat1,fail1) = partitionBag pred b1
- (sat2,fail2) = partitionBag pred b2
-partitionBag pred (ListBag vs) = (listToBag sats, listToBag fails)
- where
- (sats,fails) = partition pred vs
-
-
-foldBag :: (r -> r -> r) -- Replace TwoBags with this; should be associative
- -> (a -> r) -- Replace UnitBag with this
- -> r -- Replace EmptyBag with this
- -> Bag a
- -> r
+ Bag a {- Don't -})
+partitionBag _ EmptyBag = (EmptyBag, EmptyBag)
+partitionBag pred b@(UnitBag val)
+ = if pred val then (b, EmptyBag) else (EmptyBag, b)
+partitionBag pred (TwoBags b1 b2)
+ = (sat1 `unionBags` sat2, fail1 `unionBags` fail2)
+ where (sat1, fail1) = partitionBag pred b1
+ (sat2, fail2) = partitionBag pred b2
+partitionBag pred (ListBag vs) = (listToBag sats, listToBag fails)
+ where (sats, fails) = partition pred vs
+
+
+foldBag :: (r -> r -> r) -- Replace TwoBags with this; should be associative
+ -> (a -> r) -- Replace UnitBag with this
+ -> r -- Replace EmptyBag with this
+ -> Bag a
+ -> r
{- Standard definition
foldBag t u e EmptyBag = e
-}
-- More tail-recursive definition, exploiting associativity of "t"
-foldBag t u e EmptyBag = e
+foldBag _ _ e EmptyBag = e
foldBag t u e (UnitBag x) = u x `t` e
foldBag t u e (TwoBags b1 b2) = foldBag t u (foldBag t u e b2) b1
foldBag t u e (ListBag xs) = foldr (t.u) e xs
foldrBag :: (a -> r -> r) -> r
- -> Bag a
- -> r
+ -> Bag a
+ -> r
-foldrBag k z EmptyBag = z
+foldrBag _ z EmptyBag = z
foldrBag k z (UnitBag x) = k x z
foldrBag k z (TwoBags b1 b2) = foldrBag k (foldrBag k z b2) b1
foldrBag k z (ListBag xs) = foldr k z xs
foldlBag :: (r -> a -> r) -> r
- -> Bag a
- -> r
+ -> Bag a
+ -> r
-foldlBag k z EmptyBag = z
+foldlBag _ z EmptyBag = z
foldlBag k z (UnitBag x) = k z x
foldlBag k z (TwoBags b1 b2) = foldlBag k (foldlBag k z b1) b2
foldlBag k z (ListBag xs) = foldl k z xs
mapBag :: (a -> b) -> Bag a -> Bag b
-mapBag f EmptyBag = EmptyBag
+mapBag _ EmptyBag = EmptyBag
mapBag f (UnitBag x) = UnitBag (f x)
-mapBag f (TwoBags b1 b2) = TwoBags (mapBag f b1) (mapBag f b2)
+mapBag f (TwoBags b1 b2) = TwoBags (mapBag f b1) (mapBag f b2)
mapBag f (ListBag xs) = ListBag (map f xs)
mapBagM :: Monad m => (a -> m b) -> Bag a -> m (Bag b)
-mapBagM f EmptyBag = return EmptyBag
-mapBagM f (UnitBag x) = do { r <- f x; return (UnitBag r) }
-mapBagM f (TwoBags b1 b2) = do { r1 <- mapBagM f b1; r2 <- mapBagM f b2; return (TwoBags r1 r2) }
-mapBagM f (ListBag xs) = do { rs <- mapM f xs; return (ListBag rs) }
+mapBagM _ EmptyBag = return EmptyBag
+mapBagM f (UnitBag x) = do r <- f x
+ return (UnitBag r)
+mapBagM f (TwoBags b1 b2) = do r1 <- mapBagM f b1
+ r2 <- mapBagM f b2
+ return (TwoBags r1 r2)
+mapBagM f (ListBag xs) = do rs <- mapM f xs
+ return (ListBag rs)
mapAndUnzipBagM :: Monad m => (a -> m (b,c)) -> Bag a -> m (Bag b, Bag c)
-mapAndUnzipBagM f EmptyBag = return (EmptyBag, EmptyBag)
-mapAndUnzipBagM f (UnitBag x) = do { (r,s) <- f x; return (UnitBag r, UnitBag s) }
-mapAndUnzipBagM f (TwoBags b1 b2) = do { (r1,s1) <- mapAndUnzipBagM f b1
- ; (r2,s2) <- mapAndUnzipBagM f b2
- ; return (TwoBags r1 r2, TwoBags s1 s2) }
-mapAndUnzipBagM f (ListBag xs) = do { ts <- mapM f xs
- ; let (rs,ss) = unzip ts
- ; return (ListBag rs, ListBag ss) }
+mapAndUnzipBagM _ EmptyBag = return (EmptyBag, EmptyBag)
+mapAndUnzipBagM f (UnitBag x) = do (r,s) <- f x
+ return (UnitBag r, UnitBag s)
+mapAndUnzipBagM f (TwoBags b1 b2) = do (r1,s1) <- mapAndUnzipBagM f b1
+ (r2,s2) <- mapAndUnzipBagM f b2
+ return (TwoBags r1 r2, TwoBags s1 s2)
+mapAndUnzipBagM f (ListBag xs) = do ts <- mapM f xs
+ let (rs,ss) = unzip ts
+ return (ListBag rs, ListBag ss)
listToBag :: [a] -> Bag a
listToBag [] = EmptyBag
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