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The `Bag' type

A bag is an unordered collection of elements which may contain duplicates. To use, `import Bag'. 
data Bag elt    -- abstract

emptyBag        :: Bag elt
unitBag         :: elt -> Bag elt

consBag         :: elt       -> Bag elt -> Bag elt
snocBag         :: Bag elt   -> elt     -> Bag elt

unionBags       :: Bag elt   -> Bag elt -> Bag elt
unionManyBags   :: [Bag elt] -> Bag elt

isEmptyBag      :: Bag elt   -> Bool
elemBag         :: Eq elt => elt -> Bag elt -> Bool

filterBag       :: (elt -> Bool) -> Bag elt -> Bag elt
partitionBag    :: (elt -> Bool) -> Bag elt-> (Bag elt, Bag elt)
        -- returns the elements that do/don't satisfy the predicate

concatBag       :: Bag (Bag a) -> Bag a 
foldBag         :: (r -> r -> r) -> (a -> r) -> r -> Bag a -> r
mapBag          :: (a -> b) -> Bag a -> Bag b

listToBag       :: [elt] -> Bag elt
bagToList       :: Bag elt -> [elt]
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