Safe Haskell	None
Language	Haskell2010

Data.Semiring.Free

Description

The Free semiring.

Synopsis

Documentation

newtype Free a Source #

The free semiring. Adapted from PureScript's version, available here. Only a valid semiring if treated as a multiset, as in:

>>> Free [[1],[0]] == Free [[0],[1]]
True

Constructors

Free
Fields getFree :: [[a]]

Instances

Functor Free Source #
Methods fmap :: (a -> b) -> Free a -> Free b # (<$) :: a -> Free b -> Free a #
Applicative Free Source #
Methods pure :: a -> Free a # (<>) :: Free (a -> b) -> Free a -> Free b # (>) :: Free a -> Free b -> Free b # (<*) :: Free a -> Free b -> Free a #
Foldable Free Source #
Methods fold :: Monoid m => Free m -> m # foldMap :: Monoid m => (a -> m) -> Free a -> m # foldr :: (a -> b -> b) -> b -> Free a -> b # foldr' :: (a -> b -> b) -> b -> Free a -> b # foldl :: (b -> a -> b) -> b -> Free a -> b # foldl' :: (b -> a -> b) -> b -> Free a -> b # foldr1 :: (a -> a -> a) -> Free a -> a # foldl1 :: (a -> a -> a) -> Free a -> a # toList :: Free a -> [a] # null :: Free a -> Bool # length :: Free a -> Int # elem :: Eq a => a -> Free a -> Bool # maximum :: Ord a => Free a -> a # minimum :: Ord a => Free a -> a # sum :: Num a => Free a -> a # product :: Num a => Free a -> a #
Traversable Free Source #
Methods traverse :: Applicative f => (a -> f b) -> Free a -> f (Free b) # sequenceA :: Applicative f => Free (f a) -> f (Free a) # mapM :: Monad m => (a -> m b) -> Free a -> m (Free b) # sequence :: Monad m => Free (m a) -> m (Free a) #
Ord a => Eq (Free a) Source #	Extremely slow. For testing purposes.
Methods (==) :: Free a -> Free a -> Bool # (/=) :: Free a -> Free a -> Bool #
Ord a => Ord (Free a) Source #
Methods compare :: Free a -> Free a -> Ordering # (<) :: Free a -> Free a -> Bool # (<=) :: Free a -> Free a -> Bool # (>) :: Free a -> Free a -> Bool # (>=) :: Free a -> Free a -> Bool # max :: Free a -> Free a -> Free a # min :: Free a -> Free a -> Free a #
Read a => Read (Free a) Source #
Methods readsPrec :: Int -> ReadS (Free a) # readList :: ReadS [Free a] # readPrec :: ReadPrec (Free a) # readListPrec :: ReadPrec [Free a] #
Show a => Show (Free a) Source #
Methods showsPrec :: Int -> Free a -> ShowS # show :: Free a -> String # showList :: [Free a] -> ShowS #
Monoid (Free a) Source #
Methods mempty :: Free a # mappend :: Free a -> Free a -> Free a # mconcat :: [Free a] -> Free a #
Semiring (Free a) Source #
Methods zero :: Free a Source # one :: Free a Source # (<.>) :: Free a -> Free a -> Free a Source # (<+>) :: Free a -> Free a -> Free a Source #

liftFree :: Semiring s => (a -> s) -> Free a -> s Source #

Run a Free.

unFree :: Semiring s => Free s -> s Source #

Run a Free, interpreting it in the underlying semiring.