| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Control.Invertible.Monoidal.Free
Description
A vague analog of free monads for invariant monoidals. This can provide a simple basis for things like invertible parsers.
Synopsis
- data Free f a where
- showsFree :: (forall a'. f a' -> ShowS) -> Free f a -> ShowS
- mapFree :: (forall a'. f a' -> m a') -> Free f a -> Free m a
- foldFree :: Monoid b => (forall a'. f a' -> a' -> b) -> Free f a -> a -> b
- produceFree :: Alternative m => (forall a'. f a' -> a' -> b) -> Free f a -> a -> m b
- runFree :: Alternative f => Free f a -> f a
- parseFree :: MonadPlus m => (forall a'. f a' -> b -> m a') -> Free f a -> [b] -> m (a, [b])
- reverseFree :: Free f a -> Free f a
- freeTNF :: Free f a -> Free f a
- freeTDNF :: Free f a -> Free f a
- sortFreeTDNF :: (forall a' b'. f a' -> f b' -> Ordering) -> Free f a -> Free f a
Documentation
Produce a MonoidalAlt out of any type constructor, simply by converting each monoidal operation into a constructor.
Although a version more analogous to a free monad could be defined for instances of Functor and restricted to Monoidal, including the Yoneda transform makes this the more general case.
Constructors
| Void :: Free f Void | |
| Empty :: Free f () | |
| Free :: !(f a) -> Free f a | |
| Join :: Free f a -> Free f b -> Free f (a, b) | |
| Choose :: Free f a -> Free f b -> Free f (Either a b) | |
| Transform :: (a <-> b) -> Free f a -> Free f b |
showsFree :: (forall a'. f a' -> ShowS) -> Free f a -> ShowS Source #
Construct a string representation of a Free structure, given a way to show any f a.
mapFree :: (forall a'. f a' -> m a') -> Free f a -> Free m a Source #
Transform the type constructor within a Free.
produceFree :: Alternative m => (forall a'. f a' -> a' -> b) -> Free f a -> a -> m b Source #
foldFree over Alternative rather than Monoid.
runFree :: Alternative f => Free f a -> f a Source #
Evaluate a Free into an underlying Alternative, by evaluating >|< with <|>.
parseFree :: MonadPlus m => (forall a'. f a' -> b -> m a') -> Free f a -> [b] -> m (a, [b]) Source #
Given a way to convert b elements into any f a, use a Free to parse a list of b elements into a value.
This just uses unconsState with runFree, and is the inverse of produceFree, provided the given conversions are themselves inverses.
reverseFree :: Free f a -> Free f a Source #
freeTDNF :: Free f a -> Free f a Source #
Convert a Free to Transform Disjunctive Normal Form: reorder the terms so thet at most one Transform is on the outside, followed by Choose terms, which are above all Join terms', with Empty and Free as leaves.
Since each Join above a Choose creates a duplicate Join term, the complexity and result size can be exponential (just as with boolean logic DNF).