Copyright | (C) 2008-2015 Edward Kmett |
---|---|
License | BSD-style (see the file LICENSE) |
Maintainer | Edward Kmett <ekmett@gmail.com> |
Stability | experimental |
Portability | non-portable (fundeps, MPTCs) |
Safe Haskell | Safe |
Language | Haskell2010 |
Monads for free.
Documentation
class Monad m => MonadFree f m | m -> f where #
Monads provide substitution (fmap
) and renormalization (join
):
m>>=
f =join
(fmap
f m)
A free Monad
is one that does no work during the normalization step beyond simply grafting the two monadic values together.
[]
is not a free Monad
(in this sense) because
smashes the lists flat.join
[[a]]
On the other hand, consider:
data Tree a = Bin (Tree a) (Tree a) | Tip a
instanceMonad
Tree wherereturn
= Tip Tip a>>=
f = f a Bin l r>>=
f = Bin (l>>=
f) (r>>=
f)
This Monad
is the free Monad
of Pair:
data Pair a = Pair a a
And we could make an instance of MonadFree
for it directly:
instanceMonadFree
Pair Tree wherewrap
(Pair l r) = Bin l r
Or we could choose to program with
instead of Free
PairTree
and thereby avoid having to define our own Monad
instance.
Moreover, Control.Monad.Free.Church provides a MonadFree
instance that can improve the asymptotic complexity of code that
constructs free monads by effectively reassociating the use of
(>>=
). You may also want to take a look at the kan-extensions
package (http://hackage.haskell.org/package/kan-extensions).
See Free
for a more formal definition of the free Monad
for a Functor
.
Add a layer.
wrap (fmap f x) ≡ wrap (fmap return x) >>= f
wrap :: (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a #
Add a layer.
wrap (fmap f x) ≡ wrap (fmap return x) >>= f
(Functor f, MonadFree f m) => MonadFree f (ListT m) # | |
(Functor f, MonadFree f m) => MonadFree f (MaybeT m) # | |
Functor f => MonadFree f (Free f) # | |
Functor f => MonadFree f (F f) # | |
Monad m => MonadFree Identity (IterT m) # | |
(Functor f, MonadFree f m) => MonadFree f (ExceptT e m) # | |
(Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) # | |
(Functor f, MonadFree f m) => MonadFree f (IdentityT * m) # | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) # | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) # | |
(Functor f, MonadFree f m) => MonadFree f (StateT s m) # | |
(Functor f, MonadFree f m) => MonadFree f (StateT s m) # | |
(Functor f, Monad m) => MonadFree f (FreeT f m) # | |
MonadFree f (FT f m) # | |
(Functor f, MonadFree f m) => MonadFree f (ContT * r m) # | |
(Functor f, MonadFree f m) => MonadFree f (ReaderT * e m) # | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) # | |
(Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) # | |