free-3.3.1: Monads for free

Portability non-portable (fundeps, MPTCs) experimental Edward Kmett Safe-Inferred

Control.Monad.Free.Class

Description

Monads for free.

Synopsis

# Documentation

class Monad m => MonadFree f m | m -> f whereSource

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 `join [[a]]` smashes the lists flat.

On the other hand, consider:

``` data Tree a = Bin (Tree a) (Tree a) | Tip a
```
``` instance `Monad` Tree where
`return` = 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:

``` instance `MonadFree` Pair Tree where
`wrap` (Pair l r) = Bin l r
```

Or we could choose to program with `Free Pair` instead of `Tree` and thereby avoid having to define our own `Monad` instance.

Moreover, the `kan-extensions` package provides `MonadFree` instances that can improve the asymptotic complexity of code that constructors free monads by effectively reassociating the use of (`>>=`).

See `Free` for a more formal definition of the free `Monad` for a `Functor`.

Methods

wrap :: f (m a) -> m aSource

Add a layer.

Instances

 (Monad (ListT m), Functor f, MonadFree f m) => MonadFree f (ListT m) (Monad (IdentityT m), Functor f, MonadFree f m) => MonadFree f (IdentityT m) (Monad (MaybeT m), Functor f, MonadFree f m) => MonadFree f (MaybeT m) (Monad (Free f), Functor f) => MonadFree f (Free f) (Monad (Free f), Functor f) => MonadFree f (Free f) (Monad (F f), Functor f) => MonadFree f (F f) (Monad (ErrorT e m), Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) (Monad (WriterT w m), Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) (Monad (WriterT w m), Functor f, MonadFree f m, Monoid w) => MonadFree f (WriterT w m) (Monad (StateT s m), Functor f, MonadFree f m) => MonadFree f (StateT s m) (Monad (StateT s m), Functor f, MonadFree f m) => MonadFree f (StateT s m) (Monad (ReaderT e m), Functor f, MonadFree f m) => MonadFree f (ReaderT e m) (Monad (FreeT f m), Functor f, Monad m) => MonadFree f (FreeT f m) (Monad (RWST r w s m), Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m) (Monad (RWST r w s m), Functor f, MonadFree f m, Monoid w) => MonadFree f (RWST r w s m)