Portability MPTCs, fundeps provisional Edward Kmett None

Description

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, 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`.

Methods

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

Instances

data Free f a Source

The `Free` `MonadPlus` for a `Functor` `f`.

Formally

A `MonadPlus` `n` is a free `MonadPlus` for `f` if every monadplus homomorphism from `n` to another MonadPlus `m` is equivalent to a natural transformation from `f` to `m`.

We model this internally as if left-distribution holds. Constructors

 Pure a Free (f (Free f a)) Plus [Free f a]

Instances

 MonadTrans Free This is not a true monad transformer. It is only a monad transformer "up to `retract`". Functor f => MonadFree f (Free f) (Functor m, MonadPlus m, MonadReader e m) => MonadReader e (Free m) (Functor m, MonadPlus m, MonadWriter e m) => MonadWriter e (Free m) (Functor m, MonadState s m) => MonadState s (Free m) (Functor m, MonadPlus m, MonadError e m) => MonadError e (Free m) Functor f => Monad (Free f) Functor f => Functor (Free f) Typeable1 f => Typeable1 (Free f) Functor f => MonadPlus (Free f) Functor f => Applicative (Free f) Foldable f => Foldable (Free f) Traversable f => Traversable (Free f) Functor f => Alternative (Free f) Functor f => Apply (Free f) Functor f => Bind (Free f) (Functor m, MonadPlus m, MonadCont m) => MonadCont (Free m) (Eq (f (Free f a)), Eq a) => Eq (Free f a) (Typeable1 f, Typeable a, Data a, Data (f (Free f a))) => Data (Free f a) (Ord (f (Free f a)), Ord a) => Ord (Free f a) (Read (f (Free f a)), Read a) => Read (Free f a) (Show (f (Free f a)), Show a) => Show (Free f a) Functor f => Monoid (Free f a) Functor f => Semigroup (Free f a)

retract :: MonadPlus f => Free f a -> f aSource

`retract` is the left inverse of `lift` and `liftF`

``` `retract` . `lift` = `id`
`retract` . `liftF` = `id`
```

liftF :: (Functor f, MonadFree f m) => f a -> m aSource

A version of lift that can be used with just a Functor for f.

iter :: Functor f => (f a -> a) -> ([a] -> a) -> Free f a -> aSource

Tear down a `Free` `Monad` using iteration.

iterM :: (Monad m, Functor f) => (f (m a) -> m a) -> ([m a] -> m a) -> Free f a -> m aSource

Lift a natural transformation from `f` to `g` into a natural transformation from `FreeT f` to `FreeT g`.