Portability MPTCs, fundeps provisional Edward Kmett None

Description

Synopsis

# Documentation

data FreeF f a b Source

The base functor for a free monad.

Constructors

 Pure a Free (f b)

Instances

 Typeable1 f => Typeable2 (FreeF f) (Bifunctor (FreeF f), Bifoldable (FreeF f), Traversable f) => Bitraversable (FreeF f) Functor f => Bifunctor (FreeF f) Foldable f => Bifoldable (FreeF f) Functor f => Functor (FreeF f a) Foldable f => Foldable (FreeF f a) (Functor (FreeF f a), Foldable (FreeF f a), Traversable f) => Traversable (FreeF f a) (Eq a, Eq (f b)) => Eq (FreeF f a b) (Typeable (FreeF f a b), Typeable1 f, Typeable a, Typeable b, Data a, Data (f b), Data b) => Data (FreeF f a b) (Eq (FreeF f a b), Ord a, Ord (f b)) => Ord (FreeF f a b) (Read a, Read (f b)) => Read (FreeF f a b) (Show a, Show (f b)) => Show (FreeF f a b)

newtype FreeT f m a Source

The "free monad transformer" for a functor `f`.

Constructors

 FreeT FieldsrunFreeT :: m (FreeF f a (FreeT f m a))

Instances

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

Instances

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

FreeT is a functor from the category of functors to the category of monads.

This provides the mapping.

hoistFreeT :: (Monad m, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n bSource

Lift a monad homomorphism from `m` to `n` into a monad homomorphism from `FreeT f m` to `FreeT f n`

``hoistFreeT` :: (`Monad` m, `Functor` f) => (m ~> n) -> `FreeT` f m ~> `FreeT` f n`

transFreeT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m bSource

Lift a natural transformation from `f` to `g` into a monad homomorphism from `FreeT f m` to `FreeT g n`