Portability MPTCs, fundeps provisional Edward Kmett None

Description

Unlike `Free`, this is a true monad transformer.

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

``` wrap (fmap f x) ≡ wrap (fmap return x) >>= f
```

Instances

data IterF a b Source

Constructors

 Pure a Iter b

Instances

 Typeable2 IterF Bitraversable IterF Bifunctor IterF Bifoldable IterF Functor (IterF a) Foldable (IterF a) Traversable (IterF a) (Eq a, Eq b) => Eq (IterF a b) (Ord a, Ord b) => Ord (IterF a b) (Read a, Read b) => Read (IterF a b) (Show a, Show b) => Show (IterF a b)

data IterT m a Source

The monad supporting iteration based over a base monad `m`.

``` `IterT` ~ `FreeT` `Identity`
```

Constructors

 IterT FieldsrunIterT :: m (IterF a (IterT m a))

Instances

 MonadTrans IterT This is not a true monad transformer. It is only a monad transformer "up to `retract`". Monad m => MonadFree Identity (IterT m) (Functor m, MonadState s m) => MonadState s (IterT m) (Functor m, MonadReader e m) => MonadReader e (IterT m) Monad m => Monad (IterT m) Monad m => Functor (IterT m) Typeable1 m => Typeable1 (IterT m) MonadFix m => MonadFix (IterT m) MonadPlus m => MonadPlus (IterT m) Monad m => Applicative (IterT m) Foldable m => Foldable (IterT m) (Monad m, Traversable m) => Traversable (IterT m) MonadPlus m => Alternative (IterT m) (Monad m, Traversable1 m) => Traversable1 (IterT m) Foldable1 m => Foldable1 (IterT m) Monad m => Apply (IterT m) Monad m => Bind (IterT m) Eq (m (IterF a (IterT m a))) => Eq (IterT m a) (Typeable1 m, Typeable a, Data (m (IterF a (IterT m a))), Data a) => Data (IterT m a) Ord (m (IterF a (IterT m a))) => Ord (IterT m a) Read (m (IterF a (IterT m a))) => Read (IterT m a) Show (m (IterF a (IterT m a))) => Show (IterT m a)

delay :: (Monad f, MonadFree f m) => m a -> m aSource

retract :: Monad m => IterT m a -> m aSource

`retract` is the left inverse of `lift`

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

iter :: Monad m => (m a -> a) -> IterT m a -> aSource

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

hoistIterT :: Monad n => (forall a. m a -> n a) -> IterT m b -> IterT n bSource

Lift a monad homomorphism from `m` to `n` into a Monad homomorphism from `IterT m` to `IterT n`.