workflow-types-0.0.1: Automate keyboard\/mouse\/clipboard\/application interaction.

Workflow.Reexports

Description

Synopsis

# Documentation

A class for monads in which exceptions may be thrown.

Instances should obey the following law:

throwM e >> x = throwM e

In other words, throwing an exception short-circuits the rest of the monadic computation.

Minimal complete definition

throwM

Instances

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

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.

Instances