Copyright	(c) 2011 diagrams-core team (see LICENSE)
License	BSD-style (see LICENSE)
Maintainer	diagrams-discuss@googlegroups.com
Safe Haskell	Safe
Language	Haskell2010

Data.Monoid.Action

Description

Monoid and semigroup actions.

Synopsis

Documentation

class Action m s where #

Type class for monoid (and semigroup) actions, where monoidal values of type m "act" on values of another type s. Instances are required to satisfy the laws

```
act mempty = id
```
```
act (m1 `mappend` m2) = act m1 . act m2
```

Semigroup instances are required to satisfy the second law but with (<>) instead of mappend. Additionally, if the type s has any algebraic structure, act m should be a homomorphism. For example, if s is also a monoid we should have act m mempty = mempty and act m (s1 `mappend` s2) = (act m s1) `mappend` (act m s2).

By default, act = const id, so for a type M which should have no action on anything, it suffices to write

instance Action M s

with no method implementations.

It is a bit awkward dealing with instances of Action, since it is a multi-parameter type class but we can't add any functional dependencies---the relationship between monoids and the types on which they act is truly many-to-many. In practice, this library has chosen to have instance selection for Action driven by the first type parameter. That is, you should never write an instance of the form Action m SomeType since it will overlap with instances of the form Action SomeMonoid t. Newtype wrappers can be used to (awkwardly) get around this.

Methods

act :: m -> s -> s #

Convert a value of type m to an action on s values.

Instances

Action () l #	`()` acts as the identity.
Methods act :: () -> l -> l #
Action m s => Action (Option m) s #	`Nothing` acts as the identity; `Just m` acts as `m`.
Methods act :: Option m -> s -> s #
Action (Endo a) a #	`Endo` acts by application. Note that in order for this instance to satisfy the `Action` laws, whenever the type `a` has some sort of algebraic structure, the type `Endo a` must be considered to represent homomorphisms (structure-preserving maps) on `a`, even though there is no way to enforce this in the type system. For example, if `a` is an instance of `Monoid`, then one should only use `Endo a` values `f` with the property that `f mempty = mempty` and `f (a <> b) = f a <> f b`.
Methods act :: Endo a -> a -> a #
Action (SM a) () #
Methods act :: SM a -> () -> () #
Action m n => Action (Split m) n #	By default, the action of a split monoid is the same as for the underlying monoid, as if the split were removed.
Methods act :: Split m -> n -> n #
(Action a a', Action (SM a) l) => Action (SM a) (Option a', l) #
Methods act :: SM a -> (Option a', l) -> (Option a', l) #
(Action m r, Action n r) => Action ((:+:) m n) r #	Coproducts act on other things by having each of the components act individually.
Methods act :: (m :+: n) -> r -> r #