Presentation

An action lifts an element (the "actor") of some type s, the acting type, into a function of another type x which we call the "actee".

The class hierarchy for actions is fine-grained, which means it is flexible but sometimes cumbersome to deal with. In particular, this allows to specify specific properties on the action for a semidirect product to be a semigroup or a monoid (see Semidirect). Here is a tree summarizing the class hierarchy and their laws:

LAct                     Set action
 => LActSg               Semigroup action
     => LActMn           Monoid action
          => LTorsor     Torsor
 => LActDistrib          Distributive action
 => LActNeutral          Neutral preserving action
 => LActGen              Action generated by a set
     => LActCyclic       Cyclic action (generated by a single element)

Instances driven by the acting type

The action classes do not have functional dependencies, which can make it awkward to work with them. To avoid overlapping issues, this library chooses to drive instances by the second parameter, i.e. to _never_ write instances of the form

instance LAct SomeType s
instance RAct SomeType s

If you need such an instance, you should make a newtype. This library already provides some, such as ActSelf, ActTrivial, ActSelf', ActFold' and ActMap.

Design choices compared to existing libraries

This library is inspired by the already existing action libraries.

• The deriving mechanism is inspired by the one from the acts library. The main difference between this library and the acts library is that acts drives its instances by the actee parameter.
• The monoid-extras library drives its instances by the acting type, but does not provide a deriving mechanism. This library started as an extension of monoid-extras, but the design choices made it diverge from it.
• The idea of specifying action properties using empty classes comes from the semigroups-actions library, which inspired some design of this library. This library offers everything semigroups-actions offers, and more.