monoid-extras-0.3.3.5: Various extra monoid-related definitions and utilities

Copyright (c) 2011 diagrams-core team (see LICENSE) BSD-style (see LICENSE) diagrams-discuss@googlegroups.com None Haskell2010

Data.Monoid.MList

Description

Heterogeneous lists of monoids.

Synopsis

# Heterogeneous monoidal lists

The idea of heterogeneous lists has been around for a long time. Here, we adopt heterogeneous lists where the element types are all monoids: this allows us to leave out identity values, so that a heterogeneous list containing only a single non-identity value can be created without incurring constraints due to all the other types, by leaving all the other values out.

type (:::) a l = (Option a, l) infixr 5 Source

(*:) :: a -> l -> a ::: l infixr 5 Source

class MList l where Source

Type class for heterogeneous monoidal lists, with a single method allowing construction of an empty list.

Methods

empty :: l Source

The empty heterogeneous list of type `l`. Of course, ```empty == mempty```, but unlike `mempty`, `empty` does not require `Monoid` constraints on all the elements of `l`.

Instances

 MList () MList l => MList ((:::) a l)

# Accessing embedded values

class l :>: a where Source

The relation `l :>: a` holds when `a` is the type of an element in `l`. For example, `(Char ::: Int ::: Bool ::: Nil) :>: Int`.

Methods

inj :: a -> l Source

Inject a value into an otherwise empty heterogeneous list.

get :: l -> Option a Source

Get the value of type `a` from a heterogeneous list, if there is one.

alt :: (Option a -> Option a) -> l -> l Source

Alter the value of type `a` by applying the given function to it.

Instances

 (:>:) t a => ((:::) b t) :>: a MList t => ((:::) a t) :>: a

# Monoid actions of heterogeneous lists

Monoidal heterogeneous lists may act on one another as you would expect, with each element in the first list acting on each in the second. Unfortunately, coding this up in type class instances is a bit fiddly.

newtype SM m Source

`SM`, an abbreviation for "single monoid" (as opposed to a heterogeneous list of monoids), is only used internally to help guide instance selection when defining the action of heterogeneous monoidal lists on each other.

Constructors

 SM m

Instances

 Show m => Show (SM m) Action (SM a) () (Action a a', Action (SM a) l) => Action (SM a) (Option a', l)