Alg_structs.Monoid · alg_structs 0.1.3 · OCaml Packages

alg_structs

Interfaces and module combinators for algebraic structures

Version

Overview Documentation

IN THIS PACKAGE

library alg_structs
- module Alg_structs
  - module Applicative
    
    module Array
    
    module Let_bind
    
    module Law
    
    argument 1-A
    
    module Let_bind
    
    module List
    
    module Let_bind
    
    module Make
    
    argument 1-B
    
    module Let_bind
    
    module Option
    
    module Let_bind
    
    module type S
    
    module Let_bind
    
    module type Seed
  - module Foldable
    
    module Array
    
    module Law
    
    argument 1-F
    
    module List
    
    module Make
    
    argument 1-Seed
    
    module Option
    
    module type S
    
    module type Seed
  - module Functor
    
    module Array
    
    module Law
    
    argument 1-F
    
    module List
    
    module Make
    
    argument 1-Seed
    
    module MakeUnlabeled
    
    argument 1-Seed
    
    module Option
    
    module type S
    
    module type Seed
    
    module type UnlabeledSeed
  - module Monoid
    
    module Bool
    
    module And
    
    module Or
    
    module Dual
    
    module Make
    
    argument 1-M
    
    module Endo
    
    module Make
    
    argument 1-T
    
    module Int
    
    module Product
    
    module Sum
    
    module Law
    
    argument 1-M
    
    module Make
    
    argument 1-Seed
    
    module Option
    
    module Make
    
    argument 1-S
    
    module type S
    
    module type Seed
  - module NonEmptyList
  - module Semigroup
    
    module Bool
    
    module And
    
    module Or
    
    module Dual
    
    module Make
    
    argument 1-S
    
    module Endo
    
    module Make
    
    argument 1-T
    
    module Int
    
    module Product
    
    module Sum
    
    module Law
    
    argument 1-S
    
    module Make
    
    argument 1-S
    
    module Option
    
    module Make
    
    argument 1-S
    
    module type S
    
    module type S1
    
    module type Seed
    
    module type Seed1
  - module Triv
    
    module type S

Module Alg_structs . Monoid

Seed

module type Seed = sig ... end

The Seed needed to generate an implementation of Monoid for the type t

Interface

module type S = sig ... end

A monoid is a set of objects with an associative binary operation over it and a privileged unit element that acts as an identity.

Laws

module Law (M : S) : sig ... end

Law notes the laws that should be obeyed by any instantiation of Monoid in the form of predicates that should hold true for any arguments of the appropriate type.

Constructors

Module functors for creating implementations of Monoid

module Make (Seed : Seed) : S with type t = Seed.t

Make S is a implementation of Monoid grown from the implementation of the Seed.

val make : 'a -> ( 'a -> 'a -> 'a ) -> (module S with type t = 'a)

make (unit : t) (op : t -> t -> t) is an implementation of Monoid over the type t with the given unit and op

val of_semigroup : 
  (module Semigroup.S with type t = 'a) ->
  'a ->
  (module S
  with type t = 'a)

of_semigroup semi unit forms an implementation of Monoid by enriching the give semigroup semi with the unit

Implementations

module Bool : sig ... end

Monoids over bool

module Int : sig ... end

Monoids over int

module Option : sig ... end

Semigroups over option types

module Endo : sig ... end

See Semigroup.Endo

module Dual : sig ... end

See Semigroup.Dual