package alg_structs

You can search for identifiers within the package.

in-package search v0.2.0

On This Page

Seed
Interface
Laws
Constructors
Implementations

package alg_structs

alg_structs: Algebraic Structures in OCaml Structs
- Library alg_structs
  - Alg_structs
    
    Triv
    
    S
    
    Functor
    
    Seed
    
    UnlabeledSeed
    
    S
    
    Law
    
    Make
    
    MakeUnlabeled
    
    Option
    
    List
    
    Array
    
    Applicative
    
    Seed
    
    S
    
    Let_bind
    
    Law
    
    Make
    
    Let_bind
    
    Option
    
    Let_bind
    
    List
    
    Let_bind
    
    Array
    
    Let_bind
    
    Semigroup
    
    Seed
    
    Seed1
    
    S
    
    S1
    
    Law
    
    Make
    
    Bool
    
    Or
    
    And
    
    Int
    
    Sum
    
    Product
    
    Option
    
    Make
    
    Endo
    
    Make
    
    Dual
    
    Make
    
    Monoid
    
    Seed
    
    S
    
    Law
    
    Make
    
    Bool
    
    Or
    
    And
    
    Int
    
    Sum
    
    Product
    
    Option
    
    Make
    
    Endo
    
    Make
    
    Dual
    
    Make
    
    Foldable
    
    Seed
    
    S
    
    Law
    
    Make
    
    Option
    
    List
    
    Array
    
    NonEmptyList
- Sources
  - alg_structs
    
    alg_structs.ml
    
    alg_structs__.ml
    
    applicative.ml
    
    foldable.ml
    
    functor.ml
    
    monoid.ml
    
    nonEmptyList.ml
    
    semigroup.ml
    
    traversable.ml
    
    triv.ml
    
    util.ml

Legend:
Page
Library
Module
Module type
Parameter
Class
Class type
Source

Module `Alg_structs.Monoid`Source

An interface for a type with a binary, associative operator over it and a privileged unit value.

A Monoid is a Semigroup enriched an identity element, called unit.

Some well known monoids are

The integers under addition

type t = int
op = (+)
unit = 0

The integers under multiplication

type t = int
op = ( * )
unit = 1

Strings under concatenation

type t = string
op = (^)
unit = ""

Seed

Sourcemodule type Seed = sig ... end

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

Interface

Sourcemodule 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

Sourcemodule 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

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

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

Sourceval 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

Source

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

Sourcemodule Bool : sig ... end

Monoids over bool

Sourcemodule Int : sig ... end

Monoids over int

Sourcemodule Option : sig ... end

Semigroups over option types

Sourcemodule Endo : sig ... end

See Semigroup.Endo

Sourcemodule Dual : sig ... end

See Semigroup.Dual

package alg_structs

Module Alg_structs.MonoidSource

Seed

Interface

Laws

Constructors

Implementations

Module `Alg_structs.Monoid`Source