Alg_structs.Applicative.Law · alg_structs 0.1.3

alg_structs

Interfaces and module combinators for algebraic structures

Version

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 . Applicative . Law

Parameters

module A : S

Signature

val identity : 'a A.t -> bool

identity x: return Fun.id <*> x = x

val composition : ( 'b -> 'c ) A.t -> ( 'a -> 'b ) A.t -> 'a A.t -> bool

composition u v w: (return (%) <*> u <*> v <*> w) = (u <*> (v <*> w))

val homomorphism : ( 'a -> 'b ) -> 'a -> bool

homomorphism f x: return f <*> return x = return (f x)

val interchange : ( 'a -> 'b ) A.t -> 'a -> bool

interchange u y: (u <*> return y) = (return (fun f -> f y) <*> u)