package alg_structs

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

Legend:
Library
Module
Module type
Parameter
Class
Class type

include Semigroup.Seed

type t

The principle (and sole) type.

We can think of this set-theoretically as the carrier set of the algebraic structure or category-theoretically as the single object in the category, with each element being a morphism t -> t.

val op : t -> t -> t

op x y is an associative operation over all elements x and y of type t. Category-theoretically, this is the composition of morphisms.

val unit : t

unit is the identity element in the monoid over t.

Every implementation must ensure that for any x : t, unit is the identity element under op, thus that the equation (x * unit) = (unit * x) = x holds.