Module Control.Semigroupoid

Introduction of the semigroupoid.

Imports

• import Prelude.PreludeBase as PreludeBase

Table of Content

• Definitions

  class Semigroupoid f

  <<< ∷ Semigroupoid f ⇒ f b c → f a b → f a c 

  >>> ∷ Semigroupoid f ⇒ f a b → f b c → f a c 

• Instances

  instance Semigroupoid ->

• Functions and Values by Type

Definitions

class Semigroupoid f

Formally, a semigroupoid consists of

• a set of things called objects.
• for every two objects A and B a set Mor(A,B) of things called morphisms from A to B. If f is in Mor(A,B), we write f : A → B.
• for every three objects A, B and C a binary operation Mor(A,B) × Mor(B,C) → Mor(A,C) called composition of morphisms. The composition of f : A → B and g : B → C is written as g • f.

such that the following axiom holds:

associativity

if f : A → B, g : B → C and h : C → D then h • (g • f) = (h • g) • f.

Known Instances

->

Member Functions

• ∷ Semigroupoid f ⇒ f b c → f a b → f a c
infixr  16

morphism composition

<<< ∷ Semigroupoid f ⇒ f b c → f a b → f a c
infixr  1

Right-to-left composition. This is the same a ordinary composition with Semigroupoid.•.

>>> ∷ Semigroupoid f ⇒ f a b → f b c → f a c
infixr  1

Left-to-right composition

Instances

instance Semigroupoid ->

The semigroupoid of Frege values where morphisms are functions.

Member Functions

• ∷ (𝖆→𝖈) → (𝖇→𝖆) → 𝖇 → 𝖈
infixr  16

function composition

Functions and Values by Type

(𝖆→𝖈) → (𝖇→𝖆) → 𝖇 → 𝖈

Semigroupoid_->.•

Semigroupoid f ⇒ f a b → f b c → f a c

>>>

Semigroupoid f ⇒ f b c → f a b → f a c

<<<, Semigroupoid.•