Module algebra 

Stratum 1: Algebraic Structures — abstract patterns that recur throughout the system.

This module provides the fundamental algebraic abstractions built on top of Stratum 0 foundations. These structures capture common patterns of composition, transformation, and combination.

Hierarchy

                   Semigroup
                       │
                       ▼
                    Monoid

    Contravariant   Functor   Bifunctor
                       │
                       ▼
                  Applicative
                       │
                       ▼
                     Monad

Design Notes

Rust lacks higher-kinded types, so we use two complementary approaches:

1. Traits with associated types — for types with a single “mappable” parameter
2. Module functions — for operations on concrete types (like Option, Result)

The traits express the structure, while module functions provide ergonomic usage.

Re-exports

pub use applicative::Applicative;

pub use bifunctor::Bifunctor;

pub use contravariant::Contravariant;

pub use functor::Functor;

pub use monad::Monad;

pub use monoid::Monoid;

pub use selective::Selective;

pub use semigroup::Semigroup;

Modules

applicative

Applicative — a functor with pure and apply operations.

bifunctor

Bifunctor — a functor in two type parameters.

contravariant

Contravariant — a functor with reversed variance.

functor

Functor — a type constructor that can be mapped over.

interface

EffectInterface — typed operation-signature protocol (Koka/Eff/Frank analogue).

monad

Monad — an applicative with sequential composition.

monoid

Monoid — a semigroup with an identity element.

selective

Selective — a functor between Applicative and Monad.

semigroup

Semigroup — a type with an associative binary operation.