Module foundation 

Stratum 0: Foundations — the categorical bedrock upon which all effect abstractions rest.

This module provides the primitive mathematical constructs that form the basis of the effect system. Every higher-level abstraction (functors, monads, effects, streams) is ultimately built from these foundations.

Core Constructs

Module	Construct	Category Theory
[unit]	()	Terminal object
[never]	Never	Initial object
function	identity, compose, const_	Morphisms
product	(A, B), fst, snd, pair	Categorical product
coproduct	Either<L, R>, left, right	Categorical coproduct
isomorphism	Iso<A, B>	Isomorphic objects

Practical Utilities (Effect.ts mirrors)

Module	Construct
[either]	Either<R,L> alias + Effect.ts-named combinators
func	identity, compose, memoize, tupled (full set)
option_	Free functions over Option<T>
piping	Pipe trait (x.pipe(f))
predicate	Predicate<A> composable boolean functions
mutable_ref	MutableRef<A> synchronous interior-mutable cell

Laws

• Identity: compose(f, identity) ≡ f ≡ compose(identity, f)
• Associativity: compose(f, compose(g, h)) ≡ compose(compose(f, g), h)

Re-exports

pub use coproduct::Either;

pub use coproduct::either;

pub use coproduct::left;

pub use coproduct::right;

pub use function::absurd;

pub use function::always;

pub use function::compose;

pub use function::const_;

pub use function::flip;

pub use function::identity;

pub use function::pipe1;

pub use function::pipe2;

pub use function::pipe3;

pub use isomorphism::Iso;

pub use mutable_ref::MutableRef;

pub use never::Never;

pub use piping::Pipe;

pub use predicate::Predicate;

pub use product::bimap_product;

pub use product::fst;

pub use product::pair;

pub use product::snd;

pub use product::swap;

pub use unit::Unit;

Modules

coproduct

Coproduct — the categorical coproduct (sum) of types.

either

Either<R, L> type alias and free-function combinators — mirrors Effect.ts Either.

func

Higher-order function utilities — mirrors Effect.ts Function namespace.

function

Functions — morphisms in the category of types.

isomorphism

Isomorphism — invertible mappings between types.

mutable_ref

Synchronous interior-mutable cell — mirrors Effect.ts MutableRef style API.

never

Never — the initial object in the category of types.

option_

Free-function combinators over Option<T> — mirrors the Effect.ts Option namespace.

piping

Left-to-right function application (F#-style |>).

predicate

Composable predicates — mirrors Effect.ts Predicate namespace.

product

Product — the categorical product of types.

unit

Unit — the terminal object in the category of types.