/**
 * EVA Algebra — Composition operators.
 *
 * ⊗ Sequential: seq(f, g)(x) = g(f(x))
 * ∥ Parallel:   par(f, g)(a, b) = [f(a), g(b)]
 * ⊕ Conditional: cond(p,f,g)(x) = p(x) ? f(x) : g(x)
 */

export const seq = <A, B, C>(f: (a: A) => B, g: (b: B) => C): (a: A) => C =>
  (a) => g(f(a));

export const par = <A1, A2, B1, B2>(
  f: (a: A1) => B1, g: (a: A2) => B2
): (a: A1, b: A2) => [B1, B2] =>
  (a, b) => [f(a), g(b)];

export const cond = <T, R>(
  pred: (x: T) => boolean, f: (x: T) => R, g: (x: T) => R
): (x: T) => R =>
  (x) => pred(x) ? f(x) : g(x);

export const pipeline = <T>(init: T, steps: Array<(x: T) => T>): T =>
  steps.reduce((acc, f) => f(acc), init);

export const compose = <T>(...fns: Array<(x: T) => T>): (x: T) => T =>
  (x) => pipeline(x, fns);