import type { Magma } from './Magma'

/**
 * `Semigroup` defines an associative binary operator `combine` on given type `A`.
 * `combine` must fulfill the associativity law, which states that for a binary operation `*` on type `A`:
 *
 * ```
 * (a * b) * c === a * (b * c) for all a, b, c, in A
 * ```
 *
 * `Semigroup` defines both an uncurried function `combine_` and a curried function
 * `combine` with arguments interchanged for `pipeable` application.
 */
export interface Semigroup<A> extends Magma<A> {}

export function Semigroup<A>(combine: (x: A, y: A) => A): Semigroup<A> {
  return {
    combine_: combine,
    combine: (y) => (x) => combine(x, y)
  }
}