import { fnType, prodType } from "../type_registry.js";
import { Function } from "../metacircular.js";

// In JS, all products are encoded in the same way:
const constructor = left => right => ({left, right});
const left        = product => product.left;
const right       = product => product.right;

// Given two types A and B, create the type (A × B).
export const makeProductType = (leftType, rightType) => {
  const productType = prodType(leftType, rightType);

  const leftFnType  = fnType({in: productType, out: leftType});
  const rightFnType = fnType({in: productType, out: rightType});

  const constructorBoundType = fnType({in: rightType, out: productType});
  const constructorType      = fnType({in: leftType, out: constructorBoundType});

  return [
    {i: left       , t: leftFnType},
    {i: right      , t: rightFnType},
    {i: leftFnType , t: Function},
    {i: rightFnType, t: Function},

    {i: constructor         , t: constructorType},
    {i: constructorType     , t: Function},
    {i: constructorBoundType, t: Function},
  ];
};