// Sum-type (also called: tagged union, disjoin union, variant type)
// A Sum-type always has only two variants, called "left" and "right".
// Sum-types of more variants (called Enums) can be constructed by nesting Sum-types.

import { prodType } from "./types.js";
import { GenericType, Type } from "../primitives/types.js";
import { typedFnType } from "./types.js";
import { makeGeneric } from "../generics/generics.js";
import { sumType } from "./types.js";

export const newLeft  = left  => ({t: "L", v: left }); // 't': tag, 'v': value
export const newRight = right => ({t: "R", v: right});

// signature:
//   sum-type -> (leftType -> resultType, rightType -> resultType) -> resultType
export const match = sum => handlers =>
  sum.t === "L"
    ? handlers.l(sum.v)
    : handlers.r(sum.v);

export const ModuleSum = {l:[
  // binary type constructor
  // Type -> Type -> Type
  ...typedFnType(sumType, fnType =>
    fnType
      (Type)
      (fnType
        (Type)
        (Type)
      ),
    ),

  // a -> a | b
  ...typedFnType(newLeft, fnType =>
    makeGeneric((a, b) =>
      fnType
        (a)
        (sumType(a)(b))
    ), GenericType),

  // b -> a | b
  ...typedFnType(newRight, fnType =>
    makeGeneric((a, b) =>
      fnType
        (b)
        (sumType(a)(b))
    ), GenericType),

  // a | b -> (a -> c, b-> c) -> c
  ...typedFnType(match, fnType =>
    makeGeneric((a, b, c) =>
      fnType
        (sumType(a)(b))
        (fnType
          (prodType
            (fnType(a)(c))
            (fnType(b)(c))
          )
          (c)
        )
    ), GenericType),
]};