import { Double } from "../primitives/symbols.js";
import { nominalType, NominalType } from "../structures/nominal_type.js";
import { makeProductType } from "../structures/product.js";
import { prodType, typedFnType } from "../type_registry.js";

const PointCartesian2D = nominalType(
  "PointCartesian2D")
  // just a unique number, to make sure that our type is only equal to itself
  // BigInt("0xBBAAD62B10EE21993BA690A732DA2A6875CE4B6F5E7139D5AEC9FD887F9D24A8"))
  (prodType(Double, Double));

const PointPolar2D = nominalType(
  "PointPolar2D")
  // just a unique number, to make sure that our type is only equal to itself
  // BigInt("0x31CDAB4B3D84C4EB27D3C111FD7580E533268B72E05BD694F8B262913E018B72"))
  (prodType(Double, Double));

export const cart2polar = ({left: x, right: y}) => {
  const r = Math.sqrt(x*x + y*y);
  const θ = Math.atan(y/x);
  return {left: r, right: θ};
};

export const polar2cart = ({left: r, right: θ}) => {
  const x = r * Math.cos(θ);
  const y = r * Math.sin(θ);
  return {left: x, right: y};
}

export const translate = dx => dy => ({left: x, right: y}) => {
  return {left: x+dx, right: y+dy};
}

export const rotate = dθ => ({left: r, right: θ}) => {
  return {left: r, right: θ+dθ};
}

export const scale = dr => ({left: r, right: θ}) => {
  return {left: r+dr, right: θ};
}

const examplePoint = {left: 1, right: 2};

export const ModulePoint = {l:[
  {i: -1                 , t: Double},
  {i: 2                  , t: Double},
  {i: examplePoint       , t: PointCartesian2D},
  {i: examplePoint       , t: prodType(Double, Double)},

  ...makeProductType(Double, Double).l,

  {i: PointCartesian2D   , t: NominalType},
  {i: PointPolar2D       , t: NominalType},

  ...typedFnType(cart2polar, fnType => fnType({in: PointCartesian2D, out: PointPolar2D})),

  ...typedFnType(polar2cart, fnType => fnType({in: PointPolar2D, out: PointCartesian2D})),

  ...typedFnType(translate , fnType => fnType({in: Double, out: fnType({in: Double, out: fnType({in: PointCartesian2D, out: PointCartesian2D})})})),

  ...typedFnType(rotate, fnType => fnType({in: Double, out: fnType({in: PointPolar2D, out: PointPolar2D})})),

  ...typedFnType(scale, fnType => fnType({in: Double, out: fnType({in: PointPolar2D, out: PointPolar2D})})),
]};