import { prettyT, typedFnType } from "../structures/types.js"
import { Double } from "../primitives/types.js";
import { makeConstructor, makeConstructorType, makeGetters, makeGettersTypes, structType } from "../structures/struct.js";
import { constructorProduct } from "../structures/product.js";
import { makeTypeConstructor } from "../type_constructor.js";

const cartFields = [
  constructorProduct("x")(Double),
  constructorProduct("y")(Double),
];

const polarFields = [
  constructorProduct("r")(Double),
  constructorProduct("θ")(Double),
];

// Nominal types:
export const NPoint2DCartesian = makeTypeConstructor(Symbol('Point2DCartesian'))(0);
export const NPoint2DPolar     = makeTypeConstructor(Symbol('Point2DPolar'))(0);

// Structural types:
export const SPoint2DCartesian = structType(cartFields);  // (Double, (Double, Unit))
export const SPoint2DPolar     = structType(polarFields); // (Double, (Double, Unit))

export const constructorPoint2DCartesian = makeConstructor(cartFields);
export const constructorPoint2DPolar     = makeConstructor(polarFields);

export const constructorPoint2DCartesianFnType = makeConstructorType(NPoint2DCartesian)(cartFields);
export const constructorPoint2DPolarFnType     = makeConstructorType(NPoint2DPolar)(polarFields);

export const [getX, getY] = makeGetters(cartFields);
export const [getR, getΘ] = makeGetters(polarFields);

export const [getXFnType, getYFnType] = makeGettersTypes(NPoint2DCartesian)(cartFields);
export const [getRFnType, getΘFnType] = makeGettersTypes(NPoint2DPolar)(polarFields);

export const cart2polar = cart => {
  const x = getX(cart);
  const y = getY(cart);
  const r = Math.sqrt(x*x + y*y);
  const θ = Math.atan(y/x);
  return constructorPoint2DPolar(r)(θ);
};

export const polar2cart = polar => {
  const r = getR(polar);
  const θ = getΘ(polar);
  const x = r * Math.cos(θ);
  const y = r * Math.sin(θ);
  return constructorPoint2DCartesian(x)(y);
};

export const cart2Str = cart => {
  const x = getX(cart);
  const y = getY(cart);
  return {l: `{x: ${x}, y: ${y}}`};
};

export const polar2Str = polar => {
  const r = getR(polar);
  const θ = getΘ(polar);
  return {l: `{r: ${r}, θ: ${θ}}`};
};

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

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

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

// const examplePoint = {x: 1, y: 2};

const examplePointCart = constructorPoint2DCartesian(1)(2);
const examplePointPolar = constructorPoint2DCartesian(0)(5);

console.log(prettyT(getXFnType));

export const ModulePoint = {l:[
  // {i: -1                 , t: Double},
  // {i: 2                  , t: Double},
  // {i: examplePoint       , t: Point2DCartesian},

  {i: examplePointCart, t: SPoint2DCartesian},
  {i: examplePointCart, t: NPoint2DCartesian},

  {i: examplePointPolar, t: SPoint2DPolar},
  {i: examplePointPolar, t: NPoint2DPolar},

  // {i: SPoint2DCartesian   , t: Type},
  // {i: SPoint2DPolar       , t: Type},

  // {i: NPoint2DCartesian   , t: Type},
  // {i: NPoint2DPolar       , t: Type},

  {i: getX, t: getXFnType},
  {i: getY, t: getYFnType},
  {i: getR, t: getRFnType},
  {i: getΘ, t: getΘFnType},

  ...typedFnType(cart2polar, fnType => fnType(NPoint2DCartesian)(NPoint2DPolar)),
  ...typedFnType(polar2cart, fnType => fnType(NPoint2DPolar)(NPoint2DCartesian)),

  // ...typedFnType(polar2cart, fnType => fnType(Point2DPolar)(Point2DCartesian)),

  // // Double -> Double -> PointCartesian2D -> PointCartesian2D
  // ...typedFnType(translate, fnType =>
  //   fnType
  //     (Double)
  //     (fnType
  //       (Double)
  //       (fnType
  //         (Point2DCartesian)
  //         (Point2DCartesian)))),

  // ...typedFnType(cart2tuple, fnType => fnType(Point2DCartesian)(prodType(Double)(Double))),
  
  // ...typedFnType(polar2tuple, fnType => fnType(Point2DPolar)(prodType(Double)(Double))),

  // // Double -> PointPolar2D -> PointPolar2D
  // ...typedFnType(rotate, fnType =>
  //   fnType
  //     (Double)
  //     (fnType
  //       (Point2DPolar)
  //       (Point2DPolar))),

  // // Double -> PointPolar2D -> PointPolar2D
  // ...typedFnType(scale, fnType =>
  //   fnType
  //     (Double)
  //     (fnType
  //       (Point2DPolar)
  //       (Point2DPolar))),
]};