import { Type } from "../type.js";
import { typedFnType } from "../structures/types.js"
import { Double } from "../primitives/types.js";

// Create nominal types
export const PointCartesian2D = { symbol: Symbol('PointCartesian2D'), params: [] };
export const PointPolar2D     = { symbol: Symbol('PointPolar2D')    , params: [] };

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

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

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

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

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

  ...typedFnType(cart2polar, fnType => fnType(PointCartesian2D)(PointPolar2D)),

  ...typedFnType(polar2cart, fnType => fnType(PointPolar2D)(PointCartesian2D)),

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

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

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