// =============================================================================
// Hilbert.js | Symbols
// (c) Mathigon
// =============================================================================


import {Obj} from '@mathigon/core';


export const CONSTANTS: Obj<number> = {
  pi: Math.PI,
  π: Math.PI,
  e: Math.E
};

export const BRACKETS: Obj<string> = {
  '(': ')',
  '[': ']',
  '{': '}'
};

export const SPECIAL_OPERATORS: Obj<string> = {
  '*': '·',
  '**': '∗',
  '//': '//',
  '+-': '±',
  '–': '−',
  '-': '−',
  'xx': '×',
  'sum': '∑',
  'prod': '∏',
  'int': '∫',
  'del': '∂',
  'grad': '∇',
  'aleph': 'ℵ',
  'not': '¬',
  'AA': '∀',
  'EE': '∃',
  '\'': '’',

  '!=': '≠',
  '?=': '≟',
  '<=': '≤',
  '>=': '≥',
  'in': '∈',
  '!in': '∉',
  '==': '≡',
  '~=': '≅',
  '~~': '≈',
  'sub': '⊂',
  'sube': '⊆',
  'prop': '∝',
  'oo': '∞',
  'cap': '∩',
  'cup': '∪',

  '<-': '←',
  '->': '→',
  '=>': '⇒',
  '<=>': '⇔',
  '|->': '↦',
  'uarr': '↑',
  'darr': '↓',
  'lArr': '⇐'
};

export const SPECIAL_IDENTIFIERS: Obj<string> = {
  Gamma: 'Γ',
  Delta: 'Δ',
  Theta: 'Θ',
  Lambda: 'Λ',
  Xi: 'Ξ',
  Pi: 'Π',
  Sigma: 'Σ',
  Phi: 'Φ',
  Psi: 'Ψ',
  Omega: 'Ω',

  alpha: 'α',
  beta: 'β',
  gamma: 'γ',
  delta: 'δ',
  epsilon: 'ɛ',
  zeta: 'ζ',
  eta: 'η',
  theta: 'θ',
  iota: 'ι',
  kappa: 'κ',
  lambda: 'λ',
  mu: 'μ',
  nu: 'ν',
  xi: 'ξ',
  pi: 'π',
  rho: 'ρ',
  sigma: 'σ',
  tau: 'τ',
  upsilon: 'υ',
  phi: 'φ',
  chi: 'χ',
  psi: 'ψ',
  omega: 'ω',

  CC: 'ℂ',
  NN: 'ℕ',
  QQ: 'ℚ',
  RR: 'ℝ',
  ZZ: 'ℤ'
};

const ALPHABET = 'abcdefghijklmnopqrstuvwxyz';
const LOWERCASE = ALPHABET.split('');
const UPPERCASE = ALPHABET.toUpperCase().split('');
const GREEK = Object.values(SPECIAL_IDENTIFIERS);
export const IDENTIFIER_SYMBOLS = [...LOWERCASE, ...UPPERCASE, ...GREEK, '$'];

const SIMPLE_SYMBOLS = '|()[]{}÷,!?<>=*/+-–−~^_…°•∥⊥\'∠:%∼△';
const COMPLEX_SYMBOLS = Object.values(SPECIAL_OPERATORS);
export const OPERATOR_SYMBOLS = [...SIMPLE_SYMBOLS, ...COMPLEX_SYMBOLS];

export const FUNCTION_NAMES: Obj<string> = {
  '_': 'sub',
  '^': 'sup',
  '//': '/',
  '÷': '/'
};

const ESCAPES: Obj<string> = {
  '<': '&lt;',
  '>': '&gt;'
};

export function escape(char: string) {
  return (char in ESCAPES) ? ESCAPES[char] : char;
}

const SPECIAL_FUNCTIONS = ['abs', 'round', 'floor', 'ceil', 'max', 'min', 'mod',
  'lcm', 'gcd', 'gcf', 'log', 'exp', 'ln', 'sqrt', 'root', 'sin', 'cos', 'tan',
  'sec', 'csc', 'cot', 'cosec', 'cotan', 'arcsin', 'arccos', 'arctan', 'sinh',
  'cosh', 'tanh', 'sech', 'csch', 'coth', 'cosech'] as const;
export type SpecialFunction = typeof SPECIAL_FUNCTIONS[number];

export function isSpecialFunction(fn: string): fn is SpecialFunction {
  return SPECIAL_FUNCTIONS.includes(fn as SpecialFunction);
}

export const VOICE_STRINGS: Obj<string> = {
  '+': 'plus',
  '−': 'minus',
  '·': 'times',
  '×': 'times',
  '/': 'over',
  '//': 'divided by',
  '%': 'percent',
  '!': 'factorial',
  '±': 'plus-minus',
  '=': 'equals',
  '≠': 'does not equal',
  '≟': 'is it equal?',
  '<': 'is less than',
  '>': 'is greater than',
  '≤': 'is less than or equal to',
  '≥': 'is greater than or equal to',
  'π': 'pi',
  '≅': 'is congruent to',
  '∥': 'is parallel to',
  '⊥': 'is perpendicular to'
};

for (const name of Object.keys(SPECIAL_IDENTIFIERS)) {
  VOICE_STRINGS[SPECIAL_IDENTIFIERS[name]] = name;
}