this.MathSON = (function () {

  var unicodeToLatex = {

    '±': 'pm'

  };

  var keyToCommand = {

    numer: Fraction,

    denom: Fraction,

    sqrt: SquareRoot,

    sup: SupSub,

    sub: SupSub

  };

  function Fraction(cmd) { this.cmd = cmd; }

  Fraction.prototype.toLatex = function () {

    return [

      '\\frac{',

      this.cmd.numer.toLatex(),

      '}{',

      this.cmd.denom.toLatex(),

      '}'

    ].join('');

  };

  function SquareRoot(cmd) { this.cmd = cmd; }

  SquareRoot.prototype.toLatex = function () {

    return [

      '\\sqrt{',

      this.cmd.sqrt.toLatex(),

      '}'

    ].join('');

  };

  function SupSub(cmd) { this.cmd = cmd; }

  SupSub.prototype.toLatex = function () {

    return [

      '^{',

      this.cmd.sup.toLatex(),

      '}'

    ].join('');

  };

  function MathSON(ops) {

    if (!Array.isArray(ops)) throw 'Need Array, got ' + JSON.stringify(ops);

    if (!(this instanceof MathSON)) return new MathSON(ops);

    this.ops = ops;

  }

  MathSON.prototype.toLatex = function () {

    return this.ops.map(function (op, i, ops) {

      // for strings, translate Unicode chars to LaTeX, like ± to \pm

      if (typeof op === 'string') {

        return op.split('').map(function (ch) {

          if (ch in unicodeToLatex) {

            return '\\' + unicodeToLatex[ch] + ' ';

          }

          return ch;

        }).join('');

      }

      // for objects, 

      if (typeof op === 'object' && op !== null) {

        var Command = keyToCommand[Object.keys(op)[0]];

        if (Command) {

          var cmd = {};

          Object.keys(op).forEach(function (key) {

            if (/^[a-z]+$/i.test(key)) cmd[key] = MathSON(op[key]);

            else if (key.charAt(0) === '$') cmd[key] = op[key];

            else throw 'Unexpected key \'' + key + "'";

          });

          return new Command(cmd).toLatex();

        }

      }

      throw 'Unexpected ' + JSON.stringify(op);

    }).join('')

    .replace(/ (?![a-z])/ig, '');

  };

  MathSON.toLatex = function (ops) {

    return MathSON(ops).toLatex();

  };

  return MathSON;

}());

​

// tests

console.assert(MathSON([{numer: ['1'], denom: ['2']}]).toLatex() === '\\frac{1}{2}');

console.assert(MathSON.toLatex(['x=',

 { numer: ['-b±', { sqrt: ['b', { sup: ['2'] }, '-4ac'] }],

   denom: ['2a'] }]) === "x=\\frac{-b\\pm\\sqrt{b^{2}-4ac}}{2a}");