automated-reasoning.js

function Expr(operation, left, right) {
  return {op: operation, l: left, r: right};
}

var Add = Expr.bind(null, 'add'),
    Mult = Expr.bind(null, 'mult');

function Var(name) {
  return {name: name};
}

function opAdd(x, y) {
  return x + y;
}

function opMult(x, y) {
  return x * y;
}

function patterns(op, fn, constructor, left, right) {
  return {
    'number,number': function() {
      return op(left, right);
    },
    'object,number': function() {
      return fn(right, left);
    },
    'object,object': function() {
      return constructor(left, right);
    }
  };
}

function add(left, right) {
  var p = patterns(opAdd, add, Add, left, right);
  p['number,object'] = function() {
    return left === 0 ? right: Add(left, right);
  };
  return p[typeof left + ',' + typeof right]();
}

function mult(left, right) {
  var p = patterns(opMult, mult, Mult, left, right);
  p['number,object'] = function() {
    if (left === 1) {
      return right;
    } else if (left === 0) {
      return 0;
    } else {
      return Mult(left, right);
    }
  };
  return p[typeof left + ',' + typeof right]();
}

function simplify1(obj) {
  if (!obj.op) {
    return obj;
  }

  var operations = {
    add: add.bind(null, obj.l, obj.r),
    mult: mult.bind(null, obj.l, obj.r)
  };
  return operations[obj.op]();
}

function simplify(obj) {
  if (!obj.op) {
    return obj;
  }

  var operations = {
    add: simplify1.bind(null, Add(simplify(obj.l), simplify(obj.r))),
    mult: simplify1.bind(null, Mult(simplify(obj.l), simplify(obj.r)))
  };
  return operations[obj.op]();
}

// var e = (1 + 0 * x) * 3 + 12;
var e = Add(Mult(Add(1, Mult(0, Var('x'))), 3), 12);
JSON.stringify(simplify(e));