Custom argument parsing

/**
 * The expression parser of math.js has support for letting functions
 * parse and evaluate arguments themselves, instead of calling them with
 * evaluated arguments.
 *
 * By adding a property `raw` with value true to a function, the function
 * will be invoked with unevaluated arguments, allowing the function
 * to process the arguments in a customized way.
 */
const { create, all } = require('../..')
const math = create(all)

/**
 * Calculate the numeric integration of a function
 * @param {Function} f
 * @param {number} start
 * @param {number} end
 * @param {number} [step=0.01]
 */
function integrate (f, start, end, step) {
  let total = 0
  step = step || 0.01
  for (let x = start; x < end; x += step) {
    total += f(x + step / 2) * step
  }
  return total
}

/**
 * A transformation for the integrate function. This transformation will be
 * invoked when the function is used via the expression parser of math.js.
 *
 * Syntax:
 *
 *     integrate(integrand, variable, start, end)
 *     integrate(integrand, variable, start, end, step)
 *
 * Usage:
 *
 *     math.evaluate('integrate(2*x, x, 0, 2)')
 *     math.evaluate('integrate(2*x, x, 0, 2, 0.01)')
 *
 * @param {Array.<math.Node>} args
 *            Expects the following arguments: [f, x, start, end, step]
 * @param {Object} math
 * @param {Object} [scope]
 */
integrate.transform = function (args, math, scope) {
  // determine the variable name
  if (!args[1].isSymbolNode) {
    throw new Error('Second argument must be a symbol')
  }
  const variable = args[1].name

  // evaluate start, end, and step
  const start = args[2].compile().evaluate(scope)
  const end = args[3].compile().evaluate(scope)
  const step = args[4] && args[4].compile().evaluate(scope) // step is optional

  // create a new scope, linked to the provided scope. We use this new scope
  // to apply the variable.
  const fnScope = Object.create(scope)

  // construct a function which evaluates the first parameter f after applying
  // a value for parameter x.
  const fnCode = args[0].compile()
  const f = function (x) {
    fnScope[variable] = x
    return fnCode.evaluate(fnScope)
  }

  // execute the integration
  return integrate(f, start, end, step)
}

// mark the transform function with a "rawArgs" property, so it will be called
// with uncompiled, unevaluated arguments.
integrate.transform.rawArgs = true

// import the function into math.js. Raw functions must be imported in the
// math namespace, they can't be used via `evaluate(scope)`.
math.import({
  integrate: integrate
})

// use the function in JavaScript
function f (x) {
  return math.pow(x, 0.5)
}
console.log(math.integrate(f, 0, 1)) // outputs 0.6667254718034714

// use the function via the expression parser
console.log(math.evaluate('integrate(x^0.5, x, 0, 1)')) // outputs 0.6667254718034714

// use the function via the expression parser (2)
const scope = {}
math.evaluate('f(x) = 2 * x', scope)
console.log(math.evaluate('integrate(f(x), x, 0, 2)', scope)) // outputs 4.000000000000003