The How to Design Functions Recipe

There’s an interesting course at Coursera — Introduction to Systematic Program Design — that teaches a spesific design process for programming. The course uses Racket, a Scheme dialect, but the design techniques are easily transferable to any language.

One of the fundamental ideas is a design method for constructing functions. The link describes the process in detail, I will illustrate a simplified process using JavaScript.

Let’s say you are to implement a function that computes the factorial of a number.

Step 1: Signature, purpose and stub #

The first step is creating the signature for the function. A signature is simply a statement of the type of the input argument and the output argument. In our case that is: Number -> Number.

The purpose is a short description of what the function does, in our case: computes the factorial of n

Nest we make a stub, the outer shell of the function with a dummy return value, which should be of the right type.

// Number -> Number
// computes the factorial of n
fact = function(n) {
  return 0
}

Step 2: Define examples/tests #

Next we provide examples for how the function should work.

debug(fact(5) === 120)
debug(fact(0) === 1)

Step 3: Using the stub/template, write the function #

// Number -> Number
// computes the factorial of n
fact = function(n) {
    var res = 1;
    if (n > 1) {
        for (var i = 1; i <= n; i++) {
            res *= i;
        }
    }
    return res;
}

debug(fact(5) === 120)
debug(fact(0) === 1)

Step 3: Test, debug and refactor #

Running the tests, they both return true. Looking at the function some more we see that it can be shortened. Finally, we have:

// Number -> Number
// computes the factorial of n
fact = function(n) {
    var res = 1;
    for (var i = 2; i <= n; i++) {
        res *= i;
    }
    return res;
}

debug(fact(5) === 120)
debug(fact(0) === 1)

We run the tests again and see that they still return true.

The process has a lot in common with test driven development of course, but it’s nice to see that it can be implemented so easily in JavaScript without using any test library.