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Unit 3: Functions

Learning Objectives

Students should

  • understand the importance of function as a programming constructor and how it helps to reduce complexity and mitigate bugs.
  • be aware of two different roles a programmer can play: the implementer and the client.
  • understand the concept of abstraction barrier as a wall between the client and the implementer, including in the context of a function.

Function as an Abstraction over Computation

Another important abstraction provided by a programming language is the function (or procedure). This abstraction allows programmers to group a set of instructions and give it a name. The named set of instructions may take one or more variables as input parameters, and return zero or one values.

Like all other abstractions, defining functions allow us to think at a higher conceptual level. By composing functions at increasingly higher level of abstractions, we can build programs with increasing level of complexity.

Functions help us deal with complexity in a few ways as you will see later. For now, to understand the examples, we will first describe a basic element of a function. Note that this cannot be compiled but need to be run on Jshell. Once we have introduced the concept of a class, our code can be compiled.

Syntax

The basic syntax of a function is as follows:

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return_type function_name(param_type1 param1, param_type2 param2) {
    : // function body
}

To create a function, we have to specify the return type. If there is no return type, then we need to use the type called void1. This is then followed by the function name. We may have zero or more parameters for a function.

  • Functions allow programmers to compartmentalize computation and its effects. We can isolate the complexity to within its body: the intermediate variables exists only as local variables that has no effect outside of the function. A function only interacts with the rest of the code through its parameters and return value, and so, reduces the dependencies between variables to these well-defined interactions. Such compartmentalization reduces the complexity of code.

    Example

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    int factorial(int n) {
  if (n == 0) {
    return 1;
  } else {
    return n * factorial(n - 1);
  }
}
double e(int n) { // approximate e^n using Taylor series
  double x = 1;
  double res = 0;
  for (int i = 0; i < 10; i++) {
    res = res + (x/factorial(i));
    x = x * n;
  }
  return res;
}
// The n in factorial is different from the n in e.

  • Functions allow programmers to hide how a task is performed. The caller of the function only needs to worry about what the function does. By hiding the details of how, we gain two weapons against code complexity. First, we reduce the amount of information that we need to communicate among programmers. A fellow programmer only needs to read the documentation to understand what the parameters are for, what the return values are. There is no need for a fellow programmer to know about the intermediate variables or the internal computation used to implement the functions. Second, as the design and requirement evolve, the implementation of a function may change. But, as long as the parameters and the return value of a function remains the same, the caller of the function does not have to update the code accordingly. Reducing the need to change as the software evolves reduces the chances of introducing bugs accordingly.

    Example

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    double sinc(double x) {
  return Math.sin(x)/x;
}
// Do you need to know how to implement sin(x)?
// No!  You can simply use it!
// What you need to know is whether x supposed to be in degree or radian.

  • Functions allows us to reduce repetition in our code through code reuse. If we have the same computation that we need to perform repeatedly on different values, we can construct these computations as functions, replacing the values with parameters, and pass in the values as arguments to the function. This approach reduces the amount of boiler-plate code and has two major benefits in reducing code complexity and bugs. First, it makes the code more succinct, and therefore easier to read and understand. Second, it reduces the number of places in our code that we need to modify as the software evolves, and therefore, decreases the chance of introducing new bugs.

    Example

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    double distance(double x1, double y1, double x2, double y2) {
    : // implementation omitted
}
boolean isEquilateral(double x1, double y1,
    double x2, double y2, double x3, double y3) {
  return distance(x1, y1, x2, y2) == distance(x2, y2, x3, y3)
      && distance(x1, y1, x2, y2) == distance(x1, y1, x3, y3);
}
// Define distance once, use it 4 times!
// If we made mistake in distance, we just have to correct in one place
//   instead of 4 different places if we did not use function.

Returning More Than One Return Value?

To return more than one values, we need to use a data type that can store multiple values. At that point, it becomes a question of whether eating rice is eating one meal or hundreds of meals each consisting of a single grain of rice.

Abstraction Barrier

We can imagine an abstraction barrier between the code that calls a function and the code that defines the function body. Above the barrier, the concern is about using the function to perform a task, while below the barrier, the concern is about how to perform the task.

While many of you are used to writing a program solo, in practice, you rarely write a program with contributions from only a single person. The abstraction barrier separates the role of the programmer into two: (i) an implementer, who provides the implementation of the function, and (ii) a client, which uses the function to perform the task. Part of the aim in CS2030/S is to switch your mindset into thinking in terms of these two roles. In fact, in CS2030/S, you will be both but may be restricted to just be either a client or an implementer on specific functionality.

The abstraction barrier thus enforces a separation of concerns between the two roles. The client do not have to care how the implementer implemented the functionality. Similarly, the implementer does not have to care how the client is using the functionality as long as the client is following the specification of the functionality.

The concept of abstraction barrier applies not only to a function, but it can be applied to different levels of abstraction as well. We will see how it is used for a higher-level of abstraction in the next unit.

  1. void in Java is like a true nothingness (unlike Python None or JavaScript undefined). If a function is declared as returning a type void, it cannot even be used in assignment! ↩