Function Abstraction and Function Application

Lambda calculus—a model of computation based on functions—serves as the foundation for all functional programming languages. Not surprisingly, functions lie at the heart of the functional paradigm. In this lesson, we’ll study how OCaml implements functions, especially function abstraction and function application. Most of what is described here works similarly to other functional programming languages, such as Haskell and Scala.

Function declaration

Recall that a function abstraction is defined using lambda $\lambda$ in lambda calculus. The equivalence of $\lambda$ in OCaml is the keyword, fun. For example:

fun x -> x *. x

Here, fun declares a function that takes x as a float argument and returns its square. We typically call fun x -> x *. x a function, focusing on the result itself rather than the abstraction process.

As with lambda calculus, functions are first-class citizens in OCaml. They are normal values that are treated no more differently than numbers, strings, or boolean values. In other words, a function is an expression that evaluates to a function value. The following diagram illustrates this:

In imperative programming languages functions are not first-class citizens. Instead, they’re second-class citizens and hence do not evaluate to values. For example, assume we define the following Java function:

double square(double x) {
   return x * x;
}

This ...