This chapter gives a short introduction to functional programming languages and their structural operational semantics.

In the first sections we take a look at the characteristic features of programming languages of this kind (Section 12.1) and how they arose (Section 12.2). Then, in Section 12.3, we provide a short introduction to the theoretical foundations of functional programming languages, the λ-calculus.

Finally, in Section 12.4 we introduce the language Flan, which is a subset of ML, and show how to give it a big-step and a small-step semantics.

What is a functional programming language?

In languages such as C, Java, Pascal and Bims variable assignment is a central language construct. A program in any of these languages is essentially a highly structured sequence of variable assignments that change the contents of the store. Languages with this central characteristic are known as imperative languages. It is not particularly surprising that the environment-store model is well suited for the semantics of imperative languages.

However, there are programming languages that take a very different approach. A functional programming language is an expression-based language – a functional program is essentially a collection of declarations of functions, as opposed to a sequence of statements. A function f is a function in the sense of ordinary mathematics – given an argument x, the value of the application f(x) depends only on the value of x.