Recursive Functions

In the previous chapters, we discussed the notion of a computable function and characterised this class of functions as the ones that can be defined via Turing machines or the β-calculus. In this chapter, we give an alternative characterisation of computable functions based on the notion of a recursive function. Usually, we say that a function is recursive if it “calls itself”. Recursive functions are functions for which the result for a certain argument depends on the results obtained for other (smaller in some sense) arguments. Recursion is a very useful tool in modern programming languages, in particular when dealing with inductive data structures such as lists, trees, etc.