While Programs

Abstract

We can relate the primitive and a-recursive functions of Gödel to more modern concepts. Consider a simple programming language with variables Var =|x, y, ...} ranging over ℕ containing the following constructs:

• (i) simple assignments x := 0 x := y + 1 x := y

• (ii) sequential composition p ; q

• (iii) conditional if x < y then p else q

• (iv) for loop for y do p

• (v) while loop while x < y do p

In (iii) and (v), the relation < can be replaced by any one of >, >,, <, =, or ≠. In (ii) we can parenthesize using begin ... end if necessary.