Relational program derivation is the technique of stepwise refining a relational specification to a program by algebraic rules. The program thus obtained is correct by construction. Meanwhile, dependent type theory is rich enough to express various correctness properties to be verified by the type checker. We have developed a library, AoPA, to encode relational derivations in the dependently ty...

We propose a progressive approach to simplify teaching recursion. It is introduced by means of three instances of increasing level of difficulty. First, recursion is introduced in a “pure” form as it is found in formal grammars; its accompanying mechanisms are related to rewriting. Later, a functional programming language allows defining recursive functions and recursive data types; its mechani...

Everybody knows what recursion is and how it should be implemented in a procedural language. The first analysis of recursion implementations is due Kent Beck [Beck92], but no formalization was given. The other work on an OOP implementation of the subject is due to Boby Wolf [Wolf97], but his work only deals with one aspect of the problem: Structural Recursion. Structural Recursion is a particul...

For general information on bar recursion the reader should consult the papers of Spector [8], where it was introduced, Howard [2] and Tait [11]. In this note we shall prove that the terms of Godel's theory T (in its extensional version of Spector [8]) are closed under the rule BRo•1 of bar recursion of types 0 and 1. Our method of proof is based on the notion of an infinite term introduced by T...