A Finitary Version of the Calculus of Partial Inductive Defintions

The theory of partial inductive definitions is a mathematical formalism which has proved to be useful in a number of different applications. The fundamentals of the theory is shortly described. Partial inductive definitions and their associated calculi are essentially infinitary. To implement them on a computer, they must be given a formal finitary representation. We present such a finitary representation, and prove its soundness. The finitary representation is given in a form with and without variables. Without variables, derivations are unchanging entities. With variables, derivations can contain logical variables that can become bound by a binding environment that is extended as the derivation is constructed. The variant with variables is essentially a generalization of the pure GCLA programming language.