O.LISP theoretical basis and description

Abstract

We describe, in this article, O. LISP: a functional language based on the manipulation of expressions issued from the syntax of lambda-calculus on occurrence (λ()-caculus [8]). In this theoretical framework, the functions are constructed without variables, we essentially use indexes of occurrences and basic terms.In O. LISP new primitives, like SUBO or UNSUBO, realize, respectively, a substitution (without variable, by creating links between numbers of occurrences and arguments) and a locking on some of these links.A first version of O. LISP has been implemented on a LISP interpret We present, at the end of this article, some examples which are extracted from this implementation.