Summary: DAVID ALBRECHT Curry--Howard terms for
FRANK A. B ¨
AUERLE Linear Logic \Lambda
JOHN N. CROSSLEY
JOHN S. JEAVONS
Abstract. In this paper we 1. provide a natural deduction system for
full first­order linear logic, 2. introduce Curry--Howard--style terms for this
version of linear logic, 3. extend the notion of substitution of Curry­Howard
terms for term variables, 4. define the reduction rules for the Curry--Howard
terms and 5. outline a proof of the strong normalization for the full system
of linear logic using a development of Girard's candidates for reducibility,
thereby providing an alternative to Girard's proof using proof--nets.
Key words: Linear Logic, Curry Howard Terms, and Strong Normal­
ization.
1 Introduction
The logical system is a further development of those of Troelstra [10] and
Benton et al. [1] and the rules follow fairly traditional patterns.
On the other hand the new Curry--Howard terms involve substantial
modifications to the lambda calculus, in particular the introduction of new
operators ', Ÿ, ø and ! with their associated reduction rules. More impor­

Source: Albrecht, David - Caulfield School of Information Technology, Monash University

Collections: Computer Technologies and Information Sciences