A Lambda Term Representation Inspired by Linear Ordered Logic

Abel, Andreas; Kraus, Nicolai

Abstract

We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional information where to cut the variable context into function and argument part. This way, complete information about free variable occurrence is available at each subterm without requiring a traversal, and environments can be kept exact such that they only assign values to variables that actually occur in the associated term. Our approach avoids space leaks in interpreters that build function closures.
In this article, we prove correctness of the new representation and present an experimental evaluation of its performance in a proof checker for the Edinburgh Logical Framework.
Keywords: representation of binders, explicit substitutions, ordered contexts, space leaks, Logical Framework.

• Journal Article Type: Article
• Conference Name: Sixth International Workshop on Logical Frameworks and Meta-languages: Theory and Practice
• Conference Location: Nijmegen, The Netherlands
• Publication Date: Oct 31, 2011
• Deposit Date: Jul 15, 2020
• Publicly Available Date: Jul 24, 2020
• Journal: Electronic Proceedings in Theoretical Computer Science
• Print ISSN: 2075-2180
• Peer Reviewed: Peer Reviewed
• Volume: 71
• Pages: 1-13
• DOI: https://doi.org/10.4204/EPTCS.71.1
• Keywords: Logic in Computer Science; Programming Languages
• Public URL: https://nottingham-repository.worktribe.com/output/2461931
• Publisher URL: http://eptcs.web.cse.unsw.edu.au/paper.cgi?LFMTP11.1
• Related Public URLs: https://arxiv.org/abs/1111.0085v1