arXiv:1111.0085cs.LO
A Lambda Term Representation Inspired by Linear Ordered Logic
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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.
There are tricky aspects, and I've tripped up a few times over the years. Most annoying is trying to make a 'step' function from lambda terms to lambda terms; we either need to produce a separate closure type instead, or encode those closures to lambda terms (which may defeat…
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