Alpha-renaming of higher-order meta-expressions

Abstract

Motivated by tools for automated deduction on functional programming languages and programs, we propose a formalism to symbolically represent α-renamings for meta-expressions. The formalism is an extension of higher-order meta-syntax which allows one to α-rename all valid ground instances of a meta-expression to fulfill the distinct variable convention. The renaming mechanism may be helpful for several reasoning tasks in deduction systems. We present our approach for a meta-language which uses higher-order operators and meta-notation for recursive let-bindings, contexts, and environments. It is used in the LRSX Tool - a tool to reason on the correctness of program transformations in higher-order program calculi with respect to their operational semantics. Besides introducing symbolic α-renamings, we present and analyze algorithms for simplification of α-renamings, matching, rewriting, and checking α-equivalence of symbolically α-renamed meta-expressions.