Alpha-renaming of higher-order meta-expressions

Abstract

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. e formalism is an extension of usual higher-order meta-syntax which allows to α-rename all valid ground instances of a metaexpression to ful ll the distinct variable convention. e renaming mechanism may be helpful for several reasoning tasks in deduction systems. We present our approach for a meta-language which uses higher-order abstract syntax and a 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 a formalism to represent symbolic α-renamings, we present and analyze algorithms for simpli cation of α-renamings, matching, rewriting, and checking α-equivalence of symbolically α-renamed meta-expressions.

Automating the Diagram Method to Prove Correctness of Program Transformations

“…However, this problem can be solved by α-renaming the expression such that the DVC holds. That is why symbolic α-renaming (see [12]) is built into the LRSX Tool which is quite more complex than usual α-renaming, since it has to be performed on the meta syntax, e.g. internally symbolic renamings of the form α • S are required.…”

“…In previous work, we published results on core algorithms that are used in the tool. In [18] the underlying unification-algorithm was defined and analysed, in [13,14] a matching algorithm was developed, in [12] a procedure to alpha-rename meta-expressions was presented, and in the work [11] the encoding of the diagrams as term rewrite systems for automating the induction step was developed. However, none of these works presents the full automation of the method.…”