Soundness of the simply typed lambda calculus in ACL2

Authors:
Sol Swords;William R. Cook
Affiliations:
University of Texas at Austin;University of Texas at Austin
Venue:
ACL2 '06 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications
Year:
2006

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Abstract

To make it practical to mechanize proofs in programming language metatheory, several capabilities are required of the theorem proving framework. One must be able to represent and efficiently reason about complex recursively-defined expressions, define arbitrary induction schemes including mutual inductions over several objects and inductions over derivations, and reason about variable bindings with minimal overhead. We introduce a method for performing these proofs in ACL2, including a macro which automates the process of defining functions and theorems to facilitate reasoning about recursive data types. To illustrate this method, we present a proof in ACL2 of the soundness of the simply typed λ-calculus.