# $\alpha$Check: A mechanized metatheory model-checker

## TL;DR

$ extalpha$Check is an automatic, interactive model-checker for detecting errors in formal systems' metatheoretic properties, providing counterexamples to facilitate debugging of programming language formalisms.

## Contribution

The paper introduces $ extalpha$Check, a novel bounded model-checker for metatheoretic properties specified in nominal logic, capable of automatically finding errors and generating counterexamples.

## Key findings

- The techniques are fast enough for interactive debugging.
- The implementation supports negation-as-failure and negation elimination.
- Experimental results demonstrate practical usability.

## Abstract

The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual problem of searching for errors in such formalizations has attracted comparatively little attention. In this article, we present $\alpha$Check, a bounded model-checker for metatheoretic properties of formal systems specified using nominal logic. In contrast to the current state of the art for metatheory verification, our approach is fully automatic, does not require expertise in theorem proving on the part of the user, and produces counterexamples in the case that a flaw is detected. We present two implementations of this technique, one based on negation-as-failure and one based on negation elimination, along with experimental results showing that these techniques are fast enough to be used interactively to debug systems as they are developed.