We provide formal semantics for a large subset of the Lua programming language, in its version 5.2. We validate our model by mechanizing it and testing it against the test suite of the reference interpreter of Lua, con rming that our model accurately represents the language.In addition, we set us an ambitious goal: to target both a PL semanticist -not necessarily versed in Lua-, and a Lua developer -not necessarily versed in semantic frameworks. To the former, we present the peculiarities of the language, and how we model them in a traditional small-step operational semantics, embedded within Felleisen-Hieb's reduction semantics with evaluation contexts. e mechanization is, naturally, performed in PLT Redex, the de facto tool for mechanizing reduction semantics.To the reader unfamiliar with such concepts, we provide, to our best possible within the space limitations, a gentle introduction of the model. It is our hope that developers of the di erent Lua implementations and dialects understand the model and consider it both for testing their work and for experimenting with new language features. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for pro t or commercial advantage and that copies bear this notice and the full citation on the rst page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is

We provide the semantics of garbage collection (GC) for the Lua programming language. Of interest are the inclusion of finalizers (akin to destructors in object-oriented languages) and weak tables (a particular implementation of weak references). The model expresses several aspects relevant to GC that are not covered in Lua's documentation but that, nevertheless, affect the observable behavior of programs. Our model is mechanized and can be tested with real programs. Our long-term goal is to provide a formalized static analyzer of Lua programs to detect potential dangers. As a first step, we provide a prototype tool, LuaSafe, that typechecks programs to ensure their behavior is not affected by GC. Our model of GC is validated in practice by the experimentation with its mechanization, and in theory by proving several soundness properties.

We propose the first steps in the development of a tool to automate the translation of Redex models into a (hopefully) semantically equivalent model in Coq, and to provide tactics to help in the certification of fundamental properties of such models. The work is heavily based on a model of Redex's semantics developed by Klein et al. By means of a simple generalization of the matching problem in Redex, we obtain an algorithm suitable for its mechanization in Coq, for which we prove its soundness properties and its correspondence with the original solution proposed by Klein et al. In the process, we also adequate some parts of our mechanization to better prepare it for the future inclusion of Redex features absent in the present model, like its Kleene-star operator. Finally, we discuss future avenues of development that are enabled by this work.

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