Meta-theory à la carte

Se ha publicado un nuevo artículo de automatización del razonamiento en Coq sobre metateorías de lenguajes de programación: Meta-theory à la carte.

Sus autores son Benjamin Delaware, Bruno C. d. S. Oliveira y Tom Schrijvers.

Su resumen es

Formalizing meta-theory, or proofs about programming languages, in a proof assistant has many well-known benefits. However, the considerable effort involved in mechanizing proofs has prevented it from becoming standard practice. This cost can be amortized by reusing as much of an existing formalization as possible when building a new language or extending an existing one. Unfortunately reuse of components is typically ad-hoc, with the language designer cutting and pasting existing definitions and proofs, and expending considerable effort to patch up the results.

This paper presents a more structured approach to the reuse of formalizations of programming language semantics through the composition of modular definitions and proofs. The key contribution is the development of an approach to induction for extensible Church encodings which uses a novel reinterpretation of the universal property of folds. These encodings provide the foundation for a framework, formalized in Coq, which uses type classes to automate the composition of proofs from modular components.

Several interesting language features, including binders and general recursion, illustrate the capabilities of our framework. We reuse these features to build fully mechanized definitions and proofs for a number of languages, including a version of mini-ML. Bounded induction enables proofs of properties for non-inductive semantic functions, and mediating type classes enable proof adaptation for more feature-rich languages.

El marco descrito en el artículo, así como el caso de estudio de mini-ML se encuentra en Meta-Theory à la Carte + Modular mini-ML.