The New Rewriting Engine of Dedukti

International audienceDedukti is a type-checker for the λΠ-calculus modulo rewriting, an extension of Edinburgh’s logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF terms and types according to the rewrite rules given by the user.A key component of this engine is the matching algorithm to find which rules can be fired. In thispaper, we describe the class of rewrite rules supported by Dedukti and the new implementation ofthe matching algorithm. Dedukti supports non-linear rewrite rules on terms with binders usinghigher-order pattern-matching as in Combinatory Reduction Systems (CRS). The new matchingalgorithm extends the technique of decision trees introduced by Luc Maranget in the OCamlcompiler to this more general context

Catala: A Programming Language for the Law

Law at large underpins modern society, codifying and governing many aspects of citizens' daily lives. Oftentimes, law is subject to interpretation, debate and challenges throughout various courts and jurisdictions. But in some other areas, law leaves little room for interpretation, and essentially aims to rigorously describe a computation, a decision procedure or, simply said, an algorithm. Unfortunately, prose remains a woefully inadequate tool for the job. The lack of formalism leaves room for ambiguities; the structure of legal statutes, with many paragraphs and sub-sections spread across multiple pages, makes it hard to compute the intended outcome of the algorithm underlying a given text; and, as with any other piece of poorly-specified critical software, the use of informal language leaves corner cases unaddressed. We introduce Catala, a new programming language that we specifically designed to allow a straightforward and systematic translation of statutory law into an executable implementation. Catala aims to bring together lawyers and programmers through a shared medium, which together they can understand, edit and evolve, bridging a gap that often results in dramatically incorrect implementations of the law. We have implemented a compiler for Catala, and have proven the correctness of its core compilation steps using the F* proof assistant. We evaluate Catala on several legal texts that are algorithms in disguise, notably section 121 of the US federal income tax and the byzantine French family benefits; in doing so, we uncover a bug in the official implementation. We observe as a consequence of the formalization process that using Catala enables rich interactions between lawyers and programmers, leading to a greater understanding of the original legislative intent, while producing a correct-by-construction executable specification reusable by the greater software ecosystem

Abstract Representation of Binders in OCaml using the Bindlib Library

In Proceedings LFMTP 2018, arXiv:1807.01352International audienceThe Bindlib library for OCaml provides a set of tools for the manipulation of data structures with variable binding. It is very well suited for the representation of abstract syntax trees, and has already been used for the implementation of half a dozen languages and proof assistants (including a new version of the logical framework Dedukti). Bindlib is optimised for fast substitution, and it supports variable renaming. Since the representation of binders is based on higher-order abstract syntax, variable capture cannot arise during substitution. As a consequence, variable names are not updated at substitution time. They can however be explicitly recomputed to avoid "visual capture" (i.e., distinct variables with the same apparent name) when a data structure is displayed