ترغب بنشر مسار تعليمي؟ اضغط هنا

Touring the MetaCoq Project (Invited Paper)

101   0   0.0 ( 0 )
 نشر من قبل EPTCS
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
والبحث باللغة English
 تأليف Matthieu Sozeau




اسأل ChatGPT حول البحث

Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves are seldom verified, although they take a major share of the trusted code base in any such certification effort. In this area, proof assistants based on Higher-Order Logic enjoy stronger guarantees, as self-certified implementations have been available for some years. One cause of this difference is the inherent complexity of dependent type theories together with their extensions with inductive types, universe polymorphism and complex sort systems, and the gap between theory on paper and practical implementations in efficient programming languages. MetaCoq is a collaborative project that aims to tackle these difficulties to provide the first fully-certified realistic implementation of a type checker for the full calculus underlying the Coq proof assistant. To achieve this, we refined the sometimes blurry, if not incorrect, specification and implementation of the system. We show how theoretical tools from this community such as bidirectional type-checking, Tait-Martin-Lof/Takahashis confluence proof technique and monadic and dependently-typed programming can help construct the following artefacts: a specification of Coqs syntax and type theory, the Polymorphic Cumulative Calculus of (Co)-Inductive Constructions (PCUIC); a monad for the manipulation of raw syntax and interaction with the Coq system; a verification of PCUICs metatheory, whose main results are the confluence of reduction, type preservation and principality of typing; a realistic, correct and complete type-checker for PCUIC; a sound type and proof erasure procedure from PCUIC to untyped lambda-calculus, i.e., the core of the extraction mechanism of Coq.



قيم البحث

اقرأ أيضاً

84 - Naoki Kobayashi 2021
In this article, we give an overview of our project on higher-order program verification based on HFL (higher-order fixpoint logic) model checking. After a brief introduction to HFL, we explain how it can be applied to program verification, and summarize the current status of the project.
RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higher-dimensional constructions inspired by homotopy type theory. In the style of Nuprl, RedPRL users employ tactics to establish b ehavioral properties of cubical functional programs embodying the constructive content of proofs. Notably, RedPRL implements a two-level type theory, allowing an extensional, proof-irrelevant notion of exact equality to coexist with a higher-dimensional proof-relevant notion of paths.
111 - Giselle Reis 2021
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be designed a s a set of rules such that proofs using those rules are correct by construction. Therefore, one must consider all ways these rules can interact and prove that they satisfy certain properties which makes them well-behaved. This is called the meta-theory of a proof system. Meta-theory proofs typically involve many cases on structures with lots of symbols. The majority of cases are usually quite similar, and when a proof fails, it might be because of a sub-case on a very specific configuration of rules. Developing these proofs by hand is tedious and error-prone, and their combinatorial nature suggests they could be automated. There are various approaches on how to automate, either partially or completely, meta-theory proofs. In this paper, I will present some techniques that I have been involved in for facilitating meta-theory reasoning.
Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction. In this pap er we overview some of our results for both of these scenarios when analysing programs with loops. The class of loops we consider can be modelled by a system of linear recurrence equations with constant coefficients, called C-finite recurrences. We first describe an algorithmic approach for synthesising all polynomial equality invariants of such non-deterministic numeric single-path loops. By reverse engineering invariant synthesis, we then describe an automated method for synthesising program loops satisfying a given set of polynomial loop invariants. Our results have applications towards proving partial correctness of programs, compiler optimisation and generating number sequences from algebraic relations. This is a preprint that was invited for publication at VMCAI 2021.
The original paper on Mixed Sessions introduce the side A of the tape: there is an encoding of classical sessions into mixed sessions. Here we present side B: there is a translation of (a subset of) mixed sessions into classical session types. We pro ve that the translation is a minimal encoding, according to the criteria put forward by Kouzapas, Perez, and Yoshida.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا