scholarly journals Coinductive Natural Semantics for Compiler Verification in Coq

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1573
Author(s):  
Angel Zúñiga ◽  
Gemma Bel-Enguix
Keyword(s):  
Proof Assistant ◽  
Compiler Verification ◽  
Total Correctness

(Coinductive) natural semantics is presented as a unifying framework for the verification of total correctness of compilers in Coq (with the feature that a verified compiler can be obtained). In this way, we have a simple, easy, and intuitive framework; to carry out the verification of a compiler, using a proof assistant in which both cases are considered: terminating and non-terminating computations (total correctness).

Verification of non-functional programs using interpretations in type theory

2003 ◽  
Vol 13 (4) ◽  
pp. 709-745 ◽  
Author(s):  
JEAN-CHRISTOPHE FILLIÂTRE
Keyword(s):  
Static Analysis ◽  
Type Theory ◽  
General Framework ◽  
Specification Language ◽  
Proof Assistant ◽  
Logical Interpretation ◽  
Total Correctness ◽  
The Coq Proof Assistant ◽  
Coq Proof Assistant ◽  
Functional Features

We study the problem of certifying programs combining imperative and functional features within the general framework of type theory. Type theory is a powerful specification language which is naturally suited for the proof of purely functional programs. To deal with imperative programs, we propose a logical interpretation of an annotated program as a partial proof of its specification. The construction of the corresponding partial proof term is based on a static analysis of the effects of the program which excludes aliases. The missing subterms in the partial proof term are seen as proof obligations, whose actual proofs are left to the user. We show that the validity of those proof obligations implies the total correctness of the program. This work has been implemented in the Coq proof assistant. It appears as a tactic taking an annotated program as argument and generating a set of proof obligations. Several nontrivial algorithms have been certified using this tactic.

Verification of Content-Centric Networking Using Proof Assistant

2016 ◽  
Vol E99.B (11) ◽  
pp. 2297-2304
Author(s):  
Sosuke MORIGUCHI ◽  
Takashi MORISHIMA ◽  
Mizuki GOTO ◽  
Kazuko TAKAHASHI
Keyword(s):  
Proof Assistant ◽  
Content Centric Networking

scholarly journals CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

2011 ◽  
Vol 21 (4) ◽  
pp. 827-859 ◽  
Author(s):  
FRÉDÉRIC BLANQUI ◽  
ADAM KOPROWSKI
Keyword(s):  
Term Rewriting ◽  
Automated Verification ◽  
Proof Assistant ◽  
Proof Assistants ◽  
Active Subject ◽  
Turing Complete

Termination is an important property of programs, and is notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting. Over the years, many methods and tools have been developed to address the problem of deciding termination for specific problems (since it is undecidable in general). Ensuring the reliability of those tools is therefore an important issue.In this paper we present a library formalising important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools.The sources are freely available athttp://color.inria.fr/.

Formalization of metatheory of the Lambda Calculus in constructive type theory using the Barendregt variable convention

2021 ◽  
pp. 1-20
Author(s):  
Ernesto Copello ◽  
Nora Szasz ◽  
Álvaro Tasistro
Keyword(s):  
Type Theory ◽  
Lambda Calculus ◽  
Proof Assistant ◽  
First Order ◽  
Constructive Type Theory ◽  
Fundamental Part ◽  
Constructive Type ◽  
Free Variables ◽  
The Church ◽  
Theoretical Results

Abstarct We formalize in Constructive Type Theory the Lambda Calculus in its classical first-order syntax, employing only one sort of names for both bound and free variables, and with α-conversion based upon name swapping. As a fundamental part of the formalization, we introduce principles of induction and recursion on terms which provide a framework for reproducing the use of the Barendregt Variable Convention as in pen-and-paper proofs within the rigorous formal setting of a proof assistant. The principles in question are all formally derivable from the simple principle of structural induction/recursion on concrete terms. We work out applications to some fundamental meta-theoretical results, such as the Church–Rosser Theorem and Weak Normalization for the Simply Typed Lambda Calculus. The whole development has been machine checked using the system Agda.

scholarly journals Proving total correctness of recursive procedures

1990 ◽  
Vol 84 (2) ◽  
pp. 129-162 ◽  
Author(s):  
Pierre America ◽  
Frank de Boer
Keyword(s):  
Total Correctness ◽  
Recursive Procedures

scholarly journals Reliable Reconstruction of Fine-grained Proofs in a Proof Assistant

2021 ◽  
pp. 450-467
Author(s):  
Hans-Jörg Schurr ◽  
Mathias Fleury ◽  
Martin Desharnais
Keyword(s):  
Success Rate ◽  
Failure Rate ◽  
Proof Assistant ◽  
Proof Checking ◽  
Smt Solver ◽  
Fine Grained ◽  
Simple Rules ◽  
Detailed Evaluation ◽  
Reconstruction Time

AbstractWe present a fast and reliable reconstruction of proofs generated by the SMT solver veriT in Isabelle. The fine-grained proof format makes the reconstruction simple and efficient. For typical proof steps, such as arithmetic reasoning and skolemization, our reconstruction can avoid expensive search. By skipping proof steps that are irrelevant for Isabelle, the performance of proof checking is improved. Our method increases the success rate of Sledgehammer by halving the failure rate and reduces the checking time by 13%. We provide a detailed evaluation of the reconstruction time for each rule. The runtime is influenced by both simple rules that appear very often and common complex rules.

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