Related papers: Implementing hash-consed structures in Coq

We report on four different approaches to implementing hash-consing in Coq programs. The use cases include execution inside Coq, or execution of the extracted OCaml code. We explore the different trade-offs between faithful use of pristine…

Computational content encoded into constructive type theory proofs can be used to make computing experiments over concrete data structures. In this paper, we explore this possibility when working in Coq with chain complexes of infinite type…

Quantum branching programs (quantum binary decision diagrams, respectively) are a convenient tool for examining quantum computations using only a logarithmic amount of space. Recently several types of restricted quantum branching programs…

Good tools can bring mechanical verification to programs written in mainstream functional languages. We use hs-to-coq to translate significant portions of Haskell's containers library into Coq, and verify it against specifications that we…

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from…

We implement extraction of Coq programs to functional languages based on MetaCoq's certified erasure. We extend the MetaCoq erasure output language with typing information and use it as an intermediate representation, which we call…

While the use of formal verification techniques is well established in the development of mission-critical software, it is still rare in the production of most other kinds of software. We share our experience that a formal verification tool…

Current tabling systems suffer from an increase in space complexity, time complexity or both when dealing with sequences due to the use of data structures for tabled subgoals and answers and the need to copy terms into and from the table…

If a code base is so big and complicated that complete mechanical verification is intractable, can we still apply and benefit from verification methods? We show that by allowing a deliberate mechanized formalization gap we can shrink and…

We implement extraction of Coq programs to functional languages based on MetaCoq's certified erasure. As part of this, we implement an optimisation pass removing unused arguments. We prove the pass correct wrt. a conventional call-by-value…

We would like to use the Coq proof assistant to mechanically verify properties of Haskell programs. To that end, we present a tool, named hs-to-coq, that translates total Haskell programs into Coq programs via a shallow embedding. We apply…

We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…

interpreters are tools to compute approximations for behaviors of a program. These approximations can then be used for optimisation or for error detection. In this paper, we show how to describe an abstract interpreter using the type-theory…

This paper introduces Choice Trees (ctrees), a monad for modeling nondeterministic, recursive, and impure programs in Coq. Inspired by Xia et al.'s itrees, this novel data structure embeds computations into coinductive trees with three kind…

Exception handling is provided by most modern programming languages. It allows to deal with anomalous or exceptional events which require special processing. In computer algebra, exception handling is an efficient way to implement the…

Dependently typed programming languages such as Coq, Agda, Idris, and F*, allow programmers to write detailed specifications of their programs and prove their programs meet these specifications. However, these specifications can be violated…

We exploit (co)inductive specifications and proofs to approach the evaluation of low-level programs for the Unlimited Register Machine (URM) within the Coq system, a proof assistant based on the Calculus of (Co)Inductive Constructions type…

This paper presents three closely-related software projects, namely: docker-coq, docker-coq-action, and docker-keeper. It aims at two objectives: provide a high-level description of the available features -- to foster the use of a…

We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain. To do so, we use Coq, which is a proof assistant based on dependent type…

We present a functional programming language for specifying constraints over tree-shaped data. The language allows for Haskell-like algebraic data types and pattern matching. Our constraint compiler CO4 translates these programs into…