Related papers: Formal verification in Coq of program properties i…
The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity…
We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to…
We introduce a library which provides an abstract data type of environments, as a functor parameterized by a module defining variables, and a function which builds environments for such variables with any Type of type. Usual operations over…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Libraries of formalized mathematics use a possibly broad range of different representations for a same mathematical concept. Yet light to major manual input from users remains most often required for obtaining the corresponding variants of…
This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
Formal software verification uses mathematical techniques to establish that software has certain properties. For example, that the behaviour of a software system satisfies certain logically-specified properties. Formal methods have a long…
Applications like program synthesis sometimes require proving that a property holds for all of the infinitely many programs described by a grammar - i.e., an inductively defined set of programs. Current verification frameworks…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools…
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive families within type theory. By elaborating an inductive definition -- a…
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion…
Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed…
Software contracts allow programmers to state rich program properties using the full expressive power of an object language. However, since they are enforced at runtime, monitoring contracts imposes significant overhead and delays error…
In this paper we present a translation from the quantum programming language Quipper to the QPMC model checker, with the main aim of verifying Quipper programs. Quipper is an embedded functional programming language for quantum computation.…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
A reliable technique for deductive program verification should be proven sound with respect to the semantics of the programming language. For each different language, the construction of a separate soundness proof is often a laborious…