Related papers: Extracting Herbrand trees from Coq

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…

Programs that manipulate tree-shaped data structures often require complex, specialized proofs that are difficult to generalize and automate. This paper introduces a unified, foundational approach to verifying such programs. Central to our…

Test or prove? These two approaches to software verification have long been presented as opposites. One is dynamic, the other static: a test executes the program, a proof only analyzes the program text. A different perspective is emerging,…

We are interested in identifying and enforcing the isolation requirements of a concurrent program, i.e., concurrency control that ensures that the program meets its specification. The thesis of this paper is that this can be done…

It is well known in the Constraint Programming community that any non-binary constraint satisfaction problem (with finite domains) can be transformed into an equivalent binary one. One of the most well-known translations is the Hidden…

How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively one can check that the output produced for a…

We describe a method for building composable and extensible verification procedures within the Coq proof assistant. Unlike traditional methods that rely on run-time generation and checking of proofs, we use verified-correct procedures with…

We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…

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…

Dijkstra observed that verifying correctness of a program is difficult and conjectured that derivation of a program hand-in-hand with its proof of correctness was the answer. We illustrate this goal-oriented approach by applying it to the…

Programmers often leverage data structure libraries that provide useful and reusable abstractions. Modular verification of programs that make use of these libraries naturally rely on specifications that capture important properties about…

We describe several views of the semantics of a simple programming language as formal documents in the calculus of inductive constructions that can be verified by the Coq proof system. Covered aspects are natural semantics, denotational…

Development of energy and performance-efficient embedded software is increasingly relying on application of complex transformations on the critical parts of the source code. Designers applying such nontrivial source code transformations are…

We have developed a web-based pedagogical proof assistant, the Proof Tree Builder, that lets you apply rules upwards from the initial goal in sequent calculus and Hoare logic for a simple imperative language. We equipped our tool with a…

Herbrand's theorem is one of the most fundamental insights in logic. From the syntactic point of view, it suggests a compact representation of proofs in classical first- and higher-order logic by recording the information of which instances…

In this paper, we study classes of structures and individual structures for which programs implementing functions defined everywhere are equivalent to finite tree-programs. The programs under consideration may have cycles and at most…

Software verification is a tedious process that involves the analysis of multiple failed verification attempts, and adjustments of the program or specification. This is especially the case for complex requirements, e.g., regarding security…

We give a number of formal proofs of theorems from the field of computable analysis. Many of our results specify executable algorithms that work on infinite inputs by means of operating on finite approximations and are proven correct in the…

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…

This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we…