Related papers: Structural abstract interpretation, A formal study…
Neural networks have in recent years shown promise for helping software engineers write programs and even formally verify them. While semantic information plays a crucial part in these processes, it remains unclear to what degree popular…
This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for…
Recently, we developed an automated theorem prover for projective incidence geometry. This prover, based on a combinatorial approach using matroids, proceeds by saturation using the matroid rules. It is designed as an independent tool,…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
Compilers are a prime target for formal verification, since compiler bugs invalidate higher-level correctness guarantees, but compiler changes may become more labor-intensive to implement, if they must come with proof patches. One appealing…
Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory…
We develop a linear logical framework within the Hybrid system and use it to reason about the type system of a quantum lambda calculus. In particular, we consider a practical version of the calculus called Proto-Quipper, which contains the…
Hoare logic provides a syntax-oriented method to reason about program correctness and has been proven effective in the verification of classical and probabilistic programs. Existing proposals for quantum Hoare logic either lack completeness…
We present a refinement of the Calculus of Inductive Constructions in which one can easily define a notion of relational parametricity. It provides a new way to automate proofs in an interactive theorem prover like Coq.
We provide a novel notion of what it means to be interpretable, looking past the usual association with human understanding. Our key insight is that interpretability is not an absolute concept and so we define it relative to a target model,…
The set of integer number lists with finite length, and the set of binary trees with integer labels are both countably infinite. Many inductively defined types also have countably many elements. In this paper, we formalize the syntax of…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
Region-based type systems are a powerful tool for various kinds of program analysis. We introduce a new inference algorithm for region types based on an abstract notion of environment transformation. It analyzes the code of a method only…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…
Using a call-by-value functional language as an example, this article illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling it to describe diverging evaluations in addition to terminating…
The theory of the call-by-value lambda-calculus relies on weak evaluation and closed terms, that are natural hypotheses in the study of programming languages. To model proof assistants, however, strong evaluation and open terms are…
The use of formal analysis tools on models or source code often requires the availability of auxiliary invariants about the studied system. Abstract interpretation is currently one of the best approaches to discover useful invariants,…
We present a novel general resource analysis for logic programs based on sized types.Sized types are representations that incorporate structural (shape) information and allow expressing both lower and upper bounds on the size of a set of…