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In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
We describe techniques for synthesis and verification of recursive functional programs over unbounded domains. Our techniques build on top of an algorithm for satisfiability modulo recursive functions, a framework for deductive synthesis,…
The requirements engineering (RE) phase is pivotal in developing high-quality software. Integrating advanced modelling techniques with large language models (LLMs) and formal verification in a logical style can significantly enhance this…
In this paper we give a preliminary formalization of the p-adic numbers, in the context of the second author's univalent foundations program. We also provide the corresponding code verifying the construction in the proof assistant Coq.…
One of the effective model checking methods is to utilize the efficient decision procedure of SAT (or SMT) solvers. In a SAT-based model checking, a system and its property are encoded into a set of logic formulas and the safety is checked…
Research in uncertainty quantification (UQ) for large language models (LLMs) is increasingly important towards guaranteeing the reliability of this groundbreaking technology. We explore the integration of LLM UQ methods in argumentative…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, equality is appallingly syntactic and, as a result, exploiting equivalences is cumbersome at best.…
Reinforcement learning algorithms solve sequential decision-making problems in probabilistic environments by optimizing for long-term reward. The desire to use reinforcement learning in safety-critical settings inspires a recent line of…
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…
We develop a new intermediate weak memory model, IMM, as a way of modularizing the proofs of correctness of compilation from concurrent programming languages with weak memory consistency semantics to mainstream multi-core architectures,…
We study subsystems of open induction which are strongly connected to methods of automated inductive theorem proving. Specifically, we consider systems obtained from restricting induction to atoms, literals, clauses, and dual clauses. We…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…
Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…
Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…
We present an implementation in the Coq proof assistant of type directed partial evaluation (TDPE) algorithms for call-by-name and call-by-value versions of shift and reset delimited control operators, and in presence of strong sum types.…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…
Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the…
In order to avoid well-know paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type$_0$ : Type$_1$ :…