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Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…

Deductive verification has become a mature paradigm for the verification of industrial software. Applying deductive verification, however, requires that every function in the code base is annotated with a function contract specifying its…

This paper introduces a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification…

We present a deep embedding of Bellantoni and Cook's syntactic characterization of polytime functions. We prove formally that it is correct and complete with respect to the original characterization by Cobham that required a bound to be…

The Calculus of Audited Units (CAU) is a typed lambda calculus resulting from a computational interpretation of Artemov's Justification Logic under the Curry-Howard isomorphism; it extends the simply typed lambda calculus by providing…

Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a…

This study delves into the capabilities and limitations of Large Language Models (LLMs) in the challenging domain of conditional question-answering. Utilizing the Conditional Question Answering (CQA) dataset and focusing on generative…

We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…

The goal of our Macro Lambda Calculus project (MLC) is to encode lambda terms into interaction nets. Its software implementation will accept input in the notation similar to lambda calculus allowing macro definitions. Output is similar to…

LTL3 is a multi-valued variant of Linear-time Temporal Logic for runtime verification applications. The semantic descriptions of LTL3 in previous work are given only in terms of the relationship to conventional LTL. Our approach, by…

Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…

In mathematics, it is common practice to have several constructions for the same objects. Mathematicians will identify them modulo isomorphism and will not worry later on which construction they use, as theorems proved for one construction…

Large language models (LLMs) can potentially help with verification using proof assistants by automating proofs. However, it is unclear how effective LLMs are in this task. In this paper, we perform a case study based on two mature Rocq…

A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…

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…

Automating the translation of natural language (NL) software requirements into formal specifications remains a critical challenge in scaling formal verification practices to industrial settings, particularly in safety-critical domains.…

The denotational semantics of the untyped lambda-calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent…

Timed Automata (TA) are a very popular modeling formalism for systems with time-sensitive properties. A common task is to verify if a network of TA satisfies a given property, usually expressed in Linear Temporal Logic (LTL), or in a subset…

Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exact real number computation. I have implemented a library for reasoning and computing with complete…

LLM-based function calling enables intelligent agents to interact with external tools and environments, yet autoregressive decoding imposes a fundamental latency bottleneck that limits real-time applications such as embodied intelligence,…