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Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
We present the quantum programming language cQPL which is an extended version of QPL [P. Selinger, Math. Struct. in Comp. Sci. 14(4):527-586, 2004]. It is capable of quantum communication and it can be used to formulate all possible quantum…
We show that recent approaches of static analysis based on quantitative typing systems can be extended to programming languages with global state. More precisely, we define a call-by-value language equipped with operations to access a…
Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this…
We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. The key idea is to define two systems, one modelling…
Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple foundational model for functional computation. It is closely related to lambda calculus and term rewriting, but it has no variable binding and no pattern matching. It…
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…
We describe an application of Prolog: a type checking tool for the Q functional language. Q is a terse vector processing language, a descendant of APL, which is getting more and more popular, especially in financial applications. Q is a…
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…
In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
Human-AI conversation frequently relies on quoting earlier text-"check it with the formula I just highlighted"-yet today's large language models (LLMs) lack an explicit mechanism for locating and exploiting such spans. We formalise the…
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.…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
Proofs in proof assistants like Rocq can be brittle, breaking easily in response to changes. To address this, recent work introduced an algorithm and tool in Rocq to automatically repair broken proofs in response to changes that correspond…
Qualitative relationships illustrate how changing one property (e.g., moving velocity) affects another (e.g., kinetic energy) and constitutes a considerable portion of textual knowledge. Current approaches use either semantic parsers to…
Short Text Classification (STC) is crucial for processing and understanding the brief but substantial content prevalent on contemporary digital platforms. The STC encounters difficulties in grasping the semantic and syntactic intricacies,…
Competency Questions (CQs) are pivotal in knowledge engineering, guiding the design, validation, and testing of ontologies. A number of diverse formulation approaches have been proposed in the literature, ranging from completely manual to…
Large language models (LLMs) have shown remarkable performance in various domains, but they are constrained by massive computational and storage costs. Quantization, an effective technique for compressing models to fit resource-limited…