Related papers: Towards a Higher-Order Bialgebraic Denotational Se…
In this paper we show how the abstract behaviours of higher-order systems can be modelled as final coalgebras of suitable behavioural functors. These functors have the challenging peculiarity to be circularly defined with their own final…
This paper studies context bisimulation for higher-order processes, in the presence of parameterization (viz. abstraction). We show that the extension of higher-order processes with process parameterization retains the characterization of…
Semantic parsing aims to map natural language utterances onto machine interpretable meaning representations, aka programs whose execution against a real-world environment produces a denotation. Weakly-supervised semantic parsers are trained…
Order-sorted algebras and many sorted algebras exist in a long history with many different implementations and applications. A lot of language specifications have been defined in order-sorted algebra frameworks such as the language…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
To develop a full abstract denotational model of a process language based on prebisimulation preorder, its behavioural semantics has two problems: (1) Two processes related by a standard denotational interpretation afford the same finite…
The polarized SILL programming language uniformly integrates functional programming and session-typed message-passing concurrency. It supports general recursion, asynchronous and synchronous communication, and higher-order programs that…
Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages…
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…
This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We…
A bialgebra is a structure which is simultaneously an algebra and a coalgebra, such that the algebraic and coalgebraic parts are "compatible". Bialgebras are normally studied over a field or commutative ring. In this paper, we show how to…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics . They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability.…
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…
Operational semantics has established itself as a flexible but rigorous means to describe the meaning of programming languages. Oftentimes, it is felt necessary to keep a semantics small, for example to facilitate its use for model checking…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…