Related papers: Monoidal computer III: A coalgebraic view of compu…
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…
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
In the first part, we develop layered monoidal theories - a generalisation of monoidal theories combining descriptions of a system at several levels. Via their representation as string diagrams, monoidal theories provide a graphical syntax…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
Computer science provides an in-depth understanding of technical aspects of programming concepts, but if we want to understand how programming concepts evolve, how programmers think and talk about them and how they are used in practice, we…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Multimodal deep learning systems which employ multiple modalities like text, image, audio, video, etc., are showing better performance in comparison with individual modalities (i.e., unimodal) systems. Multimodal machine learning involves…
One of the aims of Implicit Computational Complexity is the design of programming languages with bounded computational complexity; indeed, guaranteeing and certifying a limited resources usage is of central importance for various aspects of…
This paper describes a categorical interpretation of the Wolfram Language and introduces a simple implementation of monadic types and the "do" notation. The monadic style of programming combined with the many built in functions of the…
Theoretical computer science discusses foundational issues about computations. It asks and answers questions such as "What is a computation?", "What is computable?", "What is efficiently computable?","What is information?", "What is…
We give an alternate conception of string diagrams as labeled 1-dimensional oriented cobordisms, the operad of which we denote by Cob/O, where O is the set of string labels. The axioms of traced (symmetric monoidal) categories are fully…
We investigate the complexity of isomorphisms of computable structures on cones in the Turing degrees. We show that, on a cone, every structure has a strong degree of categoricity, and that degree of categoricity is $\bf{0^{(\alpha)}}$ for…
In this paper, we extend diagrammatic reasoning in monoidal categories with algebraic operations and equations. We achieve this by considering monoidal categories that are enriched in the category of Eilenberg-Moore algebras for a monad.…
Previous computation models either have equivalent abilities in representing all computations but fail to provide primitive operators for programming complex algorithms or lack generalized expression ability to represent newly-added…
Cognitive BASIC is a minimal, BASIC-style prompting language and in-model interpreter that structures large language model (LLM) reasoning into explicit, stepwise execution traces. Inspired by the simplicity of retro BASIC, we repurpose…
We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which…
The Turing Machine is the paradigmatic case of computing machines, but there are others such as analogical, connectionist, quantum and diverse forms of unconventional computing, each based on a particular intuition of the phenomenon of…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
It is informally understood that the purpose of modal type constructors in programming calculi is to control the flow of information between types. In order to lend rigorous support to this idea, we study the category of classified sets, a…