Related papers: Evaluating Linear Functions to Symmetric Monoidal …

We study monoidal profunctors as a tool to reason and structure pure functional programs both from a categorical perspective and as a Haskell implementation. From the categorical point of view we approach them as monoids in a certain…

The fact that Applicative type class allows one to express simple parsers in a variable-less combinatorial style is well appreciated among Haskell programmers for its conceptual simplicity, ease of use, and usefulness for semi-automated…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

We introduce DisCoPy, an open source toolbox for computing with monoidal categories. The library provides an intuitive syntax for defining string diagrams and monoidal functors. Its modularity allows the efficient implementation of…

To formalize calculations in linear algebra for the development of efficient algorithms and a framework suitable for functional programming languages and faster parallelized computations, we adopt an approach that treats elements of linear…

In this document, we propose a description, via a Haskell implementation, of a generalization of the notion of regular expression allowing us to group the definitions and the methods of (tree or word) automata constructions over one generic…

We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…

This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…

The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we…

We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…

Applied category theory provides powerful mathematical tools for modelling processes and their composition. Symmetric monoidal categories, which involve series and parallel composition, are particularly well-suited for describing the…

This work is about diagrammatic languages, how they can be represented, and what they in turn can be used to represent. More specifically, it focuses on representations and applications of string diagrams. String diagrams are used to…

Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…

Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we…

Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…

Haskell functions are defined as a series of clauses consisting of patterns that are matched against the arguments in the order of definition. In case an input is not matched by any of the clauses, an error occurs. Therefore it is desirable…

Datalog is a lightweight logic programming language, based on the logic of Horn clauses. Lean, on the other hand, is a proof assistant system and language based on the Calculus of Inductive Constructions (CIC). Datalog is more constrained…

We give an exposition of the semantics of the simply-typed lambda-calculus, and its linear and ordered variants, using multi-ary structures. We define universal properties for multicategories, and use these to derive familiar rules for…

This paper introduces an inherently strict presentation of categories with products, coproducts, or symmetric monoidal products that is inspired by file systems and directories. Rather than using nested binary tuples to combine objects or…

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…