Related papers: A Categorical Programming Language
This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri…
Relational parametricity was first introduced by Reynolds for System F. Although System F provides a strong model for the type systems at the core of modern functional programming languages, it lacks features of daily programming practice…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
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…
Derivations provide a way of transporting ideas from the calculus of manifolds to algebraic settings where there is no sensible notion of limit. In this paper, we consider derivations in certain monoidal categories, called codifferential…
In Categorial Topology, given a category (as a "geometric object") we can consider its properties preserved under continuous action (a "deformation") of a comma-propagation operation. However, the Metacategory space, valid for all…
We prove an analogue of Morley's categoricity theorem where cardinality is replaced by the recursion-theoretic notion of arithmetic degree. We say that a complete arithmetically definable theory $T$ is $D$-categorical if any two…
This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to…
Databases have been studied category-theoretically for decades. The database schema -- whose purpose is to arrange high-level conceptual entities -- is generally modeled as a category or sketch. The data itself, often called an instance, is…
We present new induction principles for the syntax of dependent type theories, which we call relative induction principles. The result of the induction principle relative to a functor F into the syntax is stable over the codomain of F. We…
Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…
Category theory provides an alternative to Hilbert's Formal Axiomatic method and goes beyond Mathematical Structuralism
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
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…
After a one-year long effort of research on the field, we developed a machine learning-based classifier, tailored to predict whether a mechanical water meter would fail with passage of time and intensive use as well. A recurrent deep neural…
Affine type systems are substructural type systems where copying of information is restricted, but discarding of information is permissible at all types. Such type systems are well-suited for describing quantum programming languages,…