arXiv subjects

Jesse Sigal

Publications and source records attributed to Jesse Sigal.

3 recordsLinked to original sources

arXiv2023

Duoidally enriched Freyd categories

Freyd categories provide a semantics for first-order effectful programming languages by capturing the two different orders of evaluation for products. We enrich Freyd categories in a duoidal category, which provides a new, third choice of parallel composition. Duoidal categories have two monoidal structures which account for the sequential and parallel compositions. The traditional setting is recovered as a full coreflective subcategory for a judicious choice of duoidal category. We give several worked examples of this uniform framework, including the parameterised state monad, basic separation semantics for resources, and interesting cases of change of enrichment

cs.PL↗

arXiv2022

Conceptual Mathematics via Literate Programming

Recent developments in computer programming and in mathematics suggest that there is a strong case for a new way of introducing programming to enhance the learning of school mathematics. The article describes a collaboration of mathematics and computer science teachers to solve the Josephus problem. We demonstrate how a programming approach based on both types and functions can make a vastly improved contribution to learning mathematics than the less successful use of conventional computer programming in Scratch.

math.HO↗

arXiv2021

Automatic Differentiation via Effects and Handlers: An Implementation in Frank

Automatic differentiation (AD) is an important family of algorithms which enables derivative based optimization. We show that AD can be simply implemented with effects and handlers by doing so in the Frank language. By considering how our implementation behaves in Frank's operational semantics, we show how our code performs the dynamic creation of programs during evaluation.

cs.PL↗