I wanted to explore the mathematics behind computational effects and their relation to algebra.
My project is a report that consists of answers to questions such as,
- How can we interpret functional programming constructs through the lens of category theory?
- How is universal algebra related to computational effects?
- How to encode effects using lawvere theories?
- What's the relationship between monads and lawvere theory?
- Why are continuations special?
The report is based on papers by John Powers, Gordon Plotkin, and Martin Hyland on the relevance of universal algebra to computational effects, and the appendix consists of my understanding of category-theoretic concepts needed as preliminary for the material.