New relationship between models improves planar lambda calculus theory
On Models of the Planar Lambda Calculus
Logic in Computer Science
Summary
Figuring out how to model certain math problems can be tricky, especially when they involve planar diagrams. The authors link two existing ways of modeling the planar lambda calculus, which is a mathematical system used to study computation with planar constraints. They discovered a connection that provides a clearer representation theorem, similar to one by Scott but adapted to planar cases. This helps better understand how computations can be represented in this particular setting.
What this means in practice
- •For functional programming language designers: Develop more precise models of computation with planar constraints to improve language semantics and compiler design.
- •For diagrammatic reasoning tool developers: Enhance tools that manipulate planar diagrams by using the connection between operad-based and model-based representations.
A theory result. No direct application yet.
Authors
Chad Nester
Abstract
We construct an adjunction relating two approaches to modelling the planar lambda calculus: semi-closed operads and planar lambda-models. We use this to obtain a planar version of Scott's representation theorem.