Rewriting for Monoidal Closed Categories

This paper develops a formal string diagram language for monoidal closed categories. Previous work has shown that string diagrams for freely generated symmetric monoidal categories can be viewed as hypergraphs with interfaces, and the axioms of these categories can be realized by rewriting systems. This work proposes hierarchical hypergraphs as a suitable formalization of string diagrams for monoidal closed categories. We then show double pushout rewriting captures the axioms of these closed categories

String diagrams for free monads (functional pearl)

We show how one can reason about free monads using their universal properties rather than any concrete implementation. We introduce a graphical, two-dimensional calculus tailor-made to accommodate these properties.status: publishe