This is a nice find but it is very old news. In mathematics (and mathematical physics), these are called string diagrams. The short and simplified version of

This is a nice find but it is very old news. In mathematics (and mathematical physics), these are called string diagrams. The short and simplified version of the story: The (typed) lambda calculus 'corresponds' to cartesian closed categories. Such CCCs are a special case of monoidal categories. String diagrams are a notation for morphisms in monoidal categories. To get you started, here's a related blog post on the n-category café https://golem.ph.utexas.edu/category/2006/08/categorifying_cccs_seeing_comp.html https://golem.ph.utexas.edu/category/2006/08/categorifying_c...