The class started with a musing on notation — an example present in the Program Design by Calculation book (pag. 20, excerpt about polynomial notation). There were some good quotes, as in the previous classes, but I can only paraphrase. The first:

The concept of API was first invented by mathematicians: upon receiving something in format A, to provide something in format B.

The functions are, in the book, referred to between (2.26) and (2.32).

There were a few interesting ideas that I noted down.

this would correspond to synchronous parallel composition, with name f split g.

whereas

would be assynchronous parallel composition: product of f and g.