categories: book on categorical computability

[Dusko Pavlovic <duskgoo@gmail.com>]

The book
** Programs as diagrams:
** From categorical computability to computable categories
will be available shortly from the publisher (Springer-Nature). It is
a lengthy project, which I never started, but it seems to have gotten
almost halfway. I hope it is of interest. At least there are lots of
pictures in it, including of people you know.

Please email me at dusko@dusko.org if you would like a draft copy.

The back cover blurb:

Programs are written in many languages. It is not always clear what
they mean. In this book, they are drawn as string diagrams, in the
language of categories. Categories display a universal syntax of
mathematics. Computer scientists use them to analyze the program
semantics; programmers to display the syntax of computations. A
picture is worth 1000 words; a diagram 1000 instructions. The
string-diagrammatic depictions of computations can be viewed as
programs in a single-instruction programming language called Run. The
single instruction is called RUN and drawn as a box with a hole for
programs. It represents a universal computer, which turns out to be
unique up to isomorphism in its type universe. Any programming
language is an example, and all of its instructions can be derived
from RUN. There are many programming languages, but they all arise
from the same capability of computing, shared by computers and
programmers.

Computers changed the world. They know more about people than people
about them. In recent years, computation completely changed the
practice of science, but computer science and the theory of
computation barely changed. Computability is still thought of as
invisible ether permeating the avatars of computers: Turing machines,
lambda calculi, cellular automata, your laptop, the DNA transcription
mechanism, neural networks, organic or electronic, and so on. In
reality, there is no invisible ether. Computability is
programmability. A computer inputs a program and outputs a function.
Programs as diagrams display that and show how functions are packed in
boxes and tied by strings. They are computer-drawn, human-generated,
and tested on students.

:)
-- dusko pavlovic


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