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Z and Zermelo–Fraenkel

Z is for Z and Zermelo–Fraenkel.

Z, pronounced zed, or Z notation to give it its full name, replaced VDM as the fashionable formal specification language before itself falling out of fashion. Gallina is in fashion today, but you are more likely to have heard of the application software built around it, Coq.

Zermelo–Fraenkel set theory with the axiom of choice is the brand name assembly language of mathematics (there are a number of less well known alternatives). Your author is not aware of any large program written in this assembly language (Principia Mathematica used symbolic logic and over 300 pages to prove that 1+1=2).

While many mathematical theorems can be derived from the axioms contained in Zermelo–Fraenkel, mathematicians consider some to be a lot more interesting than others (just like developers consider some programs to be more interesting than others). There have been various attempts to automate the process of discovering ‘interesting’ theorems, with Eurisko being the most famous and controversial example.

Things to read

Automated Reasoning: Introduction and Applications by Larry Wos, Ross Overbeek, Rusty Lusk, and Jim Boyle. A gentle introduction to automated reasoning based on Otter.

… and it is done.

Readers may have noticed the sparse coverage of languages created between the mid-1990s and 2010. This was the programming language Dark ages, when everybody and his laptop was busy reinventing existing languages at Internet speed; your author willfully tried to ignore new languages during this time. The focus for reinvention has now shifted to web frameworks and interesting new ideas are easier to spot amongst the noise.

Merry Christmas and a happy New Year to you all.

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