Which is worse? Ignorance or apathy? Who knows? Who cares?
Murdoch James Gabbay
Everybody calls me Jamie.
Research and (academic) publications
I study the foundations of computer science. I’m known for inventing nominal techniques and nominal sets based on the Gabbay-Pitts model of naming and abstraction in Fraenkel-Mostowski set theory, for which Andrew and I received the 2019 Alonzo Church Award for Outstanding Contributions to Logic and Computation.
This work was initially with Andrew Pitts; then Mark Shinwell, Christian Urban, and James Cheney joined in.
DBLP says I’ve published with twenty-nine coauthors, including Maribel Fernández, Ian Mackie, Michel Reniers, Mohammed Reza Mousavi, Aad Mathijssen, Martin Hofmann, Stéphane Lengrand, Gilles Dowek, Michael Gabbay, Dominic Mulligan, Vincenzo Ciancia, Daniela Petrişan, Tadeusz Litak, Elliot Fairweather, Matteo Cimini, Claus-Peter Wirth, Dan Ghica, Aleksandar Nanevski, and Peter Kropholler.
Other publication-related items:
Since 2018 I’ve become interested in blockchains, and also the economic theory of Karl Marx (as applied to blockchains). More details on my publications list.
I’ve been published in the Times Higher Education. Here is a permalink to the article on how "The false market in degrees is ruining higher education". Many thanks to an excellent editor.
I claim to have a proof of the consistency of Quine’s NF, which has been a open problem in set theory since 1937. The claimed proof is written in this paper. Interested in discussing the proof-method, or formalising it in a theorem-prover? Get in touch!
Finally, see some tips on writing papers and managing co-authors.
Coding is hard, but the same discipline that makes theorems elegant and papers beautiful, or courses clear and lectures engaging, can help make datastructures clean and code precise. You need to learn what’s idiomatic and efficient for a given language, and learn the tooling — and this takes time! — but that’s just matter of apprenticing yourself to someone familiar with a language and being humble and listening. I’ve been fortunate to have some excellent teachers.
The code below is open-source and available on my GitHub page. I hope you like it and may find it useful:
Nominal Datatypes package for Haskell
I am pleased to announce my Nominal Datatypes package for Haskell. This includes reference implementations of the untyped lambda-calculus, System F, and an EUTxO blockchain.
At time of writing, the GitHub version uses GHC8.10, which depends on a toolstack which creates warning messages about invalid magic. Sorry about this: it’s not GHC’s fault, and it’s annoying, but harmless.
I delivered a course based on the package in the Scottish Programming Languages and Verification Summer School (SPLV) in August 2020. Speakers were myself, Maribel Fernandez (Nominal rewriting and unification), Michel Steuwer (compiler intermediate representations), and Edwin Brady (the implementation of Idris 2).
See also my written course notes, being a mildly scrubbed transcription of the live coding during the lectures.
Cairo / Python development and testing
The Cairo abstract machine is an Ethereum Layer 2 virtual hardware based on polynomials over finite fields and written in Python. The motivation for Cairo is: execute off-chain then verify on-chain. This increases the blockchain’s effective on-chain processing power, because verification is cheaper than the initial execution.
I am pleased to announce:
The integer types library brings bitwise integer emulations to Cairo, which is needed because its native numerical type is the field element.
The test library helps me to test the integer types library, and more generally it introduces honest-to-goodness property-based testing to the Cairo ecosystem.
If you use my work, I suggest you cite me as ‘Murdoch J. Gabbay’ rather than just ‘M. J. Gabbay’ because my brother Mike has the same initials.
The Gabbay-Pitts NEW quantifier
I have given academic talks on mathematics and theoretical computer science in universities and research institutes all over the world. Travelling and giving talks is a great way to improve and grow as an academic. Thanks to all those who kindly hosted me.
Treatment of invited speaker
I travel a lot, and found this helpful guide to the treatment of invited speaker (sic) in the common-room of the Central Tungus Plateau University (Okrug campus), Siberia.
I am happy to announce the Journal of Financial Technology, a free and open-access academic journal founded to provide a high quality venue to publish, promote, publicise, and develop the fusion of mathematics, statistics, computer science, finance, and law in the new field of fintech.
Handling editor and deputy editor-in-chief of the Journal of Logic of Computation.
Editor on the Journal of Applied Logics.
I have served as a referee for numerous conferences and journals. If I were smarter, perhaps I would have made a list. Be reassured though … I was very nice when I reviewed your submission.
Sometimes I remember that computers are supposed to save labour as well as create employment for mathematicians. Then I write a computer script.
I was once a keen photographer. I took urban and scenic photographs of people, landscapes, animals, insects, architecture — and anything else that reflects or generates light. When I travelled, I usually had my camera with me.
I maintain two catalogues of photos:
Until 2007 I used a Ricoh Caplio R4 — an exquisite little point-and-shoot, for its time. I learned a lot and a set of portraits, landscapes, macro shots, from my travels are online.
After that I got myself a Nikon DSLR. Take a look through my viewfinder.
I haven’t updated my online photo galleries in some time … I hope to do this when I get an opportunity.
of some things I have worked on, in no particular order.
(Stone) duality and representation theory.
Nominal rewriting and unification.
Fraenkel-mostowski set theory and models.
The NEW quantifier (LaTeX code here).
Nominal logic, first-order logic, higher-order logic.
The NEW calculus of contexts and the lambda context calculus.
Two-level nominal sets provides the most technically sophisticated account so far of the "holes" X above (though I would say that, I suppose).
A recent paper which gives a nominal sets representation theorem for the NEW-quantifier; and another which gives a nominal sets representation theorem for name-generation. Further papers are here.
The Nominal Methods Group, who are working on implementing nominal techniques in Isabelle.
I like alcohol, especially strong beers and malt whisky.
I keep some tasting notes online.
Perform a mitzva (a good deed); avoid scheduling events on Shabbat, Rosh Hashanah, Yom Kippur, Sukkot, Chanukkah, Purim, and Passover.
(Links from Philip Wadler’s homepage.)
Essays and opinions
I keep a miscellanea of opinions.
The Good, the Bad, and the Ugly
I keep a miscellanea of things I approve of, disapprove of, or am shocked by.
Hall of fame
I keep a hall of fame for programs which changed my life.
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