In this episode Pierre-Marie Pédrot, one of the main Coq/Rocq developers joins us to talk about Krivine, Kleene and Gödel Realizability Models, how it relates to the BHK interpretation and CPS Translations, and how it was all already part of Gödel's work in Dialectica!
If you enjoy the show please consider supporting us at our ko-fi: https://ko-fi.com/typetheoryforall
Links
Pierre-Marie's Website
Pierre-Marie's PhD Thesis (Very nice read)
BHK Interpretation
Type Theory Forall website
Type Theory Forall discord
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1:03:36
#45 What is Type Theory and What Properties we Should Care About - Pierre-Marie Pédrot
In this episode Pierre-Marie Pédrot who is one of the main Coq/Rocq developers joins us to talk about what is Type Theory, what is Martin-Löf Type Theory, what are the properties we should care about in our type theory and why.
If you enjoy the show please consider supporting us at our ko-fi: https://ko-fi.com/typetheoryforall
Links
Pierre-Marie's Website
Type Theory Forall website
Type Theory Forall discord
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1:21:41
#44 Theorem Prover Foundations, Lean4Lean, Metamath - Mario Carneiro
Mario Carneiro is the creator of Mathlib, Lean4Lean and Metamath0. He is currently doing his Postdoc at Chalmers University working on CakeML. In this episode we talk about foundations of theorem provers, type systems properties, semantics and interoperabilities.
If you enjoy the show please consider supporting us at our ko-fi: https://ko-fi.com/typetheoryforall
Links
Lean4Lean github
Metamath
Metamath0
Lean Foundations Discussion
Large Elimination / Singleton Elimination
Type Theory Forall website
Type Theory Forall discord
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2:13:31
#43 PL in the Industry and Summer Schools - Patrick and Eric
In this episode Eric Bond and Patrick Lafontaine joins us to talk about the life in industry vs the life in academia. Eric is a PhD student at Michigan University under Max New, he works with some pretty cool esoteric cubical agda stuff. Before starting his PhD he has spent some time at the consultancy companies Two Six Technologies and 47 Degrees doing some cool functional programming and formal methods. Before that we were pals doing an internship at Galois, and even before that he finished his masters with Benjamin Delaware at Purdue, Patrick’s current advisor. Patrick has just returned from his internship at AWS in the automated reasoning team. So in this episode we talk about their research, their academic and industry experiences, how’s the industry looking like for opportunities in PL and all that.
If you enjoy the show please consider supporting us at our ko-fi: https://ko-fi.com/typetheoryforall
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1:01:30
#42 Distributed Systems, Microservices, and Choreographies - Fabrizio Montesi
In this episode we talk with Fabrizio Montesi, a Full Professor at the University of South Denmark. He is one of the creators of the Jolie Programming Language, President of the Microservices Community and Author of the book 'Introduction to Choreographies'. In today’s episode we talk about the formal side of Distributed Sytems, session types, the calculi that model distributed systems, their type systems, their Curry-Howard correspondences, and all the main ideas around these concepts.
If you enjoy the show please consider supporting us at our ko-fi: https://ko-fi.com/typetheoryforall
Links
Fabrizio's Website
Fabrizio's Linkedin
Fabrizio's X / Twitter
Fabrizio's Mastodon
Fabrizio's Youtube
Jolie's Website