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    Technology

    Type Theory Forall

    An accessible podcast about Type Theory, Programming Languages Research and related
    topics.

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    Copyright: © CC BY 4.0

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    Latest Episodes:
    #24 The History of Isabelle - Lawrence Paulson Oct 06, 2022
    Show notes

    In this episode we interview Lawrence Paulson, one of the creating fathers of Isabelle.

    We talk about the development process, how it drew inspirations and ideas from LCF and Boyer Moore. What tools were used, it’s strenghts and weaknesses, and all about the historical context at the time! We also briefly talk about his formalization of the Gödel's Incompletenes theorems in Isabelle

    Paulson have quite an extensive CV, he is a professor at Cambridge, have published more than 100 papers, is an ACM fellow since 2008, is a member of the royal society since 2017, among many other things!

    Links

    • Larry's Website
    • Larry's Twitter
    • Larry's Blog
    #23 What is the SIGPLAN? - Jens Palsberg and Jonathan Aldrich Sep 24, 2022
    Show notes

    In this episode we talk about Sigplan, the organization behind the most important conferences and proceedings in our field. What is the SIGPLAN? What exactly does it do? How is it organized? How are things published? To answer these and many other questions we talk with Jens Palsberg, a professor at UCLA, who is the past chair of the SIGPLAN. And also Jonathan Aldrich, a professor at the CMU, who is a member of the ACM publication board.

    Links

    • Jen's Website
    • Jonathan's Website
    • Jonathan's Twitter
    • Sigplan Blog
    • Post on Hybrid Conferences
    • SIGPlAN-M Mentoring Program
    #22 Impredicativity, LEM, Realizability and more - Cody Roux Aug 12, 2022
    Show notes

    In this episode Cody Roux teaches some interesting concepts that people care about in Mathematics and Logic as a way to try to understand what is going on in the universe around us! In particular we will try to explain concepts such as Impredicativity, Excluded Middle, Group Theory, Model Theory, Kripke Models, Realizability, The Markov Principle, Cut Elimination, and other stuff!

    Links

    • Cody's website
    • Cody's dblp
    #21 Denotational Design - Conal Elliott Aug 04, 2022
    Show notes

    In this episode Conal Elliott gives a more concrete presentation on what is Denotational Design is and how to use it in practice. It is a continuation of episode #17, in which we had an in-depth philosophical conversation to explain why he believes that Denotational Design is a superior form of reasoning in the realm of computer science.

    We also continue a discussion raised by Dan Ghica on the last episode on the need for Operational Semantics and the role of elegance in reasoning and design.

    Along the way we also address the questions sent by the listeners in these last episodes.

    Links

    • Conal's website
    • Play/work with Conal
    • Conal's twitter: @conal
    • The simple essence of automatic differentiation
    • Compiling to categories
    • Generic parallel functional programming
    • Denotational design with type class morphisms

    Quotes

    • "A theory appears beautiful or elegant [...] when it’s simple; in other words when it can be expressed very concisely in terms of mathematics that we’ve already learned for some other reasons." - Murray Gell-Mann, Beauty and Elegance in Physics.

    • "In Galileo’s time, professors of philosophy and theology—the subjects were inseparable—produced grand discourses on the nature of reality, the structure of the universe, and the way the world works, all based on sophisticated metaphysical arguments. Meanwhile, Galileo measured how fast balls roll down inclined planes. How mundane! But the learned discourses, while grand, were vague. Galileo’s investigations were clear and precise. The old metaphysics never progressed, while Galileo’s work bore abundant, and at length spectacular, fruit. Galileo too cared about the big questions, but he realized that getting genuine answers requires patience and humility before the facts." - Frank Wilczek, (The Lightness of Being: Mass, Ether, and the Unification of Forces)

    • "We must make here a clear distinction between belief and faith, because, in general practice, belief has come to mean a state of mind which is almost the opposite of faith. Belief, as I use the word here, is the insistence that the truth is what one would ‘lief’ or wish it to be. The believer will open his mind to the truth on the condition that it fits in with his preconceived ideas and wishes. Faith, on the other hand, is an unreserved opening of the mind to the truth, whatever it may turn out to be. Faith has no preconceptions; it is a plunge into the unknown. Belief clings, but faith lets go. In this sense of the word, faith is the essential virtue of science, and likewise of any religion that is not self-deception." - Alan Watts (The Wisdom of Insecurity: A Message for an Age of Anxiety)

    #20 Huaweii, String Diagrams, Game Semantics - Dan R. Ghica Jun 28, 2022
    Show notes

    In this episode, me and Eric Bond have a great conversation with Dan R. Ghica, a professor at Birmingham University and Director of the Programming Language Research Lab of the Huaweii Research Centre Edinburgh. We talk about his work on both institutions, which includes topics such as Category Theory, String Diagrams, and Game Semantics. We also briefly discuss the current publication process of our field and entertain some thoughts on how to make it better. Finally, we touch on more personal topics such as his views about Elegance, making an insightful counterpoint to Conal’s opinions on Denotational Semantics vs. Operational Semantics.

    Links

    • Dan's Twitter: @danghica
    • Dan's Website
    • Job advert for Huawei positions

    Talks and Lectures

    • Dan's talk on Syntactic Trinitarianism (terms, graphs, diagrams)
    • Dan's talk on a similar, more semantics-oriented talk at TERMGRAPH
    • Dan's OPLSS course on (denotational) game semantics
    • Game semantics lectures

    Papers

    • Paper on string diagrams and their applications to reverse automatic differentiation (long paper, part of it to appear in FSCD 2020)
    • Paper on automatic differentiation and string diagrams
    • Paper on effect handlers
    • Paper on optimisation with constructive reals
    • Paper on digital circuits and string diagrams
    • Paper on functorial boxes for string diagrams
    • A Game semantics paper mentioned during the conversation
    • Decidability via game semantics
    • Landmark paper on undecidability of observational equivalence

    Other Links

    • Penrose book
    • Book on type-level string diagrams
    • Proof assistant for higher categories
    • The Programming Journal
    • Midlands Graduate School
    #19 Experience Report: Learning Coq - Patrick and Supun Jun 04, 2022
    Show notes

    In today’s episode I invite two friends of mine Patrick Lafontaine and Supun Abeysinghe. We will talk about their experience learning Coq and we guide ourselves in a survey that I gave all the 83 students in the class. The class was thought by my advisor Benjamin Delaware and I was his TA.

    Patrick researches compilers and have done work in particular with Rust. And Supun works more along the lines of machine learning in the context of systems.

    #18 Gödel's Incompleteness Theorems - Cody Roux May 19, 2022
    Show notes

    In this episode Cody Roux talks about the Gödel's Incompleteness Theorems. We go through it’s underlying historical context, Hilbert’s Program, how it relates with Turing, Church, Von Neumann, Termination and more.

    Links

    • Cody's website
    • Cody's dblp
    • The Lady or the Tiger? - Short Story
    • The Lady or the Tiger? - Amazon
    • Logicomix
    • An Introduction to Gödel's Theorems
    • Jeremy Avigad's Lecture Notes
    #17 The Lost Elegance of Computation - Conal Elliott May 09, 2022
    Show notes

    In this episode I had the pleasure to have an in-depth conversation with Conal Elliott about his life, his work, his philosophy and his many opinions about research and the current state of PL Research and how it lead him to come with the concept of Denotational Design. Conal got his PhD at CMU in the 90s under Frank Pfenning working on Higher-Order Unification, after that he has devoted his life on thinking and refining graphic computation and the tools behind it.

    Links

    • Conal's website
    • Play/work with Conal
    • Conal's twitter: @conal
    • The simple essence of automatic differentiation
    • Compiling to categories
    • Generic parallel functional programming
    • Denotational design with type class morphisms
    • Functional Images
    • Functional Reactive Animation
    • Alphabet Versus the Goddess - Leonard Shlain
    • The information - James Gleick
    • Murray Gell-Mann’s definition of beauty/elegance: "A theory appears beautiful or elegant [...] when it’s simple; in other words when it can be expressed very concisely in terms of mathematics that we’ve already learned for some other reasons."
    • A John Backus quote (from his Turing Award lecture): “Many creative computer scientists have retreated from inventing languages to inventing tools for describing them. Unfortunately, they have been largely content to apply their elegant new tools to studying the warts and moles of existing languages. After examining the appalling type structure of conventional languages, using the elegant tools developed by Dana Scott, it is surprising that so many of us remain passively content with that structure instead of energetically searching for new ones.”
    #16 Agda, K Axiom, HoTT, Rewrite Theory - Jesper Cockx Apr 02, 2022
    Show notes

    In this episode we interview Jesper Cockx, one of the core developers on Agda. We talk about the philosophy behind Agda, his work on pattern matching, the Uniqueness of Identity of Proofs, UIP for short, and why it is inconsistent with Homotopy Type Theory.

    Links

    • Jesper's Website
    • Jesper's Twitter: @agdakx
    • Jesper's PhD Thesis
    • Rewrite Theory paper
    • Pattern matching without K paper (Check his website for more)
    • EuroProofNet
    • WITS Talks on Youtube (Workshop on the Implementation of Type Systems)
    • Agda Zulip
    • Agda Mailing List
    • Ataca Github
    • Wadler's book on Agda
    • Stump's book on Agda
    #15 Coq Projects, Agda, Idris, Kind - Nitin and Eric Mar 27, 2022
    Show notes

    In this episode me, Eric and Nitin continues our conversation started in the last episode. This time we move our attention to the cool projects happening in Coq, in particular commenting through the projects mentioned in Andrew Appel’s keynote “Coq’s Vibrant Ecosystem for verification engineering” that took place in CPP’22 which is colocated with POPL and towards the end we also talk about agda, idris and Kind.

    Links

    • Nitin Twitter @NitinJohnRaj2
    • Eric Twitter @EricBond10
    • Appel's CPP Talk
    • Proof Assistants Stack Exchange
    • Coq Community
    • Leo de Moura Interview
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