POPLmark Reloaded, Part 2 Iowa Type Theory Commute podcast

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Contenido proporcionado por Aaron Stump. Todo el contenido del podcast, incluidos episodios, gráficos y descripciones de podcast, lo carga y proporciona directamente Aaron Stump o su socio de plataforma de podcast. Si cree que alguien está utilizando su trabajo protegido por derechos de autor sin su permiso, puede seguir el proceso descrito aquí https://es.player.fm/legal.

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On the Bus with Troy Vollhoffer

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On the Bus with Troy Vollhoffer podcast artwork

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From Backroom Bars to Broadway with Dustin Lynch 36:27

hace 14 días36:27

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36:27

Not many artists actually hail from Tennessee, but the scenic valleys and rolling hills of The Volunteer State are part of Dustin Lynch’s DNA. In this episode of On the Bus, Country Thunder CEO Troy Vollhoffer sits down with Dustin to discuss his journey from playing fraternity parties and weddings across the southeast to being the first country artist with a club residency at the Wynn in Las Vegas. Plus, stick around for our new segment, Thunder Strike, where Troy features upcoming festival performer Riley Green’s hit song “Damn Good Day to Leave” to give you a taste of what’s to come at Country Thunder in 2025.…

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POPLmark Reloaded, Part 2

hace un año 13:59

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MP3•Episodio en casa

Contenido proporcionado por Aaron Stump. Todo el contenido del podcast, incluidos episodios, gráficos y descripciones de podcast, lo carga y proporciona directamente Aaron Stump o su socio de plataforma de podcast. Si cree que alguien está utilizando su trabajo protegido por derechos de autor sin su permiso, puede seguir el proceso descrito aquí https://es.player.fm/legal.

I continue the discussion of POPLmark Reloaded , discussing the solutions proposed to the benchmark problem. The solutions are in the Beluga, Coq (recently renamed Rocq), and Agda provers.

… continue reading

172 episodios

#Science #Tech #Math #Aaron Stump #Programming Language #Computational Logic #Type Theory #Proof Assistants #Cedille

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POPLmark Reloaded, Part 2

Iowa Type Theory Commute

17 subscribers

published hace un año

Compartir

MP3•Episodio en casa

Contenido proporcionado por Aaron Stump. Todo el contenido del podcast, incluidos episodios, gráficos y descripciones de podcast, lo carga y proporciona directamente Aaron Stump o su socio de plataforma de podcast. Si cree que alguien está utilizando su trabajo protegido por derechos de autor sin su permiso, puede seguir el proceso descrito aquí https://es.player.fm/legal.

I continue the discussion of POPLmark Reloaded , discussing the solutions proposed to the benchmark problem. The solutions are in the Beluga, Coq (recently renamed Rocq), and Agda provers.

… continue reading

172 episodios

#Science #Tech #Math #Aaron Stump #Programming Language #Computational Logic #Type Theory #Proof Assistants #Cedille

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Iowa Type Theory Commute

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1
Introduction to the Finite Developments Theorem 15:54

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15:54

The finite developments theorem in pure lambda calculus says that if you select as set of redexes in a lambda term and reduce only those and their residuals (redexes that can be traced back as existing in the original set), then this process will always terminate. In this episode, I discuss the theorem and why I got interested in it.…

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Iowa Type Theory Commute

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Nominal Isabelle/HOL 16:18

hace 9 weeks16:18

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16:18

In this episode, I discuss the paper Nominal Techniques in Isabelle/HOL , by Christian Urban. This paper shows how to reason with terms modulo alpha-equivalence, using ideas from nominal logic. The basic idea is that instead of renamings, one works with permutations of names.

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Iowa Type Theory Commute

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The Locally Nameless Representation 19:54

hace 13 weeks19:54

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19:54

I discuss what is called the locally nameless representation of syntax with binders, following the first couple of sections of the very nicely written paper "The Locally Nameless Representation," by Charguéraud. I complain due to the statement in the paper that "the theory of λ-calculus identifies terms that are α-equivalent," which is simply not true if one is considering lambda calculus as defined by Church, where renaming is an explicit reduction step, on a par with beta-reduction. I also answer a listener's question about what "computational type theory" means. Feel free to email me any time at aaron.stump@bc.edu, or join the Telegram group for the podcast.…

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Iowa Type Theory Commute

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POPLmark Reloaded, Part 1 15:14

hace 15 weeks15:14

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15:14

I discuss the paper POPLmark Reloaded: Mechanizing Proofs by Logical Relations , which proposes a benchmark problem for mechanizing Programming Language theory.

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Iowa Type Theory Commute

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POPLmark Reloaded, Part 2 13:59

hace 15 weeks13:59

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13:59

I continue the discussion of POPLmark Reloaded , discussing the solutions proposed to the benchmark problem. The solutions are in the Beluga, Coq (recently renamed Rocq), and Agda provers.

I

Iowa Type Theory Commute

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Introduction to Formalizing Programming Languages Theory 12:20

hace 18 weeks12:20

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12:20

In this episode, I begin discussing the question and history of formalizing results in Programming Languages Theory using interactive theorem provers like Rocq (formerly Coq) and Agda.

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Iowa Type Theory Commute

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Turing's proof of normalization for STLC 17:39

hace 45 weeks17:39

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17:39

In this episode, I describe the first proof of normalization for STLC, written by Alan Turing in the 1940s. See this short note for Turing's original proof and some historical comments.

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Iowa Type Theory Commute

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Introduction to normalization for STLC 9:39

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9:39

In this episode, after a quick review of the preceding couple, I discuss the property of normalization for STLC, and talk a bit about proof methods. We will look at proofs in more detail in the coming episodes. Feel free to join the Telegram group for the podcast if you want to discuss anything (or just email me at aaron.stump@gmail.com).…

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Iowa Type Theory Commute

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Arithmetic operations in simply typed lambda calculus 9:56

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9:56

It is maybe not so well known that arithmetic operations -- at least some of them -- can be implemented in simply typed lambda calculus (STLC). Church-encoded numbers can be given the simple type (A -> A) -> A -> A, for any simple type A. If we abbreviate that type as Nat_A, then addition and multiplication can both be typed in STLC, at type Nat_A -> Nat_A -> Nat_A. Interestingly, things change with exponentiation, which we will consider in the next episode.…

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Iowa Type Theory Commute

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The curious case of exponentiation in simply typed lambda calculus 7:29

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7:29

Like addition and multiplication on Church-encoded numbers, exponentiation can be assigned a type in simply typed lambda calculus (STLC). But surprisingly, the type is non-uniform. If we abbreviate (A -> A) -> A -> A as Nat_A, then exponentiation, which is defined as \ x . \ y . y x, can be assigned type Nat_A -> Nat_(A -> A) -> Nat_A. The second argument needs to have type at strictly higher order than the first argument. This has the fascinating consequence that we cannot define self-exponentiation, \ x . exp x x. That term would reduce to \ x . x x, which is provably not typable in STLC.…

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Iowa Type Theory Commute

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More on basics of simple types 15:45

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15:45

I review the typing rules and some basic examples for STLC. I also remind listeners of the Curry-Howard isomorphism for STLC.

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Iowa Type Theory Commute

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Begin Chapter on Simple Type Theory 15:41

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15:41

In this episode, after a pretty long hiatus, I start a new chapter on simply typed lambda calculus. I present the typing rules and give some basic examples. Subsequent episodes will discuss various interesting nuances...

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Iowa Type Theory Commute

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Some advanced examples in DCS 23:16

hace 2 years23:16

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23:16

This episode presents two somewhat more advanced examples in DCS. They are Harper's continuation-based regular-expression matcher, and Bird's quickmin, which finds the least natural number not in a given list of distinct natural numbers, in linear time. I explain these examples in detail and then discuss how they are implemented in DCS, which ensures that they are terminating on all inputs.…

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Iowa Type Theory Commute

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DCS compared to termination checkers for type theories 19:45

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19:45

In this episode, I continue introducing DCS by comparing it to termination checkers in constructive type theories like Coq, Agda, and Lean. I warmly invite ITTC listeners to experiment with the tool themselves. The repo is here .

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Iowa Type Theory Commute

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Getting started with DCS 17:23

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17:23

In this episode, I talk more about the DCS tool, and invite listeners to check it out and possibly contribute! The repo is here .

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