Introduction To Normalization For STLC Iowa Type Theory Commute podcast

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Hark | 8 | The Queen's English 30:00

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30:00

Living together in a group is a strategy many animals use to survive and thrive. And a big part of what makes that living situation successful is listening. In this episode, we explore the collaborative world of the naked mole-rat. Threshold is nonprofit, listener-supported, and independently produced. You can support Threshold by donating today . To stay connected, sign up for our newsletter . Operation frog sound! Send us your frog sounds for an upcoming episode. We want you to go out, listen for frogs and toads, and record them. Just find someone croaking, and hit record on your phone. It doesn’t matter if there’s background noise. It doesn’t even matter if you’re not sure whether or not you’re hearing an amphibian—if you think you are, we would love to get a recording from you. Please also say your name and where you are in the world, and then email the recording to us at outreach@thresholdpodcast.org…

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Introduction to normalization for STLC

for ca. et år siden 9:39

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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).

… continue reading

172 episoder

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

Iowa Type Theory Commute

Iowa Type Theory Commute podcast artwork

Introduction to normalization for STLC

Iowa Type Theory Commute

17 subscribers

published for ca. et år siden

Del

MP3•Episode hjem

Indhold leveret af Aaron Stump. Alt podcastindhold inklusive episoder, grafik og podcastbeskrivelser uploades og leveres direkte af Aaron Stump eller deres podcastplatformspartner. Hvis du mener, at nogen bruger dit ophavsretligt beskyttede værk uden din tilladelse, kan du følge processen beskrevet her https://da.player.fm/legal.

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).

… continue reading

172 episoder

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

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Iowa Type Theory Commute

Iowa Type Theory Commute podcast artwork

1
Introduction to the Finite Developments Theorem 15:54

for 16 dage siden15:54

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

for 10 weeks siden16:18

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

for 14 weeks siden19:54

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

for 16 weeks siden15:14

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

for 16 weeks siden13:59

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.

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Iowa Type Theory Commute

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Introduction to Formalizing Programming Languages Theory 12:20

for 20 weeks siden12:20

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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1
Turing's proof of normalization for STLC 17:39

for 47 weeks siden17:39

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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1
Introduction to normalization for STLC 9:39

for 48 weeks siden9:39

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

Iowa Type Theory Commute podcast artwork

1
Arithmetic operations in simply typed lambda calculus 9:56

for 49 weeks siden9:56

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

for 49 weeks siden7:29

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

for 50 weeks siden15:45

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

for 51 weeks siden15:41

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

for 2 years siden23:16

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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1
DCS compared to termination checkers for type theories 19:45

for 2 years siden19:45

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

for 2 years siden17:23

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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