Iowa Type Theory Commute podcast

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Lisätty four vuotta sitten

Sisällön tarjoaa Aaron Stump. Aaron Stump tai sen podcast-alustan kumppani lataa ja toimittaa kaiken podcast-sisällön, mukaan lukien jaksot, grafiikat ja podcast-kuvaukset. Jos uskot jonkun käyttävän tekijänoikeudella suojattua teostasi ilman lupaasi, voit seurata tässä https://fi.player.fm/legal kuvattua prosessia.

Different, not broken

1
You're not supposed to be here and other Dad wisdom 29:22

6 päivää sitten29:22

Toista Myöhemmin

Listat

Tykkää

Tykätty

29:22

The world often feels rigged. And this episode is a wake-up call to recognize the barriers that exist for those who don’t fit the traditional mold. In this episode, which is a kind of tribute to my dear departed Dad, I recount some powerful lessons from the man who was a brilliant psychiatrist and my biggest champion. He taught me that if something feels off about the environment you’re in, it probably is—and it’s absolutely hella-not your fault. We dare to break into the uncomfortable truth that many workplaces are designed for a very specific demographic, leaving neurodivergent individuals, particularly those on the autism spectrum, feeling excluded. I share three stories in which my Dad imparted to me more than my fair share of his wisdom, and I'm hoping you to can feel empowered. You'll learn that we can advocate for ourselves and others to create a more inclusive work culture. Newsletter Paste this into your browser if the newsletter link is broken - https://www.lbeehealth.com/ Join our Patreon - https://differentnotbrokenpodcast.com/patreon Mentioned in this episode: Sign Up For Our Newsletter Stay updated on all the things! Get added to our newsletter mailing list. Newsletter…

Iowa Type Theory Commute

Jaa

Sarjan koti•Feed

Aaron Stump talks about type theory, computational logic, and related topics in Computer Science on his short commute.

174 jaksoa

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

Iowa Type Theory Commute

17 subscribers

updated 17 tuntia sitten

Jaa

Sarjan koti•Feed

Aaron Stump talks about type theory, computational logic, and related topics in Computer Science on his short commute.

174 jaksoa

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

Kaikki jaksot

1
Krivine's Proof of FD, Using Intersection Types 21:35

17 hours sitten21:35

21:35

Krivine's book (Section 4.2) has a proof of the Finite Developments Theorem, based on intersection types. I discuss this proof in this episode.

1
A Measure-Based Proof of Finite Developments 23:24

20 päivää sitten23:24

23:24

I discuss the paper "A Direct Proof of the Finite Developments Theorem" , by Roel de Vrijer. See also the write-up at my blog.

1
Introduction to the Finite Developments Theorem 15:54

6 weeks sitten15:54

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.…

1
Nominal Isabelle/HOL 16:18

14 weeks sitten16:18

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.

1
The Locally Nameless Representation 19:54

18 weeks sitten19:54

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.…

1
POPLmark Reloaded, Part 1 15:14

19 weeks sitten15:14

15:14

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

1
POPLmark Reloaded, Part 2 13:59

19 weeks sitten13:59

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.

1
Introduction to Formalizing Programming Languages Theory 12:20

23 weeks sitten12:20

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.

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

50 weeks sitten17:39

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.

1
Introduction to normalization for STLC 9:39

51 weeks sitten9:39

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).…

1
Arithmetic operations in simply typed lambda calculus 9:56

1 year sitten9:56

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.…

1
The curious case of exponentiation in simply typed lambda calculus 7:29

1 year sitten7:29

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.…

1
More on basics of simple types 15:45

1 year sitten15:45

15:45

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

1
Begin Chapter on Simple Type Theory 15:41

1 year sitten15:41

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...

1
Some advanced examples in DCS 23:16

2 years sitten23:16

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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