Best Aaron Stump Podcasts (2025)

1
Correction: the Correct Author of the Proof from Last Episode, and an AI flop 7:10

6d ago7:10

7:10

I correct what I said in the last episode about the author of the proof of FD from last episode based on intersection types. I also describe AI flopping when I ask it a question about this.By Aaron Stump

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

13d ago21:35

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.By Aaron Stump

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

1M ago23:24

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.By Aaron Stump

1
Introduction to the Finite Developments Theorem 15:54

2M ago15:54

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

4M ago16:18

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.By Aaron Stump

1
The Locally Nameless Representation 19:54

5M ago19:54

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 t…

1
POPLmark Reloaded, Part 2 13:59

5M ago13:59

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.By Aaron Stump

1
POPLmark Reloaded, Part 1 15:14

5M ago15:14

15:14

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

1
Introduction to Formalizing Programming Languages Theory 12:20

6M ago12:20

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.By Aaron Stump

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

12M ago17:39

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.By Aaron Stump

1
Introduction to normalization for STLC 9:39

1y ago9:39

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 [email protected]).…

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

1y ago7:29

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 a…

1
Arithmetic operations in simply typed lambda calculus 9:56

1y ago9:56

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 …

1
More on basics of simple types 15:45

1y ago15:45

15:45

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

1
Begin Chapter on Simple Type Theory 15:41

1y ago15:41

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...By Aaron Stump

1
Aaron Norton chats Little Athletics 1:14:25

1+ y ago1:14:25

1:14:25

Join your hosts Adam and Tash in this weeks episode of Two Cripples, One Pair of Legs as they sit down with Aaron Norton from Little Athletics. Adam and Tash spill the beans on the recent trip to Japan!By Media8

1
It's Been a Long Day!! 1:04:16

1+ y ago1:04:16

1:04:16

Welcome back to another episode of Two Cripples, One Pair of Legs. On this very chaotic episode, Adam is in the firing line as Tash nominates him as Moron of The Day and someone is absolutely shocked that he is helping out at a carnival. Tash and Adam also get a surprise visit from friend of the show Brett McCallum and a giant beer can!…

1
The Chair That Got Away 1:04:17

1+ y ago1:04:17

1:04:17

Join Tash and Adam on Two Cripples, One Pair of Legs for a hilarious episode filled with Tash's runaway wheelchair antics and the shocking funding woes of Swimming Australia. They're flipping the script with a heartwarming social media uplift, sharing a heartwarming DM, and give a shoutout to the "Unsung Heroes" event raising funds for carer respit…

1
2 Cripples, 1.5 Pairs of Legs 1:09:19

1+ y ago1:09:19

1:09:19

On this episode of Two Cripples, One Pair of Legs Adam and Tash dive into the inspiring journey of their special guest, Matt Curran, who lost his leg in a motorbike accident but still rides the waves in all things watersports. They also recount Tash's latest hurdle mishap (yes, another one) and share their 'epic' two weeks without a car.…

1
Yes or No? That is the Question 1:08:31

1+ y ago1:08:31

1:08:31

In this episode of Two Cripples, One Pair of Legs, Adam and Tash spill the beans on the awkward moment when someone questioned Adam's parking in a disabled spot (spoiler: he's got a great reason!), celebrate the unsung heroes of the Oceania Throwdown, weigh in on The Voice referendum, and deliver a side-splitting take on the world of disrespectful …

1
Some advanced examples in DCS 23:16

1+ y ago23:16

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 ensur…

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

1+ y ago19:45

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.By Aaron Stump

1
Part 2: Graziella Thake 53:38

1+ y ago53:38

53:38

Welcome back to another episode of Two Cripples, One Pair of Legs! In this episode Tash gets told that someone on Tik Tok has the cure to diabetes (which is actually incurable...), and Adam does a shoutout to the all-round good people over at the Atlas Collective. They then jump into Part 2 of their interview with the one and only Graziella Thake w…

1
Getting started with DCS 17:23

1+ y ago17:23

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.By Aaron Stump

1
Introduction to DCS 11:36

1+ y ago11:36

11:36

DCS is a new functional programming language I am designing and implementing with Stefan Monnier. DCS has a pure, terminating core, around which monads will be layered for possibly diverging, impure computation. In this episode, I talk about this basic design, and its rationale.By Aaron Stump

1
Part 1: Graziella Thake 56:05

1+ y ago56:05

56:05

Strap in for a hilarious and also motivating ride on this episode of Two Cripples, One Pair of Legs. In part 1 of a two part interview, Adam and Tash chat to the unstoppable Graziella Thake, CEO of Optimisation Hub. Listen in as Adam and Tash tackle equality, equity and even recount a post pub feed parking saga with its very own handwritten note. B…

1
The Worst Facebook Hack Ever 1:07:04

2y ago1:07:04

1:07:04

Welcome back to another episode of Two Cripples, One Pair of Legs. On today's episode Adam and Tash chat about Brisbane Airport renaming to traditional land name Meeanjin, but not telling anyone. They talk about a horrible Facebook hack that happened to one of their friends, chat about a wholesome fishing expo Adam took his kid to and annouce that …

1
The Cairns Special 1:13:41

2y ago1:13:41

1:13:41

Get ready to be inspired and have some laughs on this week's episode of Two Cripples One Pair of Legs. Join the unstoppable figure athlete, Julie Lindsay, as she raises awareness and takes on cancer like the boss-woman she is and then laugh along with Adam and Tash as they recount the weird and wonderful stuff that happened during their Cairns trip…

1
Semantics of subtyping 15:20

2y ago15:20

15:20

I answer a listener's question about the semantics of subtyping, by discussing two different semantics: coercive subtyping and subsumptive subtyping. The terminology I found in this paper by Zhaohui Luo; see Section 4 of the paper for a comparison of the two kinds of subtyping. With coercive subtyping, we have subtyping axioms "A

1
"Triggered" 1:07:15

2y ago1:07:15

1:07:15

Welcome back to another episode of Two Cripples, One Pair of Legs. In this week's episode, Adam and Tash welcome Caroline Bellenger into the studio. Caroline has dedicated her life to empowering other women through inspirational keynotes, coaching programs and online education while raising awareness of childhood sexual abuse and mental health stig…

1
More on type inference for simple subtypes 9:06

2y ago9:06

9:06

I continue the discussion of Mitchell's paper Type Inference with Simple Subtypes. Coming soon: a discussion of semantics of subtyping.By Aaron Stump

1
Subtyping, the golden key 9:13

2y ago9:13

9:13

In this episode, I wax rhapsodic for the potential of subtyping to improve the practice of pure functional programming, in particular by allowing functional programmers to drop various irritating function calls that are needed just to make types work out. Examples are lifting functions with monad transformers, or even just the pure/return functions…

1
A Super Charged Ep 1:28:55

2y ago1:28:55

1:28:55

Welcome back to another episode of Two Cripples, One Pair of Legs. In today's podcast Adam and Tash are joined in the studio with Brett D. Scott from Super Charged Freedom. Tash chats about runners playing "statue" while she races downhill with a siren blaring. Your hosts then thank the siren holding heroes otherwise known as lead cyclists for keep…

1
Type inference with simple subtypes 13:27

2y ago13:27

13:27

In this episode, I begin discussing a paper titled "Type Inference with Simple Subtypes," by John C. Mitchell. The paper presents algorithms for computing a type and set of subtype constraints for any term of the pure lambda calculus. I mostly focus here on how subtype constraints allow typing any term (which seems surprising). You can join the tel…

1
Basics of subtyping 8:05

2y ago8:05

8:05

In this episode, I discuss a few of the basics for what we expect from a subtyping relation on types: reflexivity, transitivity, and the variances for arrow types.By Aaron Stump

1
Begin chapter on subtyping 16:15

2y ago16:15

16:15

We begin a discussion of subtyping in functional programming. In this episode, I talk about how subtyping is a neglected feature in implemented functional programming languages (for example, not found in Haskell), and how it could be very useful for writing lighter, more elegant code. I also talk about how subtyping could help realize a new vision …

1
People Incorrectly Correcting People 1:11:41

2y ago1:11:41

1:11:41

This week on the Two Cripples, One Pair of Legs podcast, Adam and Tash welcome Rachel Condos-Fields into the studio. Rachel is the CEO and Founder of The WattleNest which was born to empower, celebrate and connect elite athletes to help mitigate financial barriers and provide pathways for talented sportspersons. Tash says something nice about Adam …

1
Falling Ass over Tit 1:15:15

2y ago1:15:15

1:15:15

On this week's episode of Two Cripples, One Pair of Legs, Adam and Tash chat about how society tend to crucify people in the media and on social media without having all (or even any) of the facts, Adam talks about a cheeky little DM he got on Instagram and Tash crowns Adam as this episodes Moron of the Day after telling her a little story about a …

1
When Intercoms and Bladders Collide 1:01:05

2y ago1:01:05

1:01:05

On this week's episode of Two Cripples, One Pair of Legs, Tash gives her take on the coronation and the amount of money spent on it. They chat about good ol' ableism, the pain of having to use intercoms to get into disabled bathrooms and remember a dear friend who recently passed.By Media8

1
A Whole Lotta Wholesome 1:09:12

2y ago1:09:12

1:09:12

Welcome to another episode of the Two Cripple, One Pair of Legs podcast. On this week's episode, Adam and Tash are joined in the studio with the boys from Everything Suarve. They chat about how they got started and everything that their Big Brother program does and stick around for a very special and wholesome edition of the Kindness Virus. Adam ch…

1
We're Not Thieves 1:25:19

2y ago1:25:19

1:25:19

On this week's episode of Two Cripples, One Pair of Legs, Adam and Tash welcome the amazingly talented, 15-year-old para national swimmer, Montana Atkinson into the studio to chat all things swimming. Adam chats about some negative (and slightly hilarious) comments he got on a picture he posted calling out ableism, Tash gets told she's "too young t…

1
Last episode discussing Observational Equality Now for Good 12:15

2y ago12:15

12:15

In this episode, I conclude my discussion of some (but hardly all!) points from Pujet and Tabareau's POPL 2022 paper, "Observational Equality -- Now for Good!". I talk a bit about the structure of the normalization proof in the paper, which uses induction recursion. See this paper by Peter Dybjer for more about that feature. Also, feel free to join…

1
Beauty Queens 1:06:51

2y ago1:06:51

1:06:51

On this week's episode of Two Cripples, One Pair of Legs, Adam and Tash welcome Mary Jane Leahy into the studio. Mary is the current Mrs. Australia, a registered Nurse and is passionate about empowering women. Adam and Tash talk about their recent trip to Noosa where they became TV stars and most importantly, the first wheelchair users to take part…

1
Here's Our Opinion 1:25:01

2y ago1:25:01

1:25:01

Welcome to another week of the Two Cripples, One Pair of Legs Podcast. In this episode, Adam threatens to expose Tash's secrets as he interviews her for the Water Cooler segment. Tash chats about her disability, what life was like living in the UK with one and why she moved back to Australia. The pair talk about the segrating of the sexes, the fact…

1
More on observational type theory 13:43

2y ago13:43

13:43

I continue discussing the Puject and Tabareau paper, "Observational Equality -- Now for Good", in particular discussing more about how the equality type simplifies based on its index (which is the type of the terms being equated by the equality type), and how proofs of equalities can be used to cast terms from one type to another. Also, in exciting…

1
It's Sally Pearson! 1:15:46

2y ago1:15:46

1:15:46

On this week's episode of the Two Cripples, One Pair of Legs Podcast your hosts Adam and Tash are joined by the one and only, World Champion and Olympic gold medallist hurdler, Sally Pearson! As Tash fan girls, Sally chats about her life, sport and what motivates her and Adam re-tells the story of when Tash 'decided' to give hurdling a go herself.…

1
Introduction to Observational Type Theory 10:10

2y ago10:10

10:10

In this episode, I introduce an important paper by Pujet and Tabareau, titled "Observational Equality: Now for Good", that develops earlier work of McBride, Swierstra, and Altenkirch (which I will cover in a later episode) on a new approach to making a type theory extensional. The idea is to have equality types reduce, within the theory, to stateme…

1
Interjection: The Liquid Tensor Experiment 12:24

2y ago12:24

12:24

I pause the chapter on extensionality in type theory to talk about something very exciting that I just learned about (though the project was completed Summer 2022): the so-called Liquid Tensor Experiment, to formalize a recent very difficult proof by a mathematician named Peter Scholze, in Lean. This is the first time in history, that I know of, wh…

1
Bye Bye Dad Bod 1:16:32

2y ago1:16:32

1:16:32

Welcome to yet another episode of the Two Cripples, One Pair of Legs Podcast! This week Adam and Tash welcome Mechanic turn Para Powerlifter, Leigh Skinner into the studio. Leigh chats about how and why he got started in Para Powerlifting, the time he met the Queen and how his water bottle kind of looks like an urn. Tash says something nice to Adam…

1
A Very 'Special' Guest 1:15:14

2+ y ago1:15:14

1:15:14

Welcome to a very 'special' episode where Tash interviews a very 'special' studio guest... Adam Sheppard. Adam chats about being a disabled kid in school, when he got his very first chair and how he got into sports. The pair talk about people being cancelled for things they did 20 years ago and Adam being cancelled and kicked off Facebook for somet…

Podcasts Worth a Listen

Aaron Stump Podcasts

Podcasts Worth a Listen