Cedille is a not-for-profit record label dedicated to extraordinary classical music and the brilliant artists who create it. We enhance the world's catalog of recorded music through audiophile-quality recordings featuring Chicago's finest musicians. Each episode of Cedille's Classical Chicago Podcast highlights a new release and feature interviews with your favorite Cedille artists. To support Cedille and its mission, please visit CedilleRecords.org
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Aaron Stump talks about type theory, computational logic, and related topics in Computer Science on his short commute.
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Episode 70 - Mary Elizabeth Bowden / Storyteller: Contemporary Concertos for Trumpet
1:12:53
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Episode 70 - Mary Elizabeth Bowden / Storyteller: Contemporary Concertos for Trumpet by Cedille RecordsBy Cedille Records
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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
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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).…
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Arithmetic operations in simply typed lambda calculus
9:56
9:56
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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 …
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The curious case of exponentiation in simply typed lambda calculus
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7:29
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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…
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Episode 69 – Austin Hartman / American Voices
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Episode 69 – Austin Hartman / American Voices by Cedille RecordsBy Cedille Records
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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
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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
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Episode 68 – Stacy Garrop / Terra Nostra
1:29:36
1:29:36
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Episode 68 – Stacy Garrop / Terra Nostra by Cedille RecordsBy Cedille Records
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Episode 67 – Will Liverman / Show Me The Way
1:42:56
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Episode 67 – Will Liverman / Show Me The Way by Cedille RecordsBy Cedille Records
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Episode 66 – John William Trotter / Miracle of Miracles — Music for Hanukkah
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Episode 66 – John William Trotter / Miracle of Miracles — Music for Hanukkah by Cedille RecordsBy Cedille Records
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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…
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DCS compared to termination checkers for type theories
19:45
19:45
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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
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Episode 65: David Skidmore/Between Breaths
1:08:59
1:08:59
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On episode of Classical Chicago, Cedille President Jim Ginsburg talks with Third Coast Percussion's David Skidmore about his experience recording Cedille's latest release, Between Breaths. The works on the album explore aspects of meditation in sound, incorporate unconventional timbres and tones, invite listeners to lose themselves within a captiva…
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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
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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
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Episode 64 Part 2 - Rachel Barton Pine and Earl Maneein
1:22:32
1:22:32
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Episode 64 Part 2 - Rachel Barton Pine and Earl Maneein by Cedille RecordsBy Cedille Records
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Episode 64 Part 1 - Rachel Barton Pine and Earl Maneein
1:24:17
1:24:17
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Episode 64 Part 1 - Rachel Barton Pine and Earl Maneein by Cedille RecordsBy Cedille Records
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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
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I continue the discussion of Mitchell's paper Type Inference with Simple Subtypes. Coming soon: a discussion of semantics of subtyping.By Aaron Stump
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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…
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Episode 63 - Mark Steven Doss/Welcome to My World
1:29:59
1:29:59
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with internationally acclaimed bass-baritone Mark Steven Doss about his prolific musical career and his experience recording his Cedille debut, "Welcome to My World." The album highlights Doss's wide range as a performer, and features performances from pianist Ken Smith and …
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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…
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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
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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 …
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Episode 62 - Jorge Federico Osorio / Conciertos Románticos
1:05:50
1:05:50
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with internationally acclaimed pianist Jorge Federico Osorio about his celebrated musical career and his experience creating Conciertos Románticos, Cedille's upcoming June 9 release comprising Mexican piano concertos and solo pieces.…
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Episode 61 - Rachel Barton Pine, Anthony McGill, and Malek Jandali / Malek Jandali: Concertos
1:49:16
1:49:16
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with violinist Rachel Barton Pine, clarinetist Anthony McGill and composer Malek Jandali, about their experiences creating Cedille's upcoming release, "Malek Jandali: Concertos."By Cedille Records
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Last episode discussing Observational Equality Now for Good
12:15
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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…
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Episode 60 - Seth Parker Woods / Difficult Grace
1:14:10
1:14:10
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with Grammy-nominated cellist Seth Parker Woods about his experience creating and recording "Difficult Grace", his first album for Cedille Records.By Cedille Records
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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…
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Introduction to Observational Type Theory
10:10
10:10
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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…
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Interjection: The Liquid Tensor Experiment
12:24
12:24
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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…
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Episode 59 – John Bruce Yeh / Chicago Clarinet Classics
1:22:52
1:22:52
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with clarinetist John Bruce Yeh, who has served the Chicago Symphony Orchestra as assistant principal clarinetist since 1979, about his experience recording "Chicago Clarinet Classics."By Cedille Records
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In this episode, I discuss the basic distinguishing rule of Extensional Martin-Loef Type Theory, namely equality reflection. This rule says that propositional equality implies definitional equality. Algorithmically, it would imply that the type checker should do arbitrary proof search during type checking, to see if two expressions are definitional…
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Episode 58 - Nicole Cabell and Craig Trompeter / L'Amant Anonyme
1:42:43
1:42:43
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with soprano Nicole Cabell and conductor Craig Trompeter about their experience creating the Haymarket Opera Company's world-premiere recording of "L'Amant Anonyme (The Anonymous Lover)", 1780 opera by Afro-French composer Joseph Bologne, Chevalier de Saint-Georges (1745–179…
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This episode begins a new chapter on extensionality in type theory, where we seek to equate terms in different ways based on their types. The basic example is function extensionality, where we would like to equate functions from A to B if given equal inputs at type A, they produce equal outputs at type B. With this definition, quicksort and mergeso…
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Papers from Formal Methods for Blockchains 2021
17:01
17:01
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In this episode, I talk about two papers from the 3rd International Workshop on Formal Methods for Blockchains, 2021. Also, I am continuing my request for your small donations ($5 or $10 would be awesome) to pay my podcast-hosting fees at Buzzsprout. To donate, click here, and then under "Gift details" select "Search for additional options" and the…
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Mi-Cho-Coq: Michelson formalized and applied, in Coq
15:34
15:34
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In this episode, I discuss this paper, "Mi-Cho-Coq, a Framework for Certifying Tezos Smart Contracts", by Bernardo et al. The paper gives a nice and very clear introduction to the Michelson language, and a formalization of it in Coq. This is used to prove a correctness property about a Multisig contract. I also kindly solicit your small donations (…
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Verification of Tezos smart contracts with K-Michelson
14:24
14:24
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In this episode (proudly wearing my "I am not an expert" hat), I discuss efforts by Runtime Verification to verify the Dexter2 defi smart contract, using their K-Michelson tool, which provides an executable description of the operational semantics of the Michelson language used for smart contracts on the Tezos blockchain.…
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Start of Season 4: Formal Methods for Blockchain
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I start off a new chapter (seventeen!) of the podcast, to talk about formal methods for blockchain systems. In the next few episodes, we will look at some verification efforts related to the Tezos blockchain.By Aaron Stump
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Episode 57 – Anthony McGill / American Stories
1:15:15
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Episode 57 – Anthony McGill / American Stories by Cedille RecordsBy Cedille Records
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Episode 56 – Joel Link / Beethoven Complete String Quartets: Volume 3 — The Late Quartets
1:10:48
1:10:48
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with the Dover Quartet's Joel Link about the chamber group's album "Beethoven Complete String Quartets: Volume 3 — The Late Quartets." This triple-CD release comprises Beethoven’s very last compositions — remarkable and often daunting works that upended the concept of the st…
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Separation Logic II: recursive predicates
11:52
11:52
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I discuss separation logic basics some more, as presented in the seminal paper by John C. Reynolds. An important idea is describing data structure using separating conjunction and recursive predicates.By Aaron Stump
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Episode 55: Rachel Barton Pine / Violin Concertos by Black Composers Through the Centuries
1:31:00
1:31:00
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On this episode of Classical Chicago, Cedille President Jim Ginsburg talks with violinist Rachel Barton Pine about Violin Concertos by Black Composers Through the Centuries: 25th anniversary edition. The album features Pine's new recording of Florence Price's Violin Concerto No. 2, with the Royal Scottish National Orchestra & Jonathon Heyward, and …
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Episode 54: Julian Velasco / As We Are
1:39:46
1:39:46
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On this episode of Classical Chicago, Cedille President Jim Ginsburg converses with saxophonist Julian Velasco, winner of Cedille Records' first-ever Emerging Artist Competition, about his upcoming debut album, As We Are.By Cedille Records
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I discuss separation logic, as presented in this seminal paper by the great John C. Reynolds. I did not go very far into the topic, so please expect a follow-up episode.By Aaron Stump
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In this episode, I talk briefly about Rust, which uses compile-time analysis to ensure that code is memory-safe (and also free of data races in concurrent code) without using a garbage collector. Fantastic! The language draws on but richly develops ideas on ownership that originated in academic research.…
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Episode 53 - Aurelien Fort Pederzoli (Black Oak Ensemble) / Avant l'orage
1:34:41
1:34:41
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Episode 53 - Aurelien Fort Pederzoli (Black Oak Ensemble) / Avant l'orage by Cedille RecordsBy Cedille Records
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I discuss the idea of statically typed region-based memory management, proposed by Tofte and Talpin. The idea is to allow programmers to declare explicitly the region from which to satisfy individual allocation requests. Regions are created in a statically scoped way, so that after execution leaves the body of the region-creation construct, the ent…
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Introduction to verified memory management
17:08
17:08
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In this episode, I start a new chapter (we are up to Chapter 16, here), about verifying safe manual management of memory. I have personally gotten pretty interested in this topic, having seen through some simple experiments with Haskell how much time can go into garbage collection for seemingly simple benchmarks. I also talk about why verifying mem…
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