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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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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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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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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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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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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 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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