Iowa Type Theory Commute

Aaron Stump

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

  1. pred 6 d.

    Coercive subtyping and coherence

    In this episode, I give further arguments in favor of coercive subtyping from a software-engineering perspective.  I also explain the critical concept of coherence.

    21 min

  2. 7. 5.

    A Strange Deal, Explained

    I explain the story from last episode.

    8 min

  3. 1. 5.

    A Strange Deal

    The Curry-Howard isomorphism for the law of excluded middle, as a radio drama.  I first saw a version of this story performed by Phil Wadler and Frank Pfenning (wearing fake horns!) at RTA in Nara, Japan in 2005.  This is my take on it.  In a subsequent episode, I will explain how the story illustrates the computational interpretation of the law of excluded middle.

    3 min

  4. 20. 4.

    Great paper: The Calculated Typer

    I discuss a nice paper I quite enjoyed reading, called The Calculated Typer, by Garby, Bahr, and Hutton.  The authors take a very nice general look at the specification of a type checker, for a very simple expression language.  They then manually derive the actual code for the type checker by effectively trying to prove that this as yet unknown code satisfies its spec.  (This is what is meant by calculating the type checker.)

    24 min

  5. 2. 4.

    Double-negation translations and CPS conversion, part 2

    In this episode, I talk about the control operator callcc, and how it is implemented during compilation using continuation-passing style (CPS).  I sketch how CPS conversion (transforming a program with callcc into one in CPS that does not need callcc any more) corresponds to double-negation translation from classical to intuitionistic logic.  The paper I am referencing is here.

    14 min

  6. 31. 3.

    Double-negation translations and CPS conversion, part 1

    In this episode, I talk about a somewhat more advanced case of the Curry-Howard isomorphism (the connection between logic and programming languages where formulas in logic are identified with types, and proofs with programs).  This is the identification of double-negation translations in logic, which go back to a paper of Kolmogorov's in 1925, with conversion to continuation-passing style (CPS), a compilation technique.  For this episode, we just discuss the idea of double-negation translation: classical theorems can be translated to intuitionistic ones, by adding some double negations.  As an example, we talk through the intuitionistic proof of the double negation of the law of excluded middle: not not (p or not p).

    14 min

  7. 3. 3.

    What are commuting conversions in proof theory?

    Commuting conversions are transformations on proofs in natural deduction, that move certain stuck inferences out of the way, so that the normal detour reductions (which correspond to beta-reduction under Curry-Howard) are enabled.  The stuck inferences are uses of disjunction elimination.  In programming terms, if you have an if-then-else (a simple case of or-elimination) where the then- and else-branches are lambda abstractions, and you apply that if-then-else to an argument, you need commuting conversions to move the argument into the branches, so you can call the functions (in the then- and else-branches) with it. See Section 10.1 of Girard's Proofs and Types for more on the problem, and a nice paper by de Groote on strong normalization with commuting conversions.

    22 min

  8. 16. 1.

    What is Control Flow Analysis for Lambda Calculus?

    I am currently on a frolic into the literature on Control Flow Analysis (CFA), and discuss what this is, for pure lambda calculus.  A wonderful reference for this is this paper by Palsberg.

    19 min
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O relácii

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

Informácie

  • Námet
    Aaron Stump
  • Aktívne
    2019 - 2026
  • Epizódy
    187
  • Hodnotenie
    Vhodné
  • Autorské práva
    © 2026 Iowa Type Theory Commute
  • Zobraziť webstránku
    Iowa Type Theory Commute

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