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. 6日前

    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 分鐘

  2. 4月20日

    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 分鐘

  3. 4月2日

    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 分鐘

  4. 3月31日

    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 分鐘

  5. 3月3日

    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 分鐘

  6. 1月16日

    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 分鐘

  7. 14/11/2025

    Measure Functions and Termination of STLC

    In this episode, I talk about what we should consider to be a measure function.  Such functions can be used to show termination of some process or program, by assigning a measure to each program, and showing that as the program computes, the measure decreases in some well-founded ordering.  But what should count as a measure function?  The context for this is RTA Open Problem 19, on showing termination for the simply typed lambda calculus using a measure function. Let's call this the start of season 7, because it seems about time for that.

    22 分鐘

  8. 22/08/2025

    Schematic Affine Recursion, Oh My!

    To solve the problem raised in the last episode, I propose schematic affine recursion.  We saw that affine lambda calculus (where lambda-bound variables are used at most once) plus structural recursion does not enforce termination, even if you restrict the recursor so that the function to be iterated is closed when you reduce ("closed at reduction").  You have to restrict it so that recursion terms are disallowed entirely unless the function to be iterated is closed ("closed at construction").  But this prevents higher-order functions like map, which need to repeat a computation involving a variable f to be mapped over the elements of a list.  The solution is to allow schematic definition of terms, using schema variables ranging over closed terms.

    19 分鐘
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關於

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

資料

  • 創作者
    Aaron Stump
  • 活躍年份
    2019年 - 2026年
  • 單集
    185
  • 分級
    兒童適宜
  • 版權
    © 2026 Iowa Type Theory Commute
  • 節目網站
    Iowa Type Theory Commute

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