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Iowa Type Theory Commute

Iowa Type Theory Commute

By: Aaron Stump
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Summary
 Aaron Stump talks about type theory, computational logic, and related topics in Computer Science on his short commute.© 2026 Iowa Type Theory Commute Mathematics Science
Episodes
  • Great paper: Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism

    Great paper: Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism
    Oct 21 2026

    I start discussing this great paper by Dunfield and Krishnaswami, about how to extend a particular approach to type inference to handle polymorphism.
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    18 mins
  • Autoformalization of Fermat's Last Theorem

    Autoformalization of Fermat's Last Theorem
    Sep 15 2026

    In this episode, I reflect on the recent announcement that Anthropic researchers have autoformalized the proof of Fermat's Last Theorem. That is, they instructed an LLM to create a computer-checkable proof, in the Lean prover, of this theorem, following existing paper proofs in the literature. The resulting proof weighs in at 13 million lines of Lean, a staggering amount.
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    14 mins
  • A Fireball of Alpha

    A Fireball of Alpha
    Aug 21 2026

    I talk about my efforts to formalize lambda-calculus with named variables and explicit alpha-equivalence, as originally proposed by Church. One reason to do that, besides just a love of being ornery, is to be able to state and prove theorems about alpha-equivalence. One example class of such theorems concern when alpha-equivalence can be avoided, in the sense that beta-reduction can proceed without any variable capture, while not requiring renaming variables. I have a companion blog post that talks about this, with a link to the repo with my Agda code so far.
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    20 mins
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