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).

You can listen to Double-negation translations and CPS conversion, part 1 online on Radio and Podcast. Open the player on this page to stream the available audio.

Double-negation translations and CPS conversion, part 1 is an episode from Iowa Type Theory Commute by Aaron Stump.

This episode is 13:48 long.

This episode was published on Mar 31, 2026.

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