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The Stunner: Linear System T is Diverging!

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Manage episode 501268069 series 2823367
Content provided by Aaron Stump. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Aaron Stump or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://podcastplayer.com/legal.

In this episode, I shoot down last episode's proposal -- at least in the version I discussed -- based on an amazing observation from an astonishing paper, "Gödel’s system T revisited", by Alves, Fernández, Florido, and Mackie. Linear System T is diverging, as they reveal through a short but clever example. It is even diverging if one requires that the iterator can only be reduced when the function to be iterated is closed (no free variables). This extraordinary observation does not sink Victor's idea of basing type theory on a terminating untyped core language, but it does sink the specific language he and I were thinking about, namely affine lambda calculus plus structural recursion.

My notes are here.

  continue reading

178 episodes

Artwork
iconShare
 
Manage episode 501268069 series 2823367
Content provided by Aaron Stump. All podcast content including episodes, graphics, and podcast descriptions are uploaded and provided directly by Aaron Stump or their podcast platform partner. If you believe someone is using your copyrighted work without your permission, you can follow the process outlined here https://podcastplayer.com/legal.

In this episode, I shoot down last episode's proposal -- at least in the version I discussed -- based on an amazing observation from an astonishing paper, "Gödel’s system T revisited", by Alves, Fernández, Florido, and Mackie. Linear System T is diverging, as they reveal through a short but clever example. It is even diverging if one requires that the iterator can only be reduced when the function to be iterated is closed (no free variables). This extraordinary observation does not sink Victor's idea of basing type theory on a terminating untyped core language, but it does sink the specific language he and I were thinking about, namely affine lambda calculus plus structural recursion.

My notes are here.

  continue reading

178 episodes

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