University of Birmingham > Talks@bham > Theoretical computer science seminar > From Brouwer's Thesis to the Fan Functional

From Brouwer's Thesis to the Fan Functional

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If you have a question about this talk, please contact Vincent Rahli.

The usual formulation of Brouwer’s Thesis (‘every bar is inductive’) uses quantification over infinite sequences of natural numbers to define what a bar is. We propose an alternative formulation that avoids infinite sequences and instead uses a coinductive definition to express the bar property. This coinductive formulation leads to a (new?) abstract version of Bar Induction which, combined with a modality for trivial truth, makes it possible to prove constructively that every continuous fuction on Cantor space is uniformly continuous. The computational content of that proof is a purely functional implementation of Tait’s Fan Functional computing the minimal modulus of uniform continuity of such functions.

This talk is part of the Theoretical computer science seminar series.

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