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A continuous computational interpretation of type theories

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If you have a question about this talk, please contact Uday Reddy.

We develop a constructive variation of Johnstone’s topological topos to provide a computational interpretation of type theory validating Brouwer’s uniform-continuity principle, so that type-theoretic proofs with the principle as an assumption have computational content. The construction of our model and the verification of the uniform-continuity principle have been formalized in intensional Martin-Löf type theory in Agda notation. Hence we obtain a program of computing least moduli of uniform continuity!

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