Quantum Homotopy Computer

  Bartosz Milewski's Programming Cafe

This is my 100th WordPress post, so I decided to pull all the stops and go into some crazy stuff where hard math and hard physics mix freely with wild speculation. I hope you will enjoy reading it as much as I enjoyed writing it.

It’s a HoTT Summer of 2013

One of my current activities is reading the new book, Homotopy Type Theory (HoTT) that promises to revolutionize the foundations of mathematics in a way that’s close to the heart of a programmer. It talks about types in the familiar sense: Booleans, natural numbers, (polymorphic) function types, tuples, discriminated unions, etc.

As do previous type theories, HoTT assumes the Curry-Howard isomorphism that establishes the correspondence between logic and type theory. The gist of it is that any theorem can be translated into a definition of a type; and its proof is equivalent to producing a value of that…

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