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This post refers to the Curry-Howard isomorphism and the Martin-Löf Type Theory.

The post makes the claim of a future 'unification' between the the describing language of math, and the operation based language of computer programming.

My questions are:

  1. Will these ideas lead to a better ability (through languages) to write provably correct code?

  2. Have the full implications of MLTT been discovered on a theoretical level?

  3. Does this post describe anything could couldn't already do in COQ or Agda?

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I don't think your question is particularly well posed. It mostly asks for opinions. Here are mine:

  1. Yes.
  2. I do not know what you mean, but the answer is probably "there is more MLTT theory to be done, although we do know a lot".
  3. You cannot do all of homotopy type theory in Coq and Agda. This is an active area of research.
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  • $\begingroup$ Ok - how would you have phrased questions relating to the original post? $\endgroup$
    – hawkeye
    Nov 16 '12 at 5:05
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    $\begingroup$ I don't know because I do not understand what the question is asking. The second question is too broad, and the obvious answer is "no". The third question is ok, I suppose. The first question asks us to predict the future. $\endgroup$
    – Andrej Bauer
    Nov 16 '12 at 5:08

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