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1. • CommentRowNumber1.
   • CommentAuthorDavid_Corfield
   • CommentTimeJun 26th 2014
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   Author: David_Corfield
   Format: MarkdownItexWe started a reading group on the HoTT book here at Kent. One question came up which I'm not sure how to answer. Say you have two algorithms, e.g., for finding the gcd of two natural numbers. one of which is efficient and one slow. Since they give the same results for each pair, we say they are equal. So the upshot is that issues to do with algorithm complexity, etc., can't be represented in UF?

   We started a reading group on the HoTT book here at Kent. One question came up which I’m not sure how to answer.

   Say you have two algorithms, e.g., for finding the gcd of two natural numbers. one of which is efficient and one slow. Since they give the same results for each pair, we say they are equal. So the upshot is that issues to do with algorithm complexity, etc., can’t be represented in UF?

2. • CommentRowNumber2.
   • CommentAuthorZhen Lin
   • CommentTimeJun 26th 2014
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   Author: Zhen Lin
   Format: MarkdownItexYes: function extensionality erases those distinctions, at least with regards to propositional equality.

   Yes: function extensionality erases those distinctions, at least with regards to propositional equality.

3. • CommentRowNumber3.
   • CommentAuthorTobias Fritz
   • CommentTimeJun 26th 2014
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   Author: Tobias Fritz
   Format: MarkdownItexThere's been a <a href="http://mathoverflow.net/questions/156238/function-extensionality-does-it-make-a-difference-why-would-one-keep-it-out-of/">closely related question</a> on MO with a great answer by Andrej Bauer.

   There’s been a closely related question on MO with a great answer by Andrej Bauer.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeJun 26th 2014
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   Author: Mike Shulman
   Format: MarkdownItexComplexity isn't represented in the sense that the two algorithms compute the same *function*, which is of course the same as the case in the rest of mathematics.

   Complexity isn’t represented in the sense that the two algorithms compute the same function, which is of course the same as the case in the rest of mathematics.