But the proofs where not studied before as mathematical structures.
Godel and any mathematician did profs, but proofs where
meta-mathematical, in the sense that they were not mathematical
objects,  although they could be formalized in a language. The same
happened with the notion of equality and equivalence etc That are
defined in a fuzzy or ad-hoc way. HOTT study how equal are two things
depending on the path from the one to the other, that is , what
topology has the proof of equality between the two.

2014/1/11, LizR <lizj...@gmail.com>:
> That sounds like (some of) what Bruno talks about. The computer programme
> known as the UD (and its trace) are "in maths". (And didn't Godel make
> proofs paths of maths?)
>
>
> On 12 January 2014 10:41, Alberto G. Corona <agocor...@gmail.com> wrote:
>
>> By the way, what about if you find a mathematical theory that show that:
>>
>> computer programs and matematical proofs  are no longer something out
>> of math, but mathematical structures and both are essentially the same
>> thing: both are paths from premises to conclussion in a  space with
>> topological properties
>>
>> And the theory stablish topological relations between these paths so
>> that proofs and computer algorithms are classified according with
>> these relations.
>>
>> That is homotopy type theory.
>>
>> http://homotopytypetheory.org/
>>
>> I´m starting to learn something about it, It is based on type theory,
>> category theory and topology. The book introduction is nice (HOTT link
>> at the bottom of the page). It seems to be a foundation of computer
>> science and math that unify both at a higher level, since proofs and
>> programs become legitimate mathematical structures
>>
>> The book:
>>
>> http://homotopytypetheory.org/2013/06/20/the-hott-book/
>>
>> --
>> Alberto.
>>
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-- 
Alberto.

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