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 <[email protected]>: > 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 <[email protected]> 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. >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. > -- Alberto. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
