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Why is it worth spending time on type theory? (2013)
Looking around there are three candidates for "foundations of mathematics": set theory category theory type theory There is a seminal paper relating these three topics: From Sets to Types to Cate...
[...] a lot of people [in the type theory community] didn't know what they really talk about (in comparison to, say, classical analysis, where the definitions are very concrete and clear). It's a constructive setting for doing mathematics, so it allows to deal carefully with what can or can't be computed/decided (see intensionality vs. extensionality, or the different notions of reduction and conversion in $\lambda$-calculus). Distinctions like these make some mathematicians uncomfortable, but they prove helpful in dealing with certain things which are maybe more interesting to computer scientists (and of course logicians).
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