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The original vision was to construct multi-sorted type theory based on refinements (as in Darin and my recent paper), in which we would have things like `Pi(A; x.B)` refine `σ ⇀ τ` when `A` refines `σ…
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Hey Guys,
I've enjoyed playing around with building proofs using funExt, all of which have normalized successfully. When I went to play around with univalence, however, I noticed that none of the pro…
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After we added `quotient` types, we lost a nice property: every closed term evaluates to a value. We have "stuck" terms such as `eq.rec H1 (quot.sound H2)` that do not evaluate to a value.
Here is a r…
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@leodemoura, here is the error message that I get.
## Environment
- Machine: 2GB Ram, 2CPU, 40GB SSD (digitalocean.com)
- OS: Ubuntu 14.04
- Compiler: `g++ (Ubuntu 4.8.4-2ubuntu1~14.04) 4.8.4`
- CMake…
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@mikeshulman would like to have something similar to [modules](https://coq.inria.fr/distrib/current/refman/Reference-Manual007.html) in Coq, or at least a way to do the following two things:
- Have un…
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I am trying to prove (constructively) that R is complete. Since the proof goes via rational approximations of reals, it seems necessary to prove it for "prereals" (regular sequences of rationals) and …
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The introduction to the book currently says
> Using all types as propositions yields a "constructive" conception of logic... which gives type theory its good computational character.
Multiple people…
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I don't fully understand how the cubical sets stuff works, so forgive me if I'm noting something obvious. Anyway, I was trying to prove that `opBool3` in the `BoolEqBool` module was equivalent to `orB…