Top new questions this week:
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I would like to know the state of the art regarding the categorical semantics of the type theory implemented by Agda — or at least some approximation of that type theory that is amenable to …
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I have trouble understanding precisely how dependent type theories are intepreted in categories (in the most simple case, for example in a locally cartesian closed category). I know that a type in …
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I am wondering whether a rule like the following is consistent with decidable conversion and type-checking for dependent type theory: $$ \frac{f\, g : (x:\mathsf{bool}) \to C~x\quad f~\mathsf{tt} \…
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I’m implementing a version of cubical type theory where the well-definedness of pattern matching functions is implied by: the well-typedness of the clauses (type check) the coverage of the patterns (…
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Because there are both Arrays and Lists in Lean4, sometimes you end up with code that has a mixture of Lists and Arrays interspersed with basic operations and conversions between the two. For example,…
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Greatest hits from previous weeks:
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I’ve been playing with Lean, trying to prove the next lemma: lemma l1_cl (A B C : Prop) : ((A → B) → C) → ((A ∧ ¬ B) ∨ C) := …
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I was looking at the MSC2020 database and I find it hard to identify a field suitable for works about proof assistants and formalised mathematics. 03B70 (“Logic in Computer Science”) might …
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A “very dependent function” is a function whose output type at input $n$ depends on its own output values at inputs $k<n$. Is there a precise definition of such things that makes sense …
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I’ve just started with Coq and I don’t understand why it does not accept rewrite in the next situation. The following exercise is from “Coq in hurry”: …
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I’ve seen in mathlib several cases where the universes are explicit, that is Type u instead of Type*. Is there any advantage in …
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I am planning to implement a FOL proof assistant in Haskell. What are some useful libraries and implementations I should be looking at? Here are some further details. I have a simple proof checker for …
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Sometimes, trying to use rw in Lean, we get an error saying motive is not type correct What does this mean? Often …
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