Top new questions this week:
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I was messing around with toy lemmas in Idris and came up with this silly proof. …
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I defined this inductive type for representing JSON elements …
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Lean, unlike e.g. Haskell, makes you prove that recursive definitions of functions will eventually terminate, if the compiler can’t do it by using structural recursion, by using …
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I’ve defined a function (foldMem below) that Lean compiles into a brecOn eliminator. I need to reason with it later on, so I’m …
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To avoid tedious repetition I have a tactic that looks something like this: Ltac unfolds := try unfold foo; try unfold bar; try unfold baz; apply some_lemma. …
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I’ve seen elaboration-zoo, pi-forall, Mini-TT, etc., all kinds of demonstrations of dependent type elaboration. However, none of them support Prop. I am interested …
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Theorem Proving in Lean highlights a distinction between definitional and propositional equality when creating recursive functions: The example above shows that the defining equations for …
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Greatest hits from previous weeks:
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Type systems, and the proof assistants based on them, are frequently divided into predicative and impredicative. What exactly does this mean? I’ve heard the slogan “impredicativity means you can’…
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In the init/logic.lean file of the Lean 3 standard library, nonempty and inhabited are defined. It seems like these two classes …
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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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Coq and Lean are two of the most common proof assistants out there (but the question of course applies to other proof assistants too). What are the main differences between Coq and Lean? Ideally it …
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A type that is a member of a universe can be coerced into a higher universe. Is that coercion injective? That is, if two elements of U1 are equal after being coerced to U2, does that imply they are …
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In category theory a presheaf is defined as a functor whose target is $\mathrm{Set}$, and the concept is used to state the Yoneda lemma. The appearance of $\mathrm{Set}$ in the definition comes from …
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I keep seeing these phrasing in some proof assistants/elaborators and their issues/internal discussions (e.g. Github search results in cooltt), that seems not that related to the actual proofs/…
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