Theorem Proving in Lean

Re:Theorem Proving in Lean by tom_mellior on Tuesday May 29, 2018 @10:10AM (#17179292)

There are tons of other ways of writing the same thing in Lean too, of course. Here is one:

    theorem and_commutative (p q : Prop) : p ∧ q → q ∧ p :=
    begin intros, simp * end

https://leanprover.github.io/live/3.4.1/#code=theorem%20and_...

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Re:Theorem Proving in Lean by kevinzz on Tuesday May 29, 2018 @06:47PM (#17183448)

In Lean you could do

  theorem and_commutative (p q : Prop) : p ∧ q → q ∧ p := by cc

for a tactic proof and

  theorem and_commutative (p q : Prop) : p ∧ q → q ∧ p := λ ⟨h,j⟩,⟨j,h⟩

for a term proof (just write down the function).

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Re:Theorem Proving in Lean by gmfawcett on Tuesday May 29, 2018 @11:04AM (#17179754)

Cool, thanks for this. I've yet to play with Lean, but it looks very interesting! (I'm hoping that my time invested in Coq will transfer reasonably well...)

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Re:Theorem Proving in Lean by tom_mellior on Tuesday May 29, 2018 @03:32PM (#17182250)

You're welcome! I'm in a similar boat, coming to this tutorial from a Coq background (and some Isabelle/HOL). I'm pleasantly surprised how similar many things are. But I'm also a bit disappointed because I was under the impression that Lean was relying on automation via Z3 a lot more. Not quite done with the tutorial yet, so there might still be some material to this effect coming up, but I'm afraid not.

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