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https://github.com/leanprover/lean4.git
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08eb78a5b2
This PR sets up the new integrated test/bench suite. It then migrates all benchmarks and some related tests to the new suite. There's also some documentation and some linting. For now, a lot of the old tests are left alone so this PR doesn't become even larger than it already is. Eventually, all tests should be migrated to the new suite though so there isn't a confusing mix of two systems.
47 lines
1.3 KiB
Lean4
47 lines
1.3 KiB
Lean4
inductive Vec (α : Type u) : Nat → Type u
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| nil : Vec α 0
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| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
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def Vec.repeat (a : α) (n : Nat) : Vec α n :=
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match n with
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| 0 => nil
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| n+1 => cons a («repeat» a n)
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instance [Inhabited α] : Inhabited (Vec α n) where
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default := Vec.repeat default n
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def Vec.map (v : Vec α n) (f : α → β) : Vec β n :=
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match n, v with
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| _, nil => nil
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| _, cons a as => cons (f a) (map as f)
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def Vec.reverse (v : Vec α n) : Vec α n :=
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let rec loop {n m : Nat} : Vec α n → Vec α m → Vec α (n + m)
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| nil, w => Nat.zero_add .. ▸ w
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| cons a as, w => Nat.add_assoc .. ▸ loop as (Nat.add_comm .. ▸ cons a w)
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loop v nil
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@[simp] theorem map_id (v : Vec α n) : v.map id = v := by
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induction v with
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| nil => rfl
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| cons a as ih => simp [Vec.map, ih]
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def foo [Add α] (v w : Vec α n) (f : α → α) (a : α) : α :=
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match n, v.map f, w.map f with
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| _, Vec.nil, Vec.nil => a
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| _, Vec.cons a .., Vec.cons b .. => a + b
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theorem ex1 (a b : Nat) (as : Vec Nat n) : foo (Vec.cons a as) (Vec.cons b as) id 0 = a + b := by
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simp [foo]
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#print ex1
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def bla (b : Bool) (f g : α → β) (a : α) : β :=
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(match b with
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| true => f | false => g) a
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theorem ex2 (h : b = false) : bla b (fun x => x + 1) id 10 = 10 := by
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simp [bla, h]
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#print ex2
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