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.
46 lines
1.3 KiB
Text
46 lines
1.3 KiB
Text
prelude -- optional
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import Init.WF
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import Init.WFTactics
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import Init.Data.Nat.Basic
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namespace Nat'
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protected def modCore (y : Nat) : Nat → Nat → Nat
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| Nat.zero, x => x
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| Nat.succ fuel, x => if 0 < y ∧ y ≤ x then Nat'.modCore y fuel (x - y) else x
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protected def mod' (x y : @& Nat) : Nat :=
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Nat'.modCore y x x
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@[simp] theorem zero_mod' (b : Nat) : Nat'.mod' 0 b = 0 := rfl
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end Nat'
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namespace Nat
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private def gcdF' (x : Nat) : (∀ x₁, x₁ < x → Nat → Nat) → Nat → Nat :=
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match x with
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| 0 => fun _ y => y
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| succ x => fun f y => f (Nat'.mod' y (succ x)) sorry (succ x)
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noncomputable def gcd' (a b : Nat) : Nat :=
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WellFounded.fix (measure id).wf gcdF' a b
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@[simp] theorem gcd'_zero_left (y : Nat) : gcd' 0 y = y :=
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rfl
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theorem gcd'_succ (x y : Nat) : gcd' (succ x) y = gcd' (Nat'.mod' y (succ x)) (succ x) :=
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rfl -- replace with `id rfl` and everything is ok
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/--
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error: (kernel) application type mismatch
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@Eq.ndrec Nat (n✝ + 1) (fun n => gcd' n 0 = n) (of_eq_true (eq_self (n✝ + 1)))
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argument has type
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n✝ + 1 = n✝ + 1
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but function has type
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(fun n => gcd' n 0 = n) (n✝ + 1) → ∀ {b : Nat}, n✝ + 1 = b → (fun n => gcd' n 0 = n) b
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-/
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#guard_msgs in
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@[simp] theorem gcd'_zero_right (n : Nat) : gcd' n 0 = n := by
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cases n <;> simp [gcd'_succ]
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end Nat
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