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.
87 lines
3.2 KiB
Text
87 lines
3.2 KiB
Text
def trailingZeros (i : Int) : Nat :=
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if h : i = 0 then 0 else aux i.natAbs i h (Nat.le_refl _) 0
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where
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aux (k : Nat) (i : Int) (hi : i ≠ 0) (hk : i.natAbs ≤ k) (acc : Nat) : Nat :=
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match k, (by omega : k ≠ 0) with
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| k + 1, _ =>
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if h : i % 2 = 0 then aux k (i / 2) (by omega) (by omega) (acc + 1)
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else acc
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termination_by structural k
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/--
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info: equations:
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@[defeq] theorem trailingZeros.aux.eq_1 : ∀ (i : Int) (hi : i ≠ 0) (acc k_2 : Nat) (x_1 : k_2 + 1 ≠ 0)
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(hk_2 : i.natAbs ≤ k_2 + 1),
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trailingZeros.aux k_2.succ i hi hk_2 acc = if h : i % 2 = 0 then trailingZeros.aux k_2 (i / 2) ⋯ ⋯ (acc + 1) else acc
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-/
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#guard_msgs(pass trace, all) in
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#print equations trailingZeros.aux
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-- set_option trace.Elab.definition.eqns true
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-- set_option trace.split.debug true
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-- set_option trace.Meta.Match.unify true
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def trailingZeros' (i : Int) : Nat :=
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if h : i = 0 then 0 else aux i.natAbs i h (Nat.le_refl _) 0
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where
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aux (k : Nat) (i : Int) (hi : i ≠ 0) (hk : i.natAbs ≤ k) (acc : Nat) : Nat :=
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match k, (by omega : k ≠ 0) with
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| k + 1, _ =>
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if h : i % 2 = 0 then aux k (i / 2) (by omega) (by omega) (acc + 1)
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else acc
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termination_by k
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/--
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info: equations:
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theorem trailingZeros'.aux.eq_1 : ∀ (i : Int) (hi : i ≠ 0) (acc k_2 : Nat) (x_1 : k_2 + 1 ≠ 0)
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(hk_2 : i.natAbs ≤ k_2 + 1),
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trailingZeros'.aux k_2.succ i hi hk_2 acc =
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if h : i % 2 = 0 then trailingZeros'.aux k_2 (i / 2) ⋯ ⋯ (acc + 1) else acc
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-/
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#guard_msgs(pass trace, all) in
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#print equations trailingZeros'.aux
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def trailingZeros2 (i : Int) : Nat :=
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if h : i = 0 then 0 else aux i.natAbs i h (Nat.le_refl _) 0
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where
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aux (k : Nat) (i : Int) (hi : i ≠ 0) (hk : i.natAbs ≤ k) (acc : Nat) : Nat :=
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match k with
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| k + 1 =>
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if h : i % 2 = 0 then aux k (i / 2) (by omega) (by omega) (acc + 1)
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else acc
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| 0 => by omega
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termination_by structural k
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/--
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info: equations:
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@[defeq] theorem trailingZeros2.aux.eq_1 : ∀ (i : Int) (hi : i ≠ 0) (acc k_2 : Nat) (hk_2 : i.natAbs ≤ k_2 + 1),
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trailingZeros2.aux k_2.succ i hi hk_2 acc =
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if h : i % 2 = 0 then trailingZeros2.aux k_2 (i / 2) ⋯ ⋯ (acc + 1) else acc
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@[defeq] theorem trailingZeros2.aux.eq_2 : ∀ (i : Int) (hi : i ≠ 0) (acc : Nat) (hk_2 : i.natAbs ≤ 0),
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trailingZeros2.aux 0 i hi hk_2 acc = acc
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-/
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#guard_msgs(pass trace, all) in
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#print equations trailingZeros2.aux
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def trailingZeros2' (i : Int) : Nat :=
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if h : i = 0 then 0 else aux i.natAbs i h (Nat.le_refl _) 0
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where
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aux (k : Nat) (i : Int) (hi : i ≠ 0) (hk : i.natAbs ≤ k) (acc : Nat) : Nat :=
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match k with
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| k + 1 =>
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if h : i % 2 = 0 then aux k (i / 2) (by omega) (by omega) (acc + 1)
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else acc
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| 0 => by omega
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termination_by k
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/--
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info: equations:
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theorem trailingZeros2'.aux.eq_1 : ∀ (i : Int) (hi : i ≠ 0) (acc k_2 : Nat) (hk_2 : i.natAbs ≤ k_2 + 1),
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trailingZeros2'.aux k_2.succ i hi hk_2 acc =
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if h : i % 2 = 0 then trailingZeros2'.aux k_2 (i / 2) ⋯ ⋯ (acc + 1) else acc
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theorem trailingZeros2'.aux.eq_2 : ∀ (i : Int) (hi : i ≠ 0) (acc : Nat) (hk_2 : i.natAbs ≤ 0),
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trailingZeros2'.aux 0 i hi hk_2 acc = acc
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-/
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#guard_msgs(pass trace, all) in
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#print equations trailingZeros2'.aux
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