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.
64 lines
1.8 KiB
Text
64 lines
1.8 KiB
Text
def Nat.bit (b : Bool) (n : Nat) : Nat :=
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cond b (2*n+1) (2*n)
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theorem Nat.bit_div_even (h : n % 2 = 0) : bit false (n / 2) = n := by
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simp [bit]
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have := Nat.div_add_mod n 2
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simp [h] at this
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assumption
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theorem Nat.bit_div_odd (h : n % 2 ≠ 0) : bit true (n / 2) = n := by
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have h : n % 2 = 1 := by
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have := mod_lt n (by decide : 2 > 0)
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revert h this
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generalize n%2 = k
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match k with
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| 0 => decide
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| 1 => decide
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| n+2 => intros; contradiction
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simp [bit]
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have := Nat.div_add_mod n 2
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simp [h] at this
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assumption
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theorem Nat.div2_lt (h : n ≠ 0) : n / 2 < n := by
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match n with
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| 1 => decide
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| 2 => decide
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| 3 => decide
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| n+4 =>
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rw [div_eq, if_pos]
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refine succ_lt_succ (Nat.lt_trans ?_ (lt_succ_self _))
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exact @div2_lt (n+2) (by simp +arith)
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simp +arith
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@[specialize]
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def Nat.binrec
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(motive : Nat → Sort u)
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(base : Unit → motive 0)
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(ind : (b : Bool) → (n : Nat) → (Unit → motive n) → motive (bit b n))
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(n : Nat) : motive n :=
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if h₁ : n = 0 then
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h₁ ▸ base ()
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else if h₂ : n % 2 = 0 then
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bit_div_even h₂ ▸ ind false (n / 2) (fun _ => binrec motive base ind (n / 2))
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else
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bit_div_odd h₂ ▸ ind true (n / 2) (fun _ => binrec motive base ind (n / 2))
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termination_by n
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decreasing_by all_goals exact Nat.div2_lt h₁
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theorem Nat.binind
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(motive : Nat → Prop)
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(base : motive 0)
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(ind : (b : Bool) → (n : Nat) → motive n → motive (bit b n))
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(n : Nat) : motive n :=
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binrec motive (fun _ => base) (fun b n ih => ind b n (ih ())) n
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set_option trace.compiler.ir.result true in
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def Nat.toBit (n : Nat) : List Bool :=
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binrec (fun _ => List Bool)
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(fun _ => [])
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(fun b n ih => b :: ih ())
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n
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#guard Nat.toBit 18 == [false, true, false, false, true]
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