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.
56 lines
1.5 KiB
Text
56 lines
1.5 KiB
Text
def f91 (n : Nat) : Option Nat :=
|
||
if n > 100
|
||
then pure (n - 10)
|
||
else f91 (n + 11) >>= f91
|
||
partial_fixpoint
|
||
|
||
section partial_correctness
|
||
|
||
-- #check f91.partial_correctness
|
||
|
||
theorem f91_partial_spec (n r : Nat) :
|
||
f91 n = some r → r = if n > 100 then n - 10 else 91 := by
|
||
apply f91.partial_correctness
|
||
intro f91 ih n r h
|
||
split at *
|
||
· simp_all
|
||
· simp only [Option.bind_eq_bind, Option.bind_eq_some_iff] at h
|
||
obtain ⟨r', hr1, hr2⟩ := h
|
||
replace hr1 := ih _ _ hr1
|
||
replace hr2 := ih _ _ hr2
|
||
clear ih
|
||
subst hr1
|
||
subst hr2
|
||
split
|
||
· simp; omega
|
||
· simp
|
||
|
||
end partial_correctness
|
||
|
||
section total_correctness
|
||
|
||
theorem f91_spec_high (n : Nat) (h : 100 < n) : f91 n = some (n - 10) := by
|
||
unfold f91; simp [*]
|
||
|
||
theorem f91_spec_low (n : Nat) (h₂ : n ≤ 100) : f91 n = some 91 := by
|
||
unfold f91
|
||
have : ¬ (100 < n) := by simp [*]
|
||
simp [*]
|
||
by_cases n < 90
|
||
· rw [f91_spec_low (n + 11) (by omega)]
|
||
simp only [Option.bind_some]
|
||
rw [f91_spec_low 91 (by omega)]
|
||
· rw [f91_spec_high (n + 11) (by omega)]
|
||
simp only [Nat.reduceSubDiff, Option.bind_some]
|
||
by_cases h : n = 100
|
||
· set_option linter.loopingSimpArgs false in
|
||
simp [*, f91]
|
||
· exact f91_spec_low (n + 1) (by omega)
|
||
|
||
theorem f91_spec (n : Nat) :
|
||
f91 n = some (if n ≤ 100 then 91 else n - 10) := by
|
||
by_cases h100 : n ≤ 100
|
||
· simp [f91_spec_low, *]
|
||
· simp [f91_spec_high, Nat.lt_of_not_le ‹_›, *]
|
||
|
||
end total_correctness
|