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.
91 lines
2.5 KiB
Text
91 lines
2.5 KiB
Text
@[coe] def Bool.toNat' : Bool → Nat
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| true => 1
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| false => 0
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instance : Coe Bool Nat where
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coe := Bool.toNat'
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@[norm_cast] theorem ofNat_band (a b : Bool) : (↑(a && b) : Nat) = ↑a &&& ↑b := by
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cases a <;> cases b <;> rfl
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example (a b c : Bool) (n : Nat) (h : n = a &&& b &&& c)
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: (↑(a && b && c) : Nat) = n := by
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push_cast
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guard_target =ₛ(↑a &&& ↑b &&& ↑c) = n
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rw [h]
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example (a b c : Bool) (n : Nat) (h : n = (a && b && c))
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: (↑a &&& ↑b &&& ↑c) = n := by
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norm_cast
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guard_target =ₛ ↑(a && b && c) = n
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rw [h]
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set_option linter.missingDocs false
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variable (an bn cn dn : Nat) (az bz cz dz : Int)
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example : (an : Int) = bn → an = bn := by intro h; exact_mod_cast h
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example : an = bn → (an : Int) = bn := by intro h; exact_mod_cast h
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example : (an : Int) < bn ↔ an < bn := by norm_cast
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example : (an : Int) ≠ (bn : Int) ↔ an ≠ bn := by norm_cast
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-- zero and one cause special problems
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example : az > (1 : Nat) ↔ az > 1 := by norm_cast
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example : az > (0 : Nat) ↔ az > 0 := by norm_cast
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example : (an : Int) ≠ 0 ↔ an ≠ 0 := by norm_cast
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example (a b : Nat) (h : False) : (a : Int) < ((2 * b : Nat) : Int) := by
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push_cast
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guard_target = (a : Int) < 2 * (b : Int)
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cases h
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example : (an : Int) + bn = (an + bn : Nat) := by norm_cast
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example (h : ((an + bn : Nat) : Int) = (an : Int) + (bn : Int)) : True := by
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push_cast at h
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guard_hyp h : (an : Int) + (bn : Int) = (an : Int) + (bn : Int)
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trivial
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example (h : ((an * bn : Nat) : Int) = (an : Int) * (bn : Int)) : True := by
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push_cast at h
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guard_hyp h : (an : Int) * (bn : Int) = (an : Int) * (bn : Int)
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trivial
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--testing numerals
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example : ((42 : Nat) : Int) = 42 := by norm_cast
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structure p (n : Int)
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example : p 42 := by
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norm_cast
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guard_target = p 42
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exact ⟨⟩
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example : an + bn = 1 ↔ (an + bn : Int) = 1 := by norm_cast
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example (h : bn ≤ an) : an - bn = 1 ↔ (an - bn : Int) = 1 := by norm_cast
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example (k : Nat) {x y : Nat} (h : ((x + y + k : Nat) : Int) = 0) : x + y + k = 0 := by
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push_cast at h
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guard_hyp h : (x : Int) + y + k = 0
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assumption_mod_cast
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example (a b : Nat) (h2 : ((a + b + 0 : Nat) : Int) = 10) :
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((a + b : Nat) : Int) = 10 := by
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push_cast
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push_cast [Int.add_zero] at h2
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exact h2
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theorem b (_h g : true) : true ∧ true := by
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constructor
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assumption_mod_cast
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assumption_mod_cast
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example : ¬n - k + 1 = 0 := by
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norm_cast
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/-! Test that we can pass simp configuration options to `norm_cast` -/
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example : ¬n - k + 1 = 0 := by
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norm_cast +singlePass
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