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.
189 lines
5.8 KiB
Text
189 lines
5.8 KiB
Text
-- In this file we use the `grobner` frontend for `grind`.
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module
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set_option grind.debug true
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open Lean.Grind
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example [CommRing α] [NoNatZeroDivisors α] (x y : α) : 3*x = 1 → 3*y = 2 → x + y = 1 := by
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grobner
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example [CommRing α] (x y : α) : 3*x = 1 → 3*y = 2 → x + y = 1 := by
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fail_if_success grobner
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sorry
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example [CommRing α] (x y : α) : x = 1 → y = 2 → 2*x + y = 4 := by
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grobner
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example [CommRing α] [IsCharP α 7] (x y : α) : 3*x = 1 → 3*y = 2 → x + y = 1 := by
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grobner
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example [CommRing α] [IsCharP α 7] (x y : α) : 2*x = 1 → 2*y = 1 → x + y = 1 := by
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grobner
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example [CommRing α] [IsCharP α 8] (x y : α) : 2*x = 1 → 2*y = 1 → x + y = 1 := by
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fail_if_success grobner
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sorry
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example [CommRing α] [IsCharP α 8] [NoNatZeroDivisors α] (x y : α) : 2*x = 1 → 2*y = 1 → x + y = 1 := by
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grobner
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example (x y : UInt8) : 3*x = 1 → 3*y = 2 → x + y = 1 := by
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grobner
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example (x y : UInt8) : 3*x = 1 → 3*y = 2 → False := by
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fail_if_success grobner
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sorry
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example [CommRing α] [NoNatZeroDivisors α] (x y : α) : 6*x = 1 → 3*y = 2 → 2*x + y = 1 := by
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grobner
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example [CommRing α] [NoNatZeroDivisors α] (x y : α) : 600000*x = 1 → 300*y = 2 → 200000*x + 100*y = 1 := by
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grobner
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example (x y : Int) : y = 0 → (x + 1)*(x - 1) + y = x^2 → False := by
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grobner
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example (x y z : BitVec 8) : z = y → (x + 1)*(x - 1)*y + y = z*x^2 + 1 → False := by
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grobner
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example [CommRing α] (x y : α) : x*y*x = 1 → x*y*y = y → y = 1 := by
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grobner
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example [CommRing α] (x y : α) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
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grobner
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example (x y : BitVec 16) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
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grobner
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example [CommRing α] (x y : α) (f : α → Nat) : x^2*y = 1 → x*y^2 = y → f (y*x) = f 1 := by
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grobner
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example [CommRing α] (x y : α) (f : α → Nat) : x^2*y = 1 → x*y^2 - y = 0 → f (y*x) = f (y*x*y) := by
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grobner
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example [CommRing α] (a b c : α)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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a^4 + b^4 + c^4 = 9 := by
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grobner
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/--
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trace: [grind.ring.assert.basis] a + b + c + -3 = 0
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[grind.ring.assert.basis] 2 * b ^ 2 + 2 * (b * c) + 2 * c ^ 2 + -6 * b + -6 * c + 4 = 0
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[grind.ring.assert.basis] 6 * c ^ 3 + -18 * c ^ 2 + 12 * c + 4 = 0
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-/
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#guard_msgs (trace) in
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example [CommRing α] (a b c : α)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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a^4 + b^4 = 9 - c^4 := by
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set_option trace.grind.ring.assert.basis true in
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grobner
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/--
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trace: [grind.ring.assert.basis] a + b + c + -3 = 0
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[grind.ring.assert.basis] b ^ 2 + b * c + c ^ 2 + -3 * b + -3 * c + 2 = 0
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[grind.ring.assert.basis] 3 * c ^ 3 + -9 * c ^ 2 + 6 * c + 2 = 0
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-/
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#guard_msgs (trace) in
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example [CommRing α] [NoNatZeroDivisors α] (a b c : α)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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a^4 + b^4 = 9 - c^4 := by
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set_option trace.grind.ring.assert.basis true in
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grobner
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example [CommRing α] (a b : α) (f : α → Nat) : a - b = 0 → f a = f b := by
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grobner
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example (a b : BitVec 8) (f : BitVec 8 → Nat) : a - b = 0 → f a = f b := by
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grobner
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example (a b c : BitVec 8) (f : BitVec 8 → Nat) : c = 255 → - a + b - 1 = c → f a = f b := by
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grobner
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example (a b c : BitVec 8) (f : BitVec 8 → Nat) : c = 255 → - a + b - 1 = c → f (2*a) = f (b + a) := by
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grobner
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/-- trace: [grind.ring.impEq] skip: b = a, k: 2, noZeroDivisors: false -/
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#guard_msgs (trace) in
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example (a b c : BitVec 8) (f : BitVec 8 → Nat) : 2*a = 1 → 2*b = 1 → f (a) = f (b) := by
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set_option trace.grind.ring.impEq true in
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fail_if_success grobner -lia
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sorry
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-- This one requires the `cutsat` solver as well.
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example (a b c : Int) (f : Int → Nat)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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f (a^4 + b^4) + f (9 - c^4) ≠ 1 := by
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grobner +lia
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-- Now we check the same example, calling `cutsat` but adding the `ring` solver.
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example (a b c : Int) (f : Int → Nat)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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f (a^4 + b^4) + f (9 - c^4) ≠ 1 := by
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cutsat +ring
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example [CommRing α] [NoNatZeroDivisors α] (a b c : α) (f : α → Nat)
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: a + b + c = 3 →
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a^2 + b^2 + c^2 = 5 →
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a^3 + b^3 + c^3 = 7 →
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f (a^4 + b^4) + f (9 - c^4) ≠ 1 := by
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grobner +lia
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example [CommRing α] [NoNatZeroDivisors α] (x y z : α) : 3*x = 1 → 3*z = 2 → 2*y = 2 → x + z + 3*y = 4 := by
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grobner
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example (x y : Fin 11) : x^2*y = 1 → x*y^2 = y → y*x = 1 := by
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grobner
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example (x y : Fin 11) : 3*x = 1 → 3*y = 2 → x + y = 1 := by
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grobner
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example (x y z : Fin 13) :
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(x + y + z) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 * (x * y + y * z + z * x) := by
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grobner
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example (x y : Fin 17) : (x + y) ^ 3 = x ^ 3 + y ^ 3 + 3 * x * y * (x + y) := by
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grobner
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example (x y : Fin 19) : (x - y) * (x ^ 2 + x * y + y ^ 2) = x ^ 3 - y ^ 3 := by
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grobner
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example (x : Fin 19) : (1 + x) ^ 5 = x ^ 5 + 5 * x ^ 4 + 10 * x ^ 3 + 10 * x ^ 2 + 5 * x + 1 := by
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grobner
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example (x : Fin 10) : (1 + x) ^ 5 = x ^ 5 + 5 * x ^ 4 - 5 * x + 1 := by
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grobner
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example (x y : Fin 3) (h : x = y) : ((x + y) ^ 3 : Fin 3) = - x^3 := by grobner
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-- Verify that `cutsat` is disabled when calling `grobner` directly.
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example (x : Nat) : x % 2 = 0 ∨ x % 2 = 1 := by
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fail_if_success grobner
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cutsat
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-- Verify that `grobner` will not perform case splits unless explicitly asked for.
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example (x : Int) (h : x^2 = 0) : (if x > 0 then x else x)^3 = 0 := by
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fail_if_success grobner
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grobner (splits := 1)
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-- Verify that `grobner` will not instantiate theorems.
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example {xs ys zs : List α} : (xs ++ ys) ++ zs = xs ++ (ys ++ zs) := by
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fail_if_success grobner
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grind
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example (x : BitVec 8) : (x - 16)*(x + 272) = x^2 := by
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grind
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example (x : BitVec 8) : (x - 16#8)*(x + 16#8) = x^2 := by
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grind
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example (x : BitVec 8) : (x - 16)*(x + 272#8) = x^2 := by
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grind
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