mirror of
https://github.com/leanprover/lean4.git
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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.
66 lines
2.4 KiB
Lean4
66 lines
2.4 KiB
Lean4
module
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import Lean.Meta.Tactic.Grind.Arith.CommRing.Poly
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open Lean.Grind.CommRing
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def w : Expr := .var 0
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def x : Expr := .var 1
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def y : Expr := .var 2
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def z : Expr := .var 3
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instance : Add Expr where
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add a b := .add a b
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instance : Sub Expr where
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sub a b := .sub a b
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instance : Neg Expr where
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neg a := .neg a
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instance : Mul Expr where
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mul a b := .mul a b
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instance : HPow Expr Nat Expr where
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hPow a k := .pow a k
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instance : OfNat Expr n where
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ofNat := .num n
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def spol' (p₁ p₂ : Poly) : Poly :=
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p₁.spol p₂ |>.spol
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def check_spoly (e₁ e₂ r : Expr) : Bool :=
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let p₁ := e₁.toPoly
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let p₂ := e₂.toPoly
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let r := r.toPoly
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let s := p₁.spol p₂
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spol' p₁ p₂ == r &&
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spol' p₂ p₁ == r.mulConst (-1) &&
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s.spol == r &&
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r == (p₁.mulMon s.k₁ s.m₁).combine (p₂.mulMon s.k₂ s.m₂)
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example : check_spoly (y^2 - x + 1) (x*y - 1 + y) (-x^2 + y + x - y^2) := by native_decide
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example : check_spoly (y - z + 1) (x*y - 1) (-x*z + 1 + x) := by native_decide
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example : check_spoly (z^3 - x*y) (z*y - 1) (z^2 - x*y^2) := by native_decide
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example : check_spoly (x + 1) (z + 1) (z - x) := by native_decide
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example : check_spoly (w^2*x - y) (w*x^2 - z) (-y*x + z*w) := by native_decide
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example : check_spoly (2*z^3 - x*y) (3*z*y - 1) (2*z^2 - 3*x*y^2) := by native_decide
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example : check_spoly (2*x + 3) (3*z + 1) (9*z - 2*x) := by native_decide
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example : check_spoly (2*y^2 - x + 1) (2*x*y - 1 + y) (-x^2 + y + x - y^2) := by native_decide
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example : check_spoly (2*y^2 - x + 1) (4*x*y - 1 + y) (-2*x^2 + y + 2*x - y^2) := by native_decide
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example : check_spoly (6*y^2 - x + 1) (4*x*y - 1 + y) (-2*x^2 + 3*y + 2*x - 3*y^2) := by native_decide
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def simp? (p₁ p₂ : Poly) : Option Poly :=
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(·.p) <$> p₁.simp? p₂
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partial def simp' (p₁ p₂ : Poly) : Poly :=
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if let some r := p₁.simp? p₂ then
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assert! r.p == (p₂.mulMon r.k₂ r.m₂).combine (p₁.mulConst r.k₁)
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simp' r.p p₂
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else
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p₁
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def check_simp' (e₁ e₂ r : Expr) : Bool :=
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r.toPoly == simp' e₁.toPoly e₂.toPoly
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example : check_simp' (x^2*y - 1) (x*y - y) (y - 1) := by native_decide
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example : check_simp' (x^2 + x + 1) (2*x + 1) 3 := by native_decide
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example : check_simp' (3*x^2 + x + y + 1) (2*x + 1) (4*y + 5) := by native_decide
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example : check_simp' (3*x^2 + x + y + 1) (2*x + y) (3*y^2 + 2*y + 4) := by native_decide
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example : check_simp' (z^4 + w^3 + x^2 + x + 1) (2*x + 1) (4*z^4 + 4*w^3 + 3) := by native_decide
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