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perf: add high priority to OfSemiring.Q instances (#12782)
This PR adds high priority to instances for `OfSemiring.Q` in the grind ring envelope. When Mathlib is imported, instance synthesis for types like `OfSemiring.Q Nat` becomes very expensive because the solver explores many irrelevant paths before finding the correct instances. By marking these instances as high priority and adding shortcut instances for basic operations (`Add`, `Sub`, `Mul`, `Neg`, `OfNat`, `NatCast`, `IntCast`, `HPow`), instance synthesis resolves quickly. 🤖 Generated with [Claude Code](https://claude.com/claude-code) --------- Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com> Co-authored-by: Kim Morrison <kim@tqft.net>
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Leonardo de Moura
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@@ -330,7 +330,7 @@ theorem toQ_inj [AddRightCancel α] {a b : α} : toQ a = toQ b → a = b := by
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obtain ⟨k, h₁⟩ := h₁
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exact AddRightCancel.add_right_cancel a b k h₁
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instance [Semiring α] [AddRightCancel α] [NoNatZeroDivisors α] : NoNatZeroDivisors (OfSemiring.Q α) where
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instance (priority := high) [Semiring α] [AddRightCancel α] [NoNatZeroDivisors α] : NoNatZeroDivisors (OfSemiring.Q α) where
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no_nat_zero_divisors := by
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intro k a b h₁ h₂
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replace h₂ : mul (natCast k) a = mul (natCast k) b := h₂
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@@ -346,7 +346,7 @@ instance [Semiring α] [AddRightCancel α] [NoNatZeroDivisors α] : NoNatZeroDiv
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replace h₂ := NoNatZeroDivisors.no_nat_zero_divisors k (a₁ + b₂) (a₂ + b₁) h₁ h₂
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apply Quot.sound; simp [r]; exists 0; simp [h₂]
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instance {p} [Semiring α] [AddRightCancel α] [IsCharP α p] : IsCharP (OfSemiring.Q α) p where
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instance (priority := high) {p} [Semiring α] [AddRightCancel α] [IsCharP α p] : IsCharP (OfSemiring.Q α) p where
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ofNat_ext_iff := by
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intro x y
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constructor
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@@ -366,7 +366,7 @@ instance {p} [Semiring α] [AddRightCancel α] [IsCharP α p] : IsCharP (OfSemir
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apply Quot.sound
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exists 0; simp [← Semiring.ofNat_eq_natCast, this]
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instance [LE α] [IsPreorder α] [OrderedAdd α] : LE (OfSemiring.Q α) where
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instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : LE (OfSemiring.Q α) where
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le a b := Q.liftOn₂ a b (fun (a, b) (c, d) => a + d ≤ b + c)
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(by intro (a₁, b₁) (a₂, b₂) (a₃, b₃) (a₄, b₄)
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simp; intro k₁ h₁ k₂ h₂
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@@ -382,14 +382,14 @@ instance [LE α] [IsPreorder α] [OrderedAdd α] : LE (OfSemiring.Q α) where
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rw [this]; clear this
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rw [← OrderedAdd.add_le_left_iff])
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instance [LE α] [IsPreorder α] [OrderedAdd α] : LT (OfSemiring.Q α) where
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instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : LT (OfSemiring.Q α) where
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lt a b := a ≤ b ∧ ¬b ≤ a
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@[local simp] theorem mk_le_mk [LE α] [IsPreorder α] [OrderedAdd α] {a₁ a₂ b₁ b₂ : α} :
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Q.mk (a₁, a₂) ≤ Q.mk (b₁, b₂) ↔ a₁ + b₂ ≤ a₂ + b₁ := by
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rfl
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instance [LE α] [IsPreorder α] [OrderedAdd α] : IsPreorder (OfSemiring.Q α) where
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instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : IsPreorder (OfSemiring.Q α) where
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le_refl a := by
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obtain ⟨⟨a₁, a₂⟩⟩ := a
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change Q.mk _ ≤ Q.mk _
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@@ -424,7 +424,7 @@ theorem toQ_le [LE α] [IsPreorder α] [OrderedAdd α] {a b : α} : toQ a ≤ to
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theorem toQ_lt [LE α] [LT α] [LawfulOrderLT α] [IsPreorder α] [OrderedAdd α] {a b : α} : toQ a < toQ b ↔ a < b := by
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simp [lt_iff_le_and_not_ge]
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instance [LE α] [IsPreorder α] [OrderedAdd α] : OrderedAdd (OfSemiring.Q α) where
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instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : OrderedAdd (OfSemiring.Q α) where
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add_le_left_iff := by
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intro a b c
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obtain ⟨⟨a₁, a₂⟩⟩ := a
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@@ -438,7 +438,7 @@ instance [LE α] [IsPreorder α] [OrderedAdd α] : OrderedAdd (OfSemiring.Q α)
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rw [← OrderedAdd.add_le_left_iff]
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-- This perhaps works in more generality than `ExistsAddOfLT`?
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instance [LE α] [LT α] [LawfulOrderLT α] [IsPreorder α] [OrderedRing α] [ExistsAddOfLT α] : OrderedRing (OfSemiring.Q α) where
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instance (priority := high) [LE α] [LT α] [LawfulOrderLT α] [IsPreorder α] [OrderedRing α] [ExistsAddOfLT α] : OrderedRing (OfSemiring.Q α) where
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zero_lt_one := by
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rw [← toQ_ofNat, ← toQ_ofNat, toQ_lt]
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exact OrderedRing.zero_lt_one
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@@ -511,7 +511,16 @@ def ofCommSemiring : CommRing (OfSemiring.Q α) :=
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{ OfSemiring.ofSemiring with
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mul_comm := mul_comm }
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attribute [instance] ofCommSemiring
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attribute [instance high] ofCommSemiring
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instance (priority := high) [CommRing (OfSemiring.Q α)] : Add (OfSemiring.Q α) := by infer_instance
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instance (priority := high) [CommRing (OfSemiring.Q α)] : Sub (OfSemiring.Q α) := by infer_instance
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instance (priority := high) [CommRing (OfSemiring.Q α)] : Mul (OfSemiring.Q α) := by infer_instance
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instance (priority := high) [CommRing (OfSemiring.Q α)] : Neg (OfSemiring.Q α) := by infer_instance
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instance (priority := high) [CommRing (OfSemiring.Q α)] : OfNat (OfSemiring.Q α) n := by infer_instance
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attribute [local instance] Semiring.natCast Ring.intCast
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instance (priority := high) [CommRing (OfSemiring.Q α)] : NatCast (OfSemiring.Q α) := by infer_instance
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instance (priority := high) [CommRing (OfSemiring.Q α)] : IntCast (OfSemiring.Q α) := by infer_instance
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instance (priority := high) [CommRing (OfSemiring.Q α)] : HPow (OfSemiring.Q α) Nat (OfSemiring.Q α) := by infer_instance
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/-
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Remark: `↑a` is notation for `OfSemiring.toQ a`.
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@@ -62,7 +62,7 @@ info: • [Command] @ ⟨79, 0⟩-⟨79, 40⟩ @ Lean.Elab.Command.elabDeclarati
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⊢ 0 ≤ n
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after no goals
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• [Term] Nat.zero_le n : 0 ≤ n @ ⟨1, 1⟩†-⟨1, 1⟩† @ Lean.Elab.Term.elabApp
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• [Completion-Id] Nat.zero_le : some LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) _uniq.35.3 @ ⟨1, 0⟩†-⟨1, 0⟩†
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• [Completion-Id] Nat.zero_le : some LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) _uniq.47.3 @ ⟨1, 0⟩†-⟨1, 0⟩†
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• [Term] Nat.zero_le : ∀ (n : Nat), 0 ≤ n @ ⟨1, 0⟩†-⟨1, 0⟩†
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• [Term] n : Nat @ ⟨1, 5⟩†-⟨1, 5⟩† @ Lean.Elab.Term.elabIdent
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• [Completion-Id] n : some Nat @ ⟨1, 5⟩†-⟨1, 5⟩†
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@@ -1,8 +1,8 @@
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[Meta.synthInstance] 💥️ OfNat ?m 1
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[Meta.synthInstance] new goal OfNat ?m 1
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[Meta.synthInstance.instances] #[@Lean.Grind.Semiring.ofNat, @One.toOfNat1, @Int16.instOfNat, @UInt64.instOfNat, @Rat.instOfNat, @Int8.instOfNat, @instOfNatFloat, @BitVec.instOfNat, Dyadic.instOfNat, @Int64.instOfNat, @instOfNat, @Id.instOfNat, @UInt16.instOfNat, instOfNatNat, @UInt32.instOfNat, @UInt8.instOfNat, @Fin.instOfNat, @ISize.instOfNat, @instOfNatFloat32, @Int32.instOfNat, @USize.instOfNat]
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[Meta.synthInstance.apply] 💥️ apply @USize.instOfNat to OfNat ?m 1
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[Meta.synthInstance.tryResolve] 💥️ OfNat ?m 1 ≟ OfNat USize ?m
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[Meta.synthInstance.instances] #[@Lean.Grind.Semiring.ofNat, @One.toOfNat1, @Int16.instOfNat, @UInt64.instOfNat, @Rat.instOfNat, @Int8.instOfNat, @instOfNatFloat, @BitVec.instOfNat, Dyadic.instOfNat, @Int64.instOfNat, @instOfNat, @Id.instOfNat, @UInt16.instOfNat, instOfNatNat, @UInt32.instOfNat, @UInt8.instOfNat, @Fin.instOfNat, @ISize.instOfNat, @instOfNatFloat32, @Int32.instOfNat, @USize.instOfNat, @Lean.Grind.CommRing.OfCommSemiring.instOfNatQ]
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[Meta.synthInstance.apply] 💥️ apply @Lean.Grind.CommRing.OfCommSemiring.instOfNatQ to OfNat ?m 1
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[Meta.synthInstance.tryResolve] 💥️ OfNat ?m 1 ≟ OfNat (Lean.Grind.Ring.OfSemiring.Q ?m) ?m
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[Meta.Tactic.simp.rewrite] Nat.add_succ:1000:
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x + 1
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==>
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@@ -3,7 +3,7 @@
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{"items":
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[{"label": "veryLongDefinitionName",
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"kind": 6,
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"data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.39"]},
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"data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.51"]},
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{"label": "veryLongDefinitionNameVeryLongDefinitionName",
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"kind": 21,
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"data":
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@@ -17,7 +17,7 @@ Resolution of veryLongDefinitionName:
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{"label": "veryLongDefinitionName",
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"kind": 6,
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"detail": "Nat",
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"data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.39"]}
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"data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.51"]}
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Resolution of veryLongDefinitionNameVeryLongDefinitionName:
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{"label": "veryLongDefinitionNameVeryLongDefinitionName",
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"kind": 21,
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@@ -28,6 +28,7 @@ Note: The following definitions were not unfolded because their definition is no
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#guard_msgs in
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example : f = 1 := rfl
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set_option pp.mvars.anonymous false in
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/--
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error: Tactic `apply` failed: could not unify the conclusion of `@rfl`
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?a = ?a
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@@ -35,7 +36,7 @@ with the goal
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f = 1
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Note: The full type of `@rfl` is
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∀ {α : Sort ?u.121} {a : α}, a = a
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∀ {α : Sort _} {a : α}, a = a
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Note: The following definitions were not unfolded because their definition is not exposed:
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f ↦ 1
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