cfc46ac17f
This PR simplifies the `grind order` module, and internalizes the order constraints. It removes the `Offset` type class because it introduced too much complexity. We now cover the same use cases with a simpler approach: - Any type that implements at least `Std.IsPreorder` - Arbitrary ordered rings. - `Nat` by the `Nat.ToInt` adapter.
127 lines
8.9 KiB
Text
127 lines
8.9 KiB
Text
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def A.foo {α : Type} [Add α] (a : α) : α × α :=
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(a, a + a)
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def B.foo {α : Type} (a : α) : α × α :=
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(a, a)
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open A
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open B
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set_option trace.Meta.synthInstance true
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/--
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info: B.foo "hello" : String × String
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---
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trace: [Meta.synthInstance] ❌️ Add String
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[Meta.synthInstance] new goal Add String
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[Meta.synthInstance.instances] #[@Lean.Grind.AddCommMonoid.toAdd, @Lean.Grind.Semiring.toAdd]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Semiring.toAdd to Add String
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[Meta.synthInstance.tryResolve] ✅️ Add String ≟ Add String
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[Meta.synthInstance] new goal Lean.Grind.Semiring String
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[Meta.synthInstance.instances] #[@Lean.Grind.Ring.toSemiring, @Lean.Grind.CommSemiring.toSemiring]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.CommSemiring.toSemiring to Lean.Grind.Semiring String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.Semiring String ≟ Lean.Grind.Semiring String
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[Meta.synthInstance] new goal Lean.Grind.CommSemiring String
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[Meta.synthInstance.instances] #[@Lean.Grind.CommRing.toCommSemiring]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.CommRing.toCommSemiring to Lean.Grind.CommSemiring String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.CommSemiring String ≟ Lean.Grind.CommSemiring String
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[Meta.synthInstance] new goal Lean.Grind.CommRing String
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[Meta.synthInstance.instances] #[@Lean.Grind.Field.toCommRing]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Field.toCommRing to Lean.Grind.CommRing String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.CommRing String ≟ Lean.Grind.CommRing String
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[Meta.synthInstance] no instances for Lean.Grind.Field String
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[Meta.synthInstance.instances] #[]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Ring.toSemiring to Lean.Grind.Semiring String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.Semiring String ≟ Lean.Grind.Semiring String
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[Meta.synthInstance] new goal Lean.Grind.Ring String
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[Meta.synthInstance.instances] #[@Lean.Grind.CommRing.toRing]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.CommRing.toRing to Lean.Grind.Ring String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.Ring String ≟ Lean.Grind.Ring String
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[Meta.synthInstance] ✅️ apply @Lean.Grind.AddCommMonoid.toAdd to Add String
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[Meta.synthInstance.tryResolve] ✅️ Add String ≟ Add String
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[Meta.synthInstance] new goal Lean.Grind.AddCommMonoid String
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[Meta.synthInstance.instances] #[@Lean.Grind.AddCommGroup.toAddCommMonoid, @Lean.Grind.NatModule.toAddCommMonoid]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.NatModule.toAddCommMonoid to Lean.Grind.AddCommMonoid String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommMonoid String ≟ Lean.Grind.AddCommMonoid String
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[Meta.synthInstance] new goal Lean.Grind.NatModule String
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[Meta.synthInstance.instances] #[@Lean.Grind.IntModule.toNatModule, @Lean.Grind.Semiring.toNatModule]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Semiring.toNatModule to Lean.Grind.NatModule String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.NatModule String ≟ Lean.Grind.NatModule String
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[Meta.synthInstance] ✅️ apply @Lean.Grind.IntModule.toNatModule to Lean.Grind.NatModule String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.NatModule String ≟ Lean.Grind.NatModule String
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[Meta.synthInstance] new goal Lean.Grind.IntModule String
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[Meta.synthInstance.instances] #[@Lean.Grind.Ring.toIntModule]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Ring.toIntModule to Lean.Grind.IntModule String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.IntModule String ≟ Lean.Grind.IntModule String
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[Meta.synthInstance] ✅️ apply @Lean.Grind.AddCommGroup.toAddCommMonoid to Lean.Grind.AddCommMonoid String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommMonoid String ≟ Lean.Grind.AddCommMonoid String
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[Meta.synthInstance] new goal Lean.Grind.AddCommGroup String
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[Meta.synthInstance.instances] #[@Lean.Grind.IntModule.toAddCommGroup, @Lean.Grind.Ring.toAddCommGroup]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Ring.toAddCommGroup to Lean.Grind.AddCommGroup String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommGroup String ≟ Lean.Grind.AddCommGroup String
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[Meta.synthInstance] ✅️ apply @Lean.Grind.IntModule.toAddCommGroup to Lean.Grind.AddCommGroup String
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommGroup String ≟ Lean.Grind.AddCommGroup String
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[Meta.synthInstance] result <not-available>
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-/
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#guard_msgs in
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-- `foo` is overloaded, the case `A.foo` is discarded because we don't have an instance `[Add String]`.
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-- However, we still want to see the trace since we used trace.Meta.synthInstance
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#check foo "hello"
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/--
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trace: [Meta.synthInstance] ❌️ Add Bool
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[Meta.synthInstance] new goal Add Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.AddCommMonoid.toAdd, @Lean.Grind.Semiring.toAdd]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Semiring.toAdd to Add Bool
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[Meta.synthInstance.tryResolve] ✅️ Add Bool ≟ Add Bool
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[Meta.synthInstance] new goal Lean.Grind.Semiring Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.Ring.toSemiring, @Lean.Grind.CommSemiring.toSemiring]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.CommSemiring.toSemiring to Lean.Grind.Semiring Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.Semiring Bool ≟ Lean.Grind.Semiring Bool
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[Meta.synthInstance] new goal Lean.Grind.CommSemiring Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.CommRing.toCommSemiring]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.CommRing.toCommSemiring to Lean.Grind.CommSemiring Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.CommSemiring Bool ≟ Lean.Grind.CommSemiring Bool
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[Meta.synthInstance] new goal Lean.Grind.CommRing Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.Field.toCommRing]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Field.toCommRing to Lean.Grind.CommRing Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.CommRing Bool ≟ Lean.Grind.CommRing Bool
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[Meta.synthInstance] no instances for Lean.Grind.Field Bool
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[Meta.synthInstance.instances] #[]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Ring.toSemiring to Lean.Grind.Semiring Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.Semiring Bool ≟ Lean.Grind.Semiring Bool
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[Meta.synthInstance] new goal Lean.Grind.Ring Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.CommRing.toRing]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.CommRing.toRing to Lean.Grind.Ring Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.Ring Bool ≟ Lean.Grind.Ring Bool
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[Meta.synthInstance] ✅️ apply @Lean.Grind.AddCommMonoid.toAdd to Add Bool
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[Meta.synthInstance.tryResolve] ✅️ Add Bool ≟ Add Bool
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[Meta.synthInstance] new goal Lean.Grind.AddCommMonoid Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.AddCommGroup.toAddCommMonoid, @Lean.Grind.NatModule.toAddCommMonoid]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.NatModule.toAddCommMonoid to Lean.Grind.AddCommMonoid Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommMonoid Bool ≟ Lean.Grind.AddCommMonoid Bool
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[Meta.synthInstance] new goal Lean.Grind.NatModule Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.IntModule.toNatModule, @Lean.Grind.Semiring.toNatModule]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Semiring.toNatModule to Lean.Grind.NatModule Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.NatModule Bool ≟ Lean.Grind.NatModule Bool
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[Meta.synthInstance] ✅️ apply @Lean.Grind.IntModule.toNatModule to Lean.Grind.NatModule Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.NatModule Bool ≟ Lean.Grind.NatModule Bool
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[Meta.synthInstance] new goal Lean.Grind.IntModule Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.Ring.toIntModule]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Ring.toIntModule to Lean.Grind.IntModule Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.IntModule Bool ≟ Lean.Grind.IntModule Bool
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[Meta.synthInstance] ✅️ apply @Lean.Grind.AddCommGroup.toAddCommMonoid to Lean.Grind.AddCommMonoid Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommMonoid Bool ≟ Lean.Grind.AddCommMonoid Bool
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[Meta.synthInstance] new goal Lean.Grind.AddCommGroup Bool
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[Meta.synthInstance.instances] #[@Lean.Grind.IntModule.toAddCommGroup, @Lean.Grind.Ring.toAddCommGroup]
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[Meta.synthInstance] ✅️ apply @Lean.Grind.Ring.toAddCommGroup to Lean.Grind.AddCommGroup Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommGroup Bool ≟ Lean.Grind.AddCommGroup Bool
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[Meta.synthInstance] ✅️ apply @Lean.Grind.IntModule.toAddCommGroup to Lean.Grind.AddCommGroup Bool
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[Meta.synthInstance.tryResolve] ✅️ Lean.Grind.AddCommGroup Bool ≟ Lean.Grind.AddCommGroup Bool
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[Meta.synthInstance] result <not-available>
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-/
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#guard_msgs in
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theorem ex : foo true = (true, true) :=
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rfl
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