edf804c70f
This PR generalizes the `noConfusion` constructions to heterogeneous equalities (assuming propositional equalities between the indices). This lays ground work for better support for applying injection to heterogeneous equalities in grind. The `Meta.mkNoConfusion` app builder shields most of the code from these changes. Since the per-constructor noConfusion principles are now more expressive, `Meta.mkNoConfusion` no longer uses the general one. In `Init.Prelude` some proofs are more pedestrian because `injection` now needs a bit more machinery. This is a breaking change for whoever uses the `noConfusion` principle manually and explicitly for a type with indices. Fixes #11450.
59 lines
2.4 KiB
Text
59 lines
2.4 KiB
Text
/-!
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This test tests and also explains the noConfusionType construction.
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It contains copies of the definitions of the constructions, for manual experimentation with
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the code, and uses `#guard_msgs` and `rfl` to compare them to the generated ones.
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This also serves as documentation to the `NoConfusionLinear` module, so do not delete or remove
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from this file without updating that module's docstring.
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-/
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-- set_option debug.skipKernelTC true
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-- set_option trace.Meta.mkNoConfusion true
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-- set_option trace.Kernel true
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-- set_option genInjectivity false
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-- set_option trace.Meta.injective true
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-- set_option trace.Meta.Tactic.injection true
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inductive Vec.{u} (α : Type) : Nat → Type u where
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| nil : Vec α 0
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| cons1 {n} : α → Vec α n → Vec α (n + 1)
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| cons2 {n} : α → Vec α n → Vec α (n + 1)
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@[reducible] protected def Vec.noConfusionType'.{u_1, u} : {α : Type} →
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Sort u_1 → {a : Nat} → Vec.{u} α a → {a : Nat} → Vec α a → Sort u_1 :=
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fun P _ x1 _ x2 =>
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Vec.casesOn x1
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(if h : x2.ctorIdx = 0 then
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Vec.nil.elim (motive := fun _ _ => Sort u_1) x2 h (P → P)
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else P)
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(fun {n} a_1 a_2 => if h : x2.ctorIdx = 1 then
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Vec.cons1.elim (motive := fun _ _ => Sort u_1) x2 h fun {n_1} a a_3 => (n = n_1 → a_1 = a → a_2 ≍ a_3 → P) → P
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else P)
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(fun {n} a_1 a_2 => if h : x2.ctorIdx = 2 then
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Vec.cons2.elim (motive := fun _ _ => Sort u_1) x2 h fun {n_1} a a_3 => (n = n_1 → a_1 = a → a_2 ≍ a_3 → P) → P
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else P)
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/--
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info: @[reducible] protected def Vec.noConfusionType.{u_1, u} : {α : Type} →
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Sort u_1 → {a : Nat} → Vec α a → {a' : Nat} → Vec α a' → Sort u_1 :=
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fun {α} P {a} t {a'} t' =>
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Vec.casesOn t (if h : t'.ctorIdx = 0 then Vec.nil.elim t' h (P → P) else P)
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(fun {n} a a_1 =>
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if h : t'.ctorIdx = 1 then Vec.cons1.elim t' h fun {n_1} a_2 a_3 => (n = n_1 → a = a_2 → a_1 ≍ a_3 → P) → P
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else P)
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fun {n} a a_1 =>
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if h : t'.ctorIdx = 2 then Vec.cons2.elim t' h fun {n_1} a_2 a_3 => (n = n_1 → a = a_2 → a_1 ≍ a_3 → P) → P else P
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-/
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#guard_msgs in
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#print Vec.noConfusionType
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example : @Vec.noConfusionType.{u_1,u} = @Vec.noConfusionType'.{u_1,u} := rfl
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-- A possibly tricky universes case (resulting universe cannot be decremented)
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inductive UnivTest.{u,v} (α : Sort v): Sort (max u v 1) where
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| mk1 : UnivTest α
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| mk2 : (x : α) → UnivTest α
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| mk3 : (x : α) → UnivTest α
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