8655f7706f
This PR changes how Lean proves the equational theorems for structural recursion. The core idea is to let-bind the `f` argument to `brecOn` and rewriting `.brecOn` with an unfolding theorem. This means no extra case split for the `.rec` in `.brecOn` is needed, and `simp` doesn't change the `f` argument which can break the definitional equality with the defined function. With this, we can prove the unfolding theorem first, and derive the equational theorems from that, like for all other ways of defining recursive functions. Backs out the changes from #10415, the old strategy works well with the new goals. Fixes #5667 Fixes #10431 Fixes #10195 Fixes #2962
35 lines
1.2 KiB
Text
35 lines
1.2 KiB
Text
inductive Ty where
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| star: Ty
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notation " ✶ " => Ty.star
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abbrev Context : Type := List Ty
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inductive Lookup : Context → Ty → Type where
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| z : Lookup (t :: Γ) t
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inductive Term : Context → Ty → Type where
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| var : Lookup Γ a → Term Γ a
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| lam : Term (✶ :: Γ) ✶ → Term Γ ✶
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| ap : Term Γ ✶ → Term Γ ✶ → Term Γ ✶
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abbrev plus : Term Γ a → Term Γ a
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| .var i => .var i
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| .lam n => .lam (plus n)
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| .ap (.lam _) m => plus m -- This case takes precedence over the next one.
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| .ap l m => (plus l).ap (plus m)
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/--
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error: failed to generate equational theorem for `plus`
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failed to generate equality theorems for `match` expression `plus.match_1`
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Γ✝ : Context
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a✝ : Ty
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motive✝ : Term Γ✝ a✝ → Sort u_1
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n✝ : Term ( ✶ :: Γ✝) ✶
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h_1✝ : (i : Lookup Γ✝ a✝) → motive✝ (Term.var i)
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h_2✝ : (n : Term ( ✶ :: Γ✝) ✶ ) → motive✝ n.lam
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h_3✝ : (a : Term ( ✶ :: Γ✝) ✶ ) → (m : Term Γ✝ ✶ ) → motive✝ (a.lam.ap m)
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h_4✝ : (l m : Term Γ✝ ✶ ) → motive✝ (l.ap m)
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⊢ (⋯ ▸ fun x motive h_1 h_2 h_3 h_4 h => ⋯ ▸ h_2 n✝) n✝.lam motive✝ h_1✝ h_2✝ h_3✝ h_4✝ ⋯ = h_2✝ n✝
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-/
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#guard_msgs in
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#print equations plus
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