f0a11b8864
types like
```
inductive Many (α : Type u) where
| none : Many α
| more : α → (Unit → Many α) → Many α
```
have a `.brecOn` only supports motives producing `Type u`, but not `Sort
u`, but our induction principles produce `Prop`. So the previous
implementation of functional induction would fail for functions that
structurally recurse over such types.
We recognize this case now and, rather hazardously, replace `.brecOn`
with `.binductionOn` (and thus `.below ` with `.ibelow` and `PProd` with
`And`). This assumes that these definitions are highly analogous.
This also improves the error message when realizing a reserved name
fails with an exception, by prepending
```
Failed to realize constant {id}:
```
to the error message.
Fixes #4320
23 lines
858 B
Text
23 lines
858 B
Text
inductive Many (α : Type u) where
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| none : Many α
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| more : α → (Unit → Many α) → Many α
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def many_map {α β : Type} (f : α → β) : Many α → Many β
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| .none => .none
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| .more x xs => Many.more (f x) (fun () => many_map f <| xs ())
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/--
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info: many_map.induct {α β : Type} (f : α → β) (motive : Many α → Prop) (case1 : motive Many.none)
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(case2 : ∀ (x : α) (xs : Unit → Many α), motive (xs ()) → motive (Many.more x xs)) : ∀ (a : Many α), motive a
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-/
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#guard_msgs in
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#check many_map.induct
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-- Unrelated, but for fun, show that we get the identical theorem from well-founded recursion
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def many_map' {α β : Type} (f : α → β) : Many α → Many β
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| .none => .none
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| .more x xs => Many.more (f x) (fun () => many_map' f <| xs ())
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termination_by m => m
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example : @many_map.induct = @many_map'.induct := rfl
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