a35e6f4af7
A `Prop`-valued inductive type is a syntactic subsingleton if it has at most one constructor and all the arguments to the constructor are in `Prop`. Such types have large elimination, so they could be defined in `Type` or `Prop` without any trouble, though users tend to expect that such types define a `Prop` and need to learn to insert `: Prop`. Currently, the default universe for types is `Type`. This PR adds a heuristic: if a type is a syntactic subsingleton with exactly one constructor, and the constructor has at least one parameter, then the `inductive` command will prefer creating a `Prop` instead of a `Type`. For `structure`, we ask for at least one field. More generally, for mutual inductives, each type needs to be a syntactic subsingleton, at least one type must have one constructor, and at least one constructor must have at least one parameter. The motivation for this restriction is that every inductive type starts with a zero constructors and each constructor starts with zero fields, and stubbed-out types shouldn't be `Prop`. Thanks to @arthur-adjedj for the investigation in #2695 and to @digama0 for formulating the heuristic. Closes #2690
28 lines
564 B
Text
28 lines
564 B
Text
inductive Term : Type
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| id2: Term -> Term -> Term
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inductive Brx: Term -> Prop
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| id2: Brx z -> Brx (Term.id2 n z)
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def Brx.interp {a} (H: Brx a): Nat :=
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match a with
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| Term.id2 n z => by
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let ⟨Hn, Hz⟩: True ∧ Brx z
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:= by cases H <;> exact ⟨by simp, by assumption⟩;
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exact Hz.interp
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def Brx.interp_nil (H: Brx a): H.interp = H.interp
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:=
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by {
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unfold interp
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rfl
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}
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/--
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info: Brx.interp.eq_1 (n z : Term) (H_2 : Brx (n.id2 z)) :
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H_2.interp =
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match ⋯ with
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| ⋯ => Hz.interp
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-/
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#guard_msgs in
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#check Brx.interp.eq_1
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