fix: improve error message for partial inhabitation and add delta deriving
#5780
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Example new output:
```text
failed to compile partial definition 'checkMyList', could not prove that type is nonempty
Possible solutions:
- Ensure that there is an 'Inhabited' or 'Nonempty' instance for
Bool × ListNode
- Add such an instance to the parameter list.
- Add a parameter of this type to the parameter list.
```
Motivated [by Zulip](https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Why.20return.20type.20of.20partial.20function.20MUST.20.60inhabited.60.3F/near/477905312)
adomani
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partial inhabitationpartial inhabitation and add delta deriving
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… from parameters (#5821) Rather than having a special pass where `mkInhabitantFor` uses the `assumption` tactic, it creates `Inhabited` instances for each parameter and just searches for an `Inhabited`/`Nonempty` instance for the return type. This makes examples like the following work: ```lean partial def f (x : X) : Bool × X := ... ``` Removes the strategy where it looks for `Inhabited`/`Nonempty` instances for every suffix of the signature. This is a follow-up to #5780. Motivated [by Zulip](https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Why.20return.20type.20of.20partial.20function.20MUST.20.60inhabited.60.3F/near/477905312).
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…eriving (leanprover#5780) Example new output: ```text failed to compile 'partial' definition 'checkMyList', could not prove that the type ListNode → Bool × ListNode is nonempty. This process uses multiple strategies: - It looks for a parameter that matches the return type. - It tries synthesizing 'Inhabited' and 'Nonempty' instances for the return type. - It tries unfolding the return type. If the return type is defined using the 'structure' or 'inductive' command, you can try adding a 'deriving Nonempty' clause to it. ``` The inhabitation prover now also unfolds definitions when trying to prove inhabitation. For example, ```lean def T (α : Type) := α × α partial def f (n : Nat) : T Nat := f n ``` Motivated [by Zulip](https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Why.20return.20type.20of.20partial.20function.20MUST.20.60inhabited.60.3F/near/477905312)
tobiasgrosser
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… from parameters (leanprover#5821) Rather than having a special pass where `mkInhabitantFor` uses the `assumption` tactic, it creates `Inhabited` instances for each parameter and just searches for an `Inhabited`/`Nonempty` instance for the return type. This makes examples like the following work: ```lean partial def f (x : X) : Bool × X := ... ``` Removes the strategy where it looks for `Inhabited`/`Nonempty` instances for every suffix of the signature. This is a follow-up to leanprover#5780. Motivated [by Zulip](https://leanprover.zulipchat.com/#narrow/channel/113489-new-members/topic/Why.20return.20type.20of.20partial.20function.20MUST.20.60inhabited.60.3F/near/477905312).
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Example new output:
The inhabitation prover now also unfolds definitions when trying to prove inhabitation. For example,
Motivated by Zulip