249530f3c1
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).
61 lines
1.8 KiB
Text
61 lines
1.8 KiB
Text
/-!
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# `partial` inhabitation with delta derivation
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-/
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set_option pp.mvars false
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/-!
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In the following, `partial` needs to unfold the return type to find an Inhabited instance.
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-/
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def MyGreatType (α : Type) := α × α
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partial def myLessGreatFunction (n : Nat) : MyGreatType Nat := myLessGreatFunction n
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/-!
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In the following, it needs to unfold underneath a forall.
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-/
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def MyGreaterType (α : Type) := α → MyGreatType α
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partial def myEvenLessGreatFunction (n : Nat) : MyGreaterType Nat := myEvenLessGreatFunction n
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/-!
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Regression test: can use existing parameter.
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-/
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partial def test1 (x : α) : α := test1 x
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/-!
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Regression test: can use Inhabited instance in parameter list.
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-/
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partial def test2 [Inhabited α] (n : Nat) : α := test2 n
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/-!
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Regression test: can use Nonempty instance in parameter list.
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-/
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partial def test3 [Nonempty α] (n : Nat) : α := test3 n
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/-!
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Error message.
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-/
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/--
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error: failed to compile 'partial' definition 'test4', could not prove that the type
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{α : Sort u_1} → Nat → α
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is nonempty.
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This process uses multiple strategies:
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- It looks for a parameter that matches the return type.
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- It tries synthesizing 'Inhabited' and 'Nonempty' instances for the return type, while making every parameter into a local 'Inhabited' instance.
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- It tries unfolding the return type.
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If the return type is defined using the 'structure' or 'inductive' command, you can try adding a 'deriving Nonempty' clause to it.
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-/
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#guard_msgs in partial def test4 (n : Nat) : α := test4 n
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/-!
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Add arguments as inhabited instances.
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Example adapted from 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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-/
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inductive ListNode where
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| mk : Nat → Option ListNode → ListNode
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partial def checkMyList (head : ListNode) : Bool × ListNode := checkMyList head
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