Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
a026bc7edb
Projects like mathlib like to define projection functions with extra structure, for example one could imagine defining `Multiset.card : Multiset α →+ Nat`, which bundles the fact that `Multiset.card (m1 + m2) = Multiset.card m1 + Multiset.card m2` for all `m1 m2 : Multiset α`. A problem though is that so far this has prevented dot notation from working: you can't write `(m1 + m2).card = m1.card + m2.card`. With this PR, now you can. The way it works is that "LValue resolution" will apply CoeFun instances when trying to resolve which argument should receive the object of dot notation. A contrived-yet-representative example: ```lean structure Equiv (α β : Sort _) where toFun : α → β invFun : β → α infixl:25 " ≃ " => Equiv instance: CoeFun (α ≃ β) fun _ => α → β where coe := Equiv.toFun structure Foo where n : Nat def Foo.n' : Foo ≃ Nat := ⟨Foo.n, Foo.mk⟩ variable (f : Foo) #check f.n' -- Foo.n'.toFun f : Nat ``` Design note 1: While LValue resolution attempts to make use of named arguments when positional arguments cannot be used, when we apply CoeFun instances we disallow making use of named arguments. The rationale is that argument names for CoeFun instances tend to be random, which could lead dot notation randomly succeeding or failing. It is better to be uniform, and so it uniformly fails in this case. Design note 2: There is a limitation in that this will *not* make use of the values of any of the provided arguments when synthesizing the CoeFun instances (see the tests for an example), since argument elaboration takes place after LValue resolution. However, we make sure that synthesis will fail rather than choose the wrong CoeFun instance. Performance note: Such instances will be synthesized twice, once during LValue resolution, and again when applying arguments. This also adds in a small optimization to the parameter list computation in LValue resolution so that it lazily reduces when a relevant parameter hasn't been found yet, rather than using `forallTelescopeReducing`. It also switches to using `forallMetaTelescope` to make sure the CoeFun synthesis will fail if multiple instances could apply. Getting this to pretty print will be deferred to future work. Closes #1910 |
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