Lean 4 fork for HoTT-compatible kernel extensions (Path types, transport, HITs). Maintained against upstream leanprover/lean4.
671ce7afd3
this improves support for structural recursion over inductive *predicates* when there are reflexive arguments. Consider ```lean inductive F: Prop where | base | step (fn: Nat → F) -- set_option trace.Meta.IndPredBelow.search true set_option pp.proofs true def F.asdf1 : (f : F) → True | base => trivial | step f => F.asdf1 (f 0) termination_by structural f => f` ``` Previously the search for the right induction hypothesis would fail with ``` could not solve using backwards chaining x✝¹ : F x✝ : x✝¹.below f : Nat → F a✝¹ : ∀ (a : Nat), (f a).below a✝ : Nat → True ⊢ True ``` The backchaining process will try to use `a✝ : Nat → True`, but then has no idea what to use for `Nat`. There are three steps here to fix this. 1. We let-bind the function's type before the whole process. Now the goal is ``` funType : F → Prop := fun x => True x✝ : x✝¹.below f : Nat → F a✝¹ : ∀ (a : Nat), (f a).below a✝ : ∀ (a : Nat), funType (f a) ⊢ funType (f 0) ``` 2. Instead of using the general purpose backchaining proof search, which is more powerful than we need here (we need on recursive search and no backtracking), we have a custom search that looks for local assumptions that provide evidence of `funType`, and extracts the arguments from that “type” application to construct the recursive call. Above, it will thus unify `f a =?= f 0`. 3. In order to make progress here, we also turn on use `withoutProofIrrelevance`, because else `isDefEq` is happy to say “they are equal” without actually looking at the terms and thus assigning `?a := 0`. This idea of let-binding the function's motive may also be useful for the other recursion compilers, as it may simplify the FunInd construction. This is to be investigated. fixes #4751 |
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