A Limited Case for Reification by Type Inference
summary
Reification by type inference shows that Coq’s notation system plus type inference can build a structured representation of curried argument types without Ltac: an inductive unquery_types and a denote function are used, recursive notations insert an uncurry/denote trick at each binder, and cbv reduction and unification drive inversion of denote to cons the type list. The demo implements arbitrary-arity uncurrying, a notation-driven insertion technique that produces a reified type list, and a function that reverses the curry structure; it works for this restricted pattern but requires a unit tail or CPS cleanup.
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