A weak HOAS approach to the POPLmark Challenge

Capitalizing on previous encodings and formal developments about nominal calculi and type systems, we propose a weak Higher-Order Abstract Syntax formalization of the type language of pure System F<: within Coq, a proof assistant based on the Calculus of Inductive Constructions. Our encoding allows us to accomplish the proof of the transitivity property of algorithmic subtyping, which is in fact the first of the three tasks stated by the POPLmark Challenge, a set of problems that capture the most critical issues in formalizing programming language metatheory.