On monadic parametricity of second-order functionals

Abstract

How can one rigorously specify that a given ML functional f : (int → int) → int is pure , i.e., f produces no computational effects except those produced by evaluation of its functional argument? In this paper, we introduce a semantic notion of monadic parametricity for second-order functionals which is a form of purity. We show that every monadically parametric f admits a question-answer strategy tree representation. We discuss possible applications of this notion, e.g., to the verification of generic fixpoint algorithms. The results are presented in two settings: a total set-theoretic setting and a partial domain-theoretic one. All proofs are formalized by means of the proof assistant Coq. © 2013 Springer-Verlag.