Proof Pearl: From Concrete to Functional Unparsing

Abstract

We provide a proof that the elegant trick of Olivier Danvy for expressing printf-like functions without dependent types is correct, where formats are encoded by functional expressions in continuation-passing style. Our proof is formalized in the Calculus of Inductive Constructions. We stress a methodological point: when one proves equalities between functions, a common temptation is to introduce a comprehension axiom and then to prove that the considered functions are extensionally equal. Rather than weakening the result (and adding an axiom), we prefer to strenghten the inductive argumentation in order to stick to the intensional equality.