A Meta Language for Programming with Bound Names Modulo Renaming

Andrew M. Pitts and Murdoch J. Gabbay


This paper describes work in progress on the design of an ML-style metalanguage FreshML for programming with recursively defined functions on user-defined, concrete data types whose constructors may involve variable binding. Up to operational equivalence, values of such FreshML data types can faithfully encode terms modulo alpha-conversion for a wide range of object languages in a straightforward fashion. The design of FreshML is `semantically driven', in that it arises from the model of variable binding in set theory with atoms given by the authors in [Gabbay and Pitts 1999]. The language has a type constructor for abstractions over names (=atoms) and facilities for declaring locally fresh names. Moreover, recursive definitions can use a form of pattern-matching on bound names in abstractions. The crucial point is that the FreshML type system ensures that these features can only be used in well-typed programs in ways that are insensitive to renaming of bound names.