Generative Unbinding of Names

TL;DR

This paper demonstrates that in FreshML-like languages, it is possible to extend the operations on names beyond equality testing, including ordering and numerical functions, without losing the core correctness of name binding semantics.

Contribution

It proves that additional relations and functions on names can be incorporated without compromising alpha-equivalence and contextual equivalence, given the dynamic name state is considered.

Findings

Almost any relation or numerical function on names can be added

Adding these operations does not break alpha-equivalence correctness

The dynamic state of names is crucial for maintaining correctness

Abstract

This paper is concerned with the form of typed name binding used by the FreshML family of languages. Its characteristic feature is that a name binding is represented by an abstract (name,value)-pair that may only be deconstructed via the generation of fresh bound names. The paper proves a new result about what operations on names can co-exist with this construct. In FreshML the only observation one can make of names is to test whether or not they are equal. This restricted amount of observation was thought necessary to ensure that there is no observable difference between alpha-equivalent name binders. Yet from an algorithmic point of view it would be desirable to allow other operations and relations on names, such as a total ordering. This paper shows that, contrary to expectations, one may add not just ordering, but almost any relation or numerical function on names without disturbing the fundamental correctness result about this form of typed name binding (that object-level alpha-equivalence precisely corresponds to contextual equivalence at the programming meta-level), so long as one takes the state of dynamically created names into account.