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.

FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving statically scoped binding operations. User-declared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming bound variables explicitly. This may have the computational effect of swapping bound names with freshly generated ones; previous work on FreshML used a complicated static type system inferring information about the 'freshness' of names for expressions in order to tame this effect. The main contribution of this paper is to show (perhaps surprisingly) that a standard type system without freshness inference, coupled with a conventional treatment of fresh name generation, suffices for FreshML's crucial correctness property that values of datatypes involving binders are operationally equivalent if and only if they represent a-equivalent pieces of object-level syntax. This is established via a novel denotational semantics. FreshML without static freshness inference is no more impure than ML and experience with it shows that it supports a programming style pleasingly close to informal practice when it comes to dealing with object-level syntax modulo a-equivalence.