Generalizing generalized tries

A trie is a search tree scheme that employs the structure of search keys to organize information. Tries were originally devised as a means to represent a collection of records indexed by strings over a xed alphabet. Based on work by C.P. Wadsworth and others, R.H. Connelly and F.L. Morris generalized the concept to permit indexing by elements of an arbitrary monomorphic datatype. Here we go one step further and deene tries and operations on tries generically for arbitrary rst-order polymorphic datatypes. The derivation is based on techniques recently developed in the context of polytypic programming. It is well known that for the implementation of generalized tries nested datatypes and poly-morphic recursion are needed. Implementing tries for polymorphic datatypes places even greater demands on the type system: it requires rank-2 type signatures and higher-order polymorphic nested datatypes. Despite these requirements the deenition of generalized tries for polymorphic datatypes is surprisingly simple which is mostly due to the framework of polytypic programming.