A groupoid of isomorphic data transformations

Abstract

As a variation on the known theme of Gödel numberings, isomorphisms defining data type transformations in a strongly typed functional language are organized as a finite groupoid using a higher order combinator language that unifies popular data types as diverse as natural numbers, finite sequences, digraphs, hypergraphs and finite permutations with more exotic ones like hereditarily finite functions, sets and permutations. © 2009 Springer-Verlag Berlin Heidelberg.