“Everything Is Everything” Revisited: Shapeshifting Data Types with Isomorphisms and Hylomorphisms
Paul Tarau · Complex Systems · 2009
This paper is an exploration of isomorphisms between elementary data types (e.g., natural numbers, sets, finite functions, graphs, hypergraphs) and their extension to hereditarily finite universes through hylomor-phisms derived from ranking/unranking and pairing/unpairing opera-tions. An embedded higher order combinator language provides any-to-any encodings automatically. A few examples of free algorithms obtained by transferring operations between data types are shown. Other applications range from stream iterators on combinatorial ob-jects to succinct data representations and the generation of random instances. 1.