The gentle art of levitation

We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arises by interpreting its description--a first-class value in a datatype of descriptions. Moreover, the latter itself has a description. Datatype-generic programming thus becomes ordinary programming. We show some of the resulting generic operations and deploy them in particular, useful ways on the datatype of datatype descriptions itself. Simulations in existing systems suggest that this apparently self-supporting setup is achievable without paradox or infinite regress.

• Type: Conference
• Year: 2010
• Where: ICFP
• Authors: James Chapman, Pierre-Évariste Dagand, Conor McBride, Peter Morris
• Keywords: Datatype, Datatype Descriptions, ICFP 2010, Inductive Datatype Arises, Programming Languages