The gentle art of levitation

Authors:
James Chapman;Pierre-Évariste Dagand;Conor McBride;Peter Morris
Affiliations:
Tallinn University of Technology, Tallinn, Estonia;University of Strathclyde, Glasgow, United Kingdom;University of Strathclyde, Glasgow, United Kingdom;University of Nottingham, Nottingham, United Kingdom
Venue:
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Year:
2010

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Abstract

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.