Exploring the regular tree types

Authors:
Peter Morris;Thorsten Altenkirch;Conor McBride
Affiliations:
School of Computer Science and Information Technology, University of Nottingham;School of Computer Science and Information Technology, University of Nottingham;School of Computer Science and Information Technology, University of Nottingham
Venue:
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Year:
2004

Citing 20
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Abstract

In this paper we use the Epigram language to define the universe of regular tree types—closed under empty, unit, sum, product and least fixpoint. We then present a generic decision procedure for Epigram's in-built equality at each type, taking a complementary approach to that of Benke, Dybjer and Jansson [7]. We also give a generic definition of map, taking our inspiration from Jansson and Jeuring [21]. Finally, we equip the regular universe with the partial derivative which can be interpreted functionally as Huet's notion of ‘zipper', as suggested by McBride in [27] and implemented (without the fixpoint case) in Generic Haskell by Hinze, Jeuring and Löh [18]. We aim to show through these examples that generic programming can be ordinary programming in a dependently typed language.