A few constructions on constructors

Authors:
Conor McBride;Healfdene Goguen;James McKinna
Affiliations:
School of Computer Science and Information Technology, University of Nottingham;AT&T Labs, Florham Park, New Jersey;School of Computer Science, University of St Andrews
Venue:
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Year:
2004

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Abstract

We present four constructions for standard equipment which can be generated for every inductive datatype: case analysis, structural recursion, no confusion, acyclicity. Our constructions follow a two-level approach—they require less work than the standard techniques which inspired them [11,8]. Moreover, given a suitably heterogeneous notion of equality, they extend without difficulty to inductive families of datatypes. These constructions are vital components of the translation from dependently typed programs in pattern matching style [7] to the equivalent programs expressed in terms of induction principles [21] and as such play a crucial behind-the-scenes rôle in Epigram [25].