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Generic Programming for Dependent Types Constructing Strictly Positive Families

Summary: Generic Programming for Dependent Types
Constructing Strictly Positive Families
Peter Morris Thorsten Altenkirch
University of Nottingham, UK
We begin by revisiting the idea of using a universe of types to
write generic programs in a dependently typed setting by con-
structing a universe for Strictly Positive Types (SPTs). Here we
extend this construction to cover dependent types, i.e. Strictly Pos-
itive Families (SPFs), thereby fixing a gap left open in previous
work. Using the approach presented here we are able to represent
all of Epigram's datatypes within Epigram including the universe
of datatypes itself.
Keywords Data type generic programming, dependently typed
programming, Epigram
1. Introduction
In a dependently typed language like Epigram [8, 7, 3] generic pro-
gramming is normal programing. This is achieved by defining a
universe [6, 10] consisting of a type of names U : and a fam-


Source: Altenkirch, Thorsten - School of Computer Science, University of Nottingham


Collections: Computer Technologies and Information Sciences