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Summary: Constructing Strictly Positive Families
Peter Morris Thorsten Altenkirch Neil Ghani
School of Computer Science and Information Technology
University of Nottingham, England,
Email:{pwm,txa,nxg}@cs.nott.ac.uk
Abstract
In order to represent, compute and reason with ad-
vanced data types one must go beyond the traditional
treatment of data types as being inductive types and,
instead, consider them as inductive families. Strictly
positive types (SPTs) form a grammar for defining in-
ductive types and, consequently, a fundamental ques-
tion in the the theory of inductive families is what
constitutes a corresponding grammar for inductive
families.
This paper answers this question in the form of
strictly positive families or SPFs. We show that these
SPFs can be used to represent and compute with a va-
riety of advanced data types, that generic programs
can naturally be written over the universe of SPFs
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