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Constructing Strictly Positive Families Peter Morris and Thorsten Altenkirch

Summary: Constructing Strictly Positive Families
Peter Morris and Thorsten Altenkirch
School of Computer Science and Information Technology
University of Nottingham
We present an inductive definition of a universe containing codes for strictly positive
families (SPFs) such as vectors or simply typed lambda terms. This construction
extends the usual definition of inductive strictly positive types as given in previous
joint work with McBride. We relate this to Indexed Containers, which were recently
proposed in joint work with Ghani, Hancock and McBride. We demonstrate by example
how dependent types can be encoded in this universe and give examples for generic
Keywords: datatypes, containers, universes, generic programming, dependent types, Epigram
In a dependently typed language like Epigram [9, 8, 5] generic programming is normal programing.
This is achieved by defining a universe [?, ?] consisting of a type of names U : and a family
of elements El : U indexed by type names. We have exploited this opportunity in [10] by
defining the universe of regular tree types and developing generic programs and proofs for this
universe. However, there is an obvious asymmetry in our previous definitions where we exploit


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


Collections: Computer Technologies and Information Sciences