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Summary: Constructing Polymorphic Programs with Quotient
Types
Michael Abbott 1 , Thorsten Altenkirch 2 , Neil Ghani 1 , and Conor McBride 3
1 Department of Mathematics and Computer Science, University of Leicester
michael@araneidae.co.uk, ng13@mcs.le.ac.uk
2 School of Computer Science and Information Technology, Nottingham University
txa@cs.nott.ac.uk
3 Department of Computer Science, University of Durham
c.t.mcbride@durham.ac.uk
Abstract. The efficient representation and manipulation of data is one of the
fundamental tasks in the construction of large software systems. Parametric
polymorphism has been one of the most successful approaches to date but, as of yet,
has not been applicable to programming with quotient datatypes such as unordered
pairs, cyclic lists, bags etc. This paper provides the basis for writing polymorphic
programs over quotient datatypes by extending our recently developed theory of
containers.
1 Introduction
The efficient representation and manipulation of data is one of the fundamental tasks
in the construction of large software systems. More precisely, one aims to achieve
amongst other properties: i) abstraction so as to hide implementation details and thereby
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