 
Summary: Representations of first order function types
as terminal coalgebras
Thorsten Altenkirch
txa@cs.nott.ac.uk
School of Computer Science and Information Technology
University of Nottingham, UK
Abstract. We show that function types which have only initial algebras
for regular functors in the domains, i.e. first order function types, can
be represented by terminal coalgebras for certain nested functors. The
representation exploits properties of op
limits and local colimits.
1 Introduction
The work presented here is inspired by discussions the author had some years
ago with Healfdene Goguen in Edinburgh on the question Can function types
be represented inductively? or maybe more appropriately: Can function types be
represented algebraically?.
In programming and type theory the universe of types can be divided as
follows:
function types (cartesian closure)
algebraic types
