 
Summary: Indexed Containers
Thorsten Altenkirch1
, Neil Ghani1
, Peter Hancock1
, Conor McBride1
, and
Peter Morris1
School of Computer Science and Information Technology,
Nottingham University
{txa,nxg,pgh,ctm,pwm}@cs.nott.ac.uk
Abstract. The search for an expressive calculus of datatypes in which
canonical algorithms can be easily written and proven correct has proved
to be an enduring challenge to the theoretical computer science commu
nity. Approaches such as polynomial types, strictly positive types and
inductive types have all met with some success but they tend not to
cover important examples such as types with variable binding, types
with constraints, nested types, dependent types etc.
In order to compute with such types, we generalise from the traditional
treatment of types as free standing entities to families of types which
have some form of indexing. The hallmark of such indexed types is that
