Summary: Indexed Containers
Thorsten Altenkirch Peter Morris
University of Nottingham
We show that the syntactically rich notion of inductive
families can be reduced to a core type theory with a fixed
number of type constructors exploiting the novel notion of
indexed containers. Indexed containers generalize simple
containers, capturing strictly positive families instead of
just strictly positive types, without having to extend the core
type theory. Other applications of indexed containers in-
clude datatype-generic programming and reasoning about
polymorphic functions. The construction presented here has
been formlized using the Agda system.
Inductive datatypes are a central feature of modern Type
Theory (e.g. COQ ) or functional programming (e.g.
) . A simple example is the type (or set) of de