  Continuation Calculus (CC), introduced by Geron and Geuvers, is a simple
foundational model for functional computation. It is closely related to lambda
calculus and term rewriting, but it has no variable binding and no pattern
matching. It is Turing complete and evaluation is deterministic. Notions like
"call-by-value" and "call-by-name" computation are available by choosing
appropriate function definitions: e.g. there is a call-by-value and a
call-by-name addition function. In the present paper we extend CC with types,
to be able to define data types in a canonical way, and functions over these
data types, defined by iteration. Data type definitions follow the so-called
"Scott encoding" of data, as opposed to the more familiar "Church encoding".
The iteration scheme comes in two flavors: a call-by-value and a call-by-name
iteration scheme. The call-by-value variant is a double negation variant of
call-by-name iteration. The double negation translation allows to move between
call-by-name and call-by-value.
