Induction by Coinduction and Control Operators in Call-by-Name

This paper studies emulation of induction by coinduction in a call-by-name language with control operators. Since it is known that call-by-name programming languages with control operators cannot have general initial algebras, interaction of induction and control operators is often restricted to effect-free functions. We show that some class of such restricted inductive types can be derived from full coinductive types by the power of control operators. As a typical example of our results, the type of natural numbers is represented by the type of streams. The underlying idea is a counterpart of the fact that some coinductive types can be expressed by inductive types in call-by-name pure language without side-effects.