Duality between call-by-name recursion and call-by-value iteration

Abstract

We investigate the duality between call-by-name recursion and call-by-value iteration in the λμ-calculi and their models. Semantically, we consider that iteration is the dual notion of recursion. Syntactically, we extend the call-by-name λμ-calculus and the call-by-value one with a fixed-point operator and an iteration operator, respectively. This paper shows that the dual translations between the call-by-name λμ-calculus and the call-by-value one, which is constructed by Selinger, can be expanded to our extended λμ-calculi. Another result of this study provides uniformity principles for those operators.