Scalar and vector iteration

摘要

In “Monadic Computation and Iterative Algebraic Theories” Elgot [3] introduced the notion of a vector iterative theory and showed that vector iterative theories have a close connection with several aspects of the theory of computation. In private conversations Elgot formulated the notion of a scalar iterative theory and raised the question whether scalar and vector iterative theories coincide. We answer this question in the affirmative.