A note on elimination of simplest recursions

Automatic program transformation, such as specialization, often introduces intermediate recursions that compute partial functions on parameters that are directly defined by simple recursive definitions. Replacing these recursive definitions by one-step definitions not only simplifies the residual program, but also allows more useful information to be propagated to remaining parts of the program, for continuing specialization.We give an easily recognized characterization of a class of recursive definitions, called syntactical monomials, that can be transformed to one-step definitions. We show our transformation is meaningful for specialization of interpreters and self-application of specializers.