The Logic of Recursive Equations

Antonius J. C. Hurkens, Monica McArthur, Yiannis N. Moschovakis, Lawrence S. Moss, Glen T. Whitney

Abstract: We study logical systems for reasoning about equations involving recursive definitions. In particular, we are interested in “propositional” fragments of the functional language of recursion FLR [18, 17], i.e., without the value passing or abstraction allowed in FLR. The “pure,” propositional fragment FLR0 turns out to coincide with the iteration theories of [1]. Our main focus here concerns the sharp contrast between the simple class of valid identities and the very complex consequence relation over several natural classes of models.