Infinite Computation in the Equivalent Transformation Model

Abstract

There are many logic programs that do not terminate but perform useful computation in some sense. The usual theory of logic programming adopts least fixpoints to define the meaning of programs, which fails to capture the intended meaning of infinite computation. To give an appropriate sense to useful infinite computation, the theory of logic programming has adopted greatest fixpoints in place of least fixpoints. However, this solution developed in logic paradigm can not explain finite and infinite computation in a unified manner. This paper proposes a new approach to infinite computation based on the equivalent transformation paradigm, where infinite computation is regarded as repeated equivalent transformations and is given appropriate sense in the same way as the usual finite computation.