Denotation by Transformation - Towards Obtaining a Denotational Semantics by Transformation to Point-free Style
It has often been observed that a point-free style of programming provides a more abstract view on programs. We aim to use the gain in abstraction to obtain a denotational semantics for functional logic languages in a straightforward way. Here we propose a set of basic operations based on which arbitrary functional logic programs can be transformed to point-free programs. The resulting programs are strict but, nevertheless, the semantics of the original program is preserved. There is a one-to-one mapping from the primitives introduced by the transformation to operations in relation algebra. This mapping can be extended to obtain a relation algebraic model for the whole program. This yields a denotational semantics which is on one hand closely related to point-free functional logic programs and on the other hand connects to the well developed field of algebraic logic including automatic proving.