Some Mathematical Properties of the Functional Programming Language FP

This paper will introduce the function systems approach to study the mathematicalproperties of Backus functional programming language FP.Here,a function system isdefined as a set of functions o FP.In the paper,we define the notions of complete,orthogonaland orthonormal systems,and prove their principal properties.These properties are used in thediscussion of the completeness of FP program algebra and properties of the expansion ofprogram in orthogonal systems.