Some Mathematical Properties of the Functional Programming Language FP

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