The Algebra of Functional Programs: Function Level Reasoning, Linear Equations, and Extended Definitions

In [Back78] we introduced a functional style of programming in which variable-free programs are built from a set of primitive programs by a small set of combining forms or functionals and by recursive definitions. The programs of this "FP" style are all strict functions (of a single argument) that map a set of "objects" into itself. This set of objects is the closure under cartesian products of some given set of atoms. The earlier paper suggested that FP systems have the following properties: (a) extremely simple semantics, (b) existence of closed-form, non-recursive expressions for many functions that are normally recursively defined, (c) programs exhibit a clear hierarchical structure in which high level programs can be combined to form higher level programs, (d) the principal FP combining forms are the operations of a powerful algebra of programs that can be used to transform programs and to solve equations for recursively defined programs.

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