The new math of computer programming

Structured programming has proved to be an important methodology for systematic program design and development. Structured programs are identified as compound function expressions in the algebra of functions. The algebraic properties of these function expressions permit the reformulation (expansion as well as reduction) of a nested subexpression independently of its environment, thus modeling what is known as stepwise program refinement as well as program execution. Finally, structured programming is characterized in terms of the selection and solution of certain elementary equations defined in the algebra of functions. These solutions can be given in general formulas, each involving a single parameter, which display the entire freedom available in creating correct structured programs.

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