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.
CACM January, 1975
Mills, H. D.
