Programs as Mathematical Objects
According to John Backus, in order for computing to become more of a science or an engineering discipline and less of an art, it should first become a mathematical discipline and for that, it would be important to make the program space is a mathematical space with respect to program-forming or functional operations, and to distinguish it from the value space with its specific value-construction operations.
Informally, a space S is a set Sv of values and a set So of the operations on Sv ranging from (Sv)n in So and are interrelated by algebraic properties.
The most useful of these are those that display some kind of symmetry, such as the distributive property that relates two operations OA and OB such that the combination of OA with values formed with OB can be expressed as OB combining values formed with OA.
The more useful the properties of the elements of So have, the stronger the algebraic structure and the mathematical structure of the space S will be stronger.