1. A program that accepts the definition of an operation that is to be
accomplished, and automatically constructs a program for the purpose. The
earliest example of this kind of program was the son generator, which took a
specification of the file format and the sorted order required, and produced a
sorting program. This was followed by report generators, which constructed
programs to print reports from files containing information in a specified
format. The best-known program of this kind is RPG II.
2. An element g of a group G with the property that the various powers
g0, g1, g2,.....
ultimately include all the elements of G. Such a group is said to be a cyclic
group; it is also an abelian group. Generators can
also be defined for monoids
in a similar way.
The set of generators S of a group G is a subset of G having the property that
every element of G can be expressed as a combination of elements of S.