Exercise composition: From environment properties to composed problems

Abstract

It is well known that (1) problems have a structure, (2) often this structure comes from its input, output or internal objects, (3) this structure organizes the problem resolution. Decomposition of a problem by its structure is a typical path in problem resolution. In this article we will do the inverse: composition of simple problems using structure-builder operators. We will start by (1) discuss problem structures, (2) select a set of important structure-builder operators, (3) study their properties, (4) apply them to a simple math case-study.