  This paper is devoted to heuristic aspects of the so-called idempotent
calculus. There is a correspondence between important, useful and interesting
constructions and results over the field of real (or complex) numbers and
similar constructions and results over idempotent semirings in the spirit of N.
Bohr's correspondence principle in Quantum Mechanics.
  Some problems nonlinear in the traditional sense (for example, the Bellman
equation and its generalizations) turn out to be linear over a suitable
semiring; this linearity considerably simplifies the explicit construction of
solutions.
  The theory is well advanced and includes, in particular, new integration
theory, new linear algebra, spectral theory and functional analysis. It has a
wide range of applications.
  Besides a survey of the subject, in this paper the correspondence principle
is used to develop an approach to object-oriented software and hardware design
for algorithms of idempotent calculus.
