Transformation of Applicative Specifications into Imperative ...

CHAPTER 1. INTRODUCTION
This stepwise development uses the invent-and-verify approach, meaning
that in each step a new specification is invented. It is verified that this new
specification is a correct development of the previous specification in the
sense that the new specification conforms to the previous specification.
The RAISE Method suggest a certain order of development, which is
illustrated in Figure 1.1.
Applicative
Imperative
Concurrent
Abstract
Algebraic
Concrete
Model oriented
S1 2 S
S2 '
S3
Figure 1.1: Development process using the RAISE Method.
When the initial specification containing the requirements of the system
is made, an abstract applicative specification S1 is developed, possibly using
several steps. An abstract applicative specification contains abstract types
such as sorts. Signatures and axioms are preferred over explicit function
definitions.
When the abstract applicative specification S1 is made, a concrete applicative
specification S2 is developed. In a concrete applicative specification
concrete types such as maps are used and explicit function definitions are
preferred. In order to verify that the development step from S1 to S2 is
correct, a development relation is formulated asserting that the concrete
applicative specification implements the abstract applicative specification:
S2 S1. Justification of this relation shows that the development step is
correct.
Then a concrete imperative specification S3 is developed. In a concrete
imperative specification variables are defined and explicit function definitions
are used. The verification of this development step is done either informally
or formally. If the informally verification method is used, it is checked
whether the method for the transition described in [Hax99, p. 17] is followed
correctly. If the formal verification method is used, the imperative axioms
corresponding to the applicative axioms for the abstract applicative specification
are formulated and justified for the concrete imperative specification.
A development relation cannot be formulated for this step.
2