BPMN and Beyond Business process modelling notation, workflow ...

ASM Foundations of Database Management 11
3.1 Refinements of Database Systems
Given two abstract database systems M and M ∗ . The refinement of M DB to
M ∗ is based on
a refinement of signatures S M to S M ∗ that associates functions and values of
S M with those on S M ∗
a states of interest correspondence between the states of interest DBS and DBS ∗
defined over S M and S M ∗ correspondingly,
abstract computation segments DBS 1 , ...., DBS m on M and DBS ∗ 1, ...., DBS ∗ n
on M and M ∗ ,
locations of interest (DB, DB ∗ ) defined on S × S ∗ and
an equivalence relation ≡ on locations of interest.
M ∗ is a correct refinement of M if there for each M-run DBS ∗ 0, ...., DBS ∗ k, ...
there is an M-run and sequences i 0 < i 1 < .... and j 0 < j 1 < ... such that
i 0 = j 0 = 0 DB ik ≡ DB ∗ j k
for each k and either
– both runs terminate and their final states are the last pair of equivalent
states, or
– both runs and both sequences are infinite.
A refinement is called complete refinement if M DB is a correct refinement of
M ∗ DB ∗ and M∗ DB ∗ is a correct refinement of M DB.
We distinguish between
– structure refinement that is based on a notion of schema equivalence and
state equivalence,
– functionality refinement that is based on a notion of schema equivalence and
a notion of coherence, and
– state refinement that uses the notion of equivalence and coherence.
3.2 Deriving Plans and Primitives for Refinement
The perspectives and styles of modelling rule the kind of refinement styles. As
an example we consider structure-oriented strategies of development:
Inside-out refinement: Inside-out refinement uses the current ASM machine
for extending it by additional part. These parts are hocked onto the current
specification without changing it.
Top-down refinement: Top-down refinement uses decomposition of functions
in the vocabulary and refinement of rules. Additionally, the ASM may be
extended by functions and rules that are not yet considered.
Bottom-up refinement: Bottom-up refinement uses composition and generalisation
of functions and of rules to more general or complex. Bottom-up
refinement also uses generation of new functions and rules that are not yet
considered.
Modular refinement: Modular refinement is based on parqueting of applications
and separation of concern. Refinement is only applied to one module
and does not affect others. Modules may also be decomposed.