Difference between revisions of "Rewriting rules for event model decomposition"
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== Simplification rules on Event-B predicates == | == Simplification rules on Event-B predicates == | ||
+ | * If <math>P(x_1,...,x_n,y)~</math> is equal (<math>\defi</math>) to <math>y = Q(x_1,...,x_n)~</math>, then the <math>\exists y.P(x1,...,x_n,y)</math> predicate is true, and it may be deleted in conjunctive predicates (<math>\land</math>) where it appears. | ||
+ | * The <math>(\exists z.P(x_1,...,x_n,z) \land Q(y_1,...,y_m))</math> predicate, where <math>z \notin \{y_1,...,y_n\}</math>, may be rewritten as <math>(\exists z.P(x_1,...,x_n,z)) \land Q(y_1,...,y_m)</math>. | ||
== Rewriting rules for the Event-B actions == | == Rewriting rules for the Event-B actions == |
Revision as of 09:38, 3 July 2009
The purpose of this page is to list and justify the rewriting / simplification rules applied in the event model decomposition when building the external events, and more especially their actions.
Contents
Rewriting rules for the Event-B assignments
As detailed in the modelling language, the Event-B assignments are formed of two parts:
- a left-hand side, which is a list of free identifiers.
- a right-hand side.
There are various kinds of assignments:
- The
("becomes such that") assignment is the most general (non-deterministic) assignment, where a predicate is given on the before and after values of assigned identifiers. The after values of the assigned identifiers are denoted by a primed identifier whose prefix is the assigned identifier.
- The
("becomes equal to") assignment is the deterministic assignment where an expression is given for each assigned identifier.
- The
("becomes member of") assignment is the set-based (non-deterministic) assignment, where a set expression is given for the assigned identifier.
Let and
be variables, and
and
be expressions. In the following table, the left-hand assignments are equivalent (
) to the right-hand ones:
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Thus, each Event-B assignment can be expressed in a "becomes such that" form.
Simplification rules on Event-B predicates
- If
is equal (
) to
, then the
predicate is true, and it may be deleted in conjunctive predicates (
) where it appears.
- The
predicate, where
, may be rewritten as
.
Rewriting rules for the Event-B actions
Let and
be variables, and
and
be predicates. The following equivalence applies :
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