Difference between revisions of "Rewriting rules for event model decomposition"

From Event-B
Jump to navigationJump to search
imported>Pascal
 
imported>Pascal
(No difference)

Revision as of 16:02, 2 July 2009

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, \bcmsuch, 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, \bcmeq is the deterministic assignment, where an expression is given for each assigned identifier.
  • The "becomes member of" assignment, \bcmin is the set-based (non-deterministic) assignment, where a set expression is given for the assigned identifier.

Let v and w be variables, and E and F be expressions. In the following table, the left-hand assignments are equivalent (\defi) to the right-hand ones:

v \bcmeq E v \bcmsuch v' = E
v,w \bcmeq E,F v \bcmeq E \pprod w \bcmeq F
v(E) \bcmeq F v \bcmeq v \ovl \{E \mapsto F\}
v \bcmin E v \bcmsuch v' \in E

Thus, each Event-B assignment can be expressed in a "becomes such that" form.