Section 16.2.4 gives a syntactic definition of a valid TLA formula, which is defined inductively from a few base rules. Since []<>(<<A>>_v \/ <<B>>_v) cannot be built from those rules, it's not a valid TLA formula, even though it's a temporal formula. But you can construct []<><<A \/ B>>_v, which is logically equivalent.
H
--Reviewing, I find that a temporal formula is an assertion about behaviors. So a temporal formula maps from behaviors (i.e. infinite sequences of steps, including stuttering steps) to bools.
An action, on the other hand, is an ordinary formula with primed and unprimed variables. I suppose it maps from steps to bools.
In Specifying Systems 8.3, the book discusses what happens when substituting actions for temporal formulas in TLA tautologies, and it says that the resulting formulas might not be TLA formulas. For example, if A and B are actions:
"[]<>(<<A>>_v \/ <<B>>_v) isn't a TLA formula."
Why isn't it? And why does the book go on to imply that "substituting <<A \/ B>>_v for <<A>>_v \/ <<B>>_v" turns it into a TLA formula?
Thanks.
--Chapter 8 of “Specifying Systems” often makes a distinction between an action and a temporal formula, but I’m having trouble finding any definitions earlier the book that tell me what the difference is. Is it this?: actions are ordinary formulas with primed variables and/or ENABLED, and temporal formulas also permit [] and <>. --
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