# Re: [tlaplus] Execution semantics of \/

"Any one of them may be executed" means that the next state may correspond to either action. If you want both actions to be executed then you should write Action1 /\ Action2. With a disjunction, you have a branching point with possible successors according to Action1 or Action2 (actually, an action need not determine a unique successor state, think of x' \in {"a", "b", "c"}). TLC will compute all successors that correspond to some enabled action and then continue from these, as I tried to explain previously.

TLC complains about incompletely specified successor states if it cannot determine a finite set of values for each of the primed state variables. For example, Action1 does not specify what values y may take in the successor state. According to the TLA+ semantics, it can have any value, including {}, -42, "foobar", [x \in Int |-> x*x] etc. There are uncountably many possible values, and TLC has no way of enumerating them all.

Regards,
Stephan

On 04 Aug 2014, at 13:35, Sidharth Kshatriya <sid.ks...@xxxxxxxxx> wrote:

> Curious about the question I asked, I ran the following:
>
> --------------------------------- MODULE cs ---------------------------------
> EXTENDS Integers, Sequences
> VARIABLES x, y
>
> vars == << x, y >>
> Init == (x = 5) /\ (y = 6)
> Action1 == x' = x + 5
> Action2 == y' = y + 5
> Next == Action1 \/ Action2
> Spec == Init /\ [][Next]_vars
>
> What interesting is that it seems one branch *is* taken (whether Action1 or Action2). Here I get the error
> "Successor state is not completely specified by the next-state action."
>
> My thought here is that since both actions should have been enabled, the next state assignment should have been figured out for both x and y.
>
> On Monday, 4 August 2014 16:55:50 UTC+5:30, Sidharth Kshatriya  wrote:
>> Thanks for your quick explanation.
>>
>>
>>
>> "any one of them may be executed" --> does that mean that all of them that are enabled are executed?
>>
>>
>>
>> Lets take:
>>
>>
>>
>> Action1 == (x' = x + 5)
>>
>> Action2 == (y' = y + 5)
>>
>>
>>
>> What does Next == Action1 \/ Action2 here mean? (Note that I've deliberately omitted any preconditions for both Actions so that they are always enabled)
>>
>>
>>
>> Does it mean that *both* x and y increase in value by 5 or does it mean that only one of them increases in value by 5 "simultaneously" in a single time step?
>>
>>
>>
>>
>>
>> On Monday, 4 August 2014 16:46:52 UTC+5:30, Stephan Merz  wrote:
>>
>>> Dear Sidharth,
>>
>>>
>>
>>>
>>
>>> you shouldn't really think of a TLA specification as being executed: it is a description of the possible behaviors of your system. (Although it turns out that TLC can effectively compute the behaviors for the subset of TLA+ that it accepts.) Then a disjunction A \/ B \/ C in the next-state relation means that the transition from the current state to the next one should satisfy (at least) one of the action formulas A, B or C. If several actions are enabled, either can one can actually happen, so "any one of them may be executed". And yes,
>>
>>>
>>
>>>
>>
>>>   \E i \in 1 .. 4 : A(i)
>>
>>>
>>
>>>
>>
>>> is the same as
>>
>>>
>>
>>>
>>
>>>   A(1) \/ A(2) \/ A(3) \/ A(4).
>>
>>>
>>
>>>
>>
>>> For example, think of A(i) being an action that models the input of value i to the system, then it is very reasonable to expect that the system should accept any value (in the domain of the inputs).
>>
>>>
>>
>>>
>>
>>> During verification, TLC will compute all possible branches at such a point and explore the subsequent behaviors. (That's where the state explosion problem in model checking comes from.) When evaluating the next-state relation, TLC computes the sets of all successor states (i.e., valuations of the primed variables) that make the formula true. Therefore it will indeed evaluate all the operands of a disjunction – note that this problem is different from a simple evaluation of a propositional formula to a Boolean value, since the values of the primed variables are initially unknown.
>>
>>>
>>
>>>
>>
>>> Hope this helps,
>>
>>>
>>
>>>
>>
>>> Stephan
>>
>>>
>>
>>>
>>
>>> On Monday, August 4, 2014 12:27:39 PM UTC+2, Sidharth Kshatriya wrote:Hi Folks,
>>
>>> I have a question regarding \/ . What does \/ mean when a system is actually executing a specification?
>>
>>> Say,
>>
>>> Next == Action1 \/ Action2 \/ Action3
>>
>>> Now, lets say, Action1 and Action2 might both be enabled at a particular point of execution of an algorithm (i.e. they are non interleaving). Note that each action may relate primed and unprimed variables to each other.
>>
>>> Now does Next step here mean that Action1 *and* Action2 will be executed? Or does it mean that the *both* may be executed or any one of them many executed?
>>
>>> The reason I am confused is because:
>>
>>> TRUE == TRUE \/ DONTCARE
>>
>>> TRUE == TRUE \/ FALSE
>>
>>> TRUE == TRUE \/ TRUE
>>
>>> Basically is short circuit evaluation implicit in the execution semantics? Do we evaluate all operands of an \/?
>>
>>> Similarly we may have:
>>
>>> Next == \E i \in 1..4 Action(i)
>>
>>> Is this the same as:
>>
>>> Next == Action(1) \/ Action(2) \/ Action(3) \/ Action(4)
>>
>>>
>>
>>> Thanks,
>>
>>> Sidharth
>
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--
Stephan Merz