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*From*: Karolis Petrauskas <k.petrauskas@xxxxxxxxx>*Date*: Tue, 21 May 2024 17:14:07 +0300*References*: <e6ae5a2d-4fed-4a6b-83f5-e211a540737bn@googlegroups.com> <006C3949-160B-4F99-AFF1-86A3652A7851@gmail.com> <6a37ca7d-e03e-4c5e-afc5-603b3ed5c736n@googlegroups.com> <D923A267-B96B-44F8-A7F3-54CECD8A4C8D@gmail.com> <2f021f54-5da3-4b47-ad23-1efd260a8244n@googlegroups.com> <78ca6604-e088-43dd-a184-9159f8ca9394n@googlegroups.com> <2673743f-02ee-47bd-91ee-8cf142fd41e6n@googlegroups.com> <feb13c29-ea41-4742-9497-5b979d1f6093n@googlegroups.com> <7b55e800-59e2-4ee1-967c-7fb1e9c7b8e9@gmail.com> <3e3e996b-e96b-432e-bdc1-80c3af1da0afn@googlegroups.com>

I probably took a too simple way. This says OK for me.

---- MODULE a ----

EXTENDS TLAPS

THEOREM ASSUME NEW TEMPORAL P, <>[]<>P PROVE []<>P

BY PTL

====

EXTENDS TLAPS

THEOREM ASSUME NEW TEMPORAL P, <>[]<>P PROVE []<>P

BY PTL

====

Karolis

On Tue, May 21, 2024 at 5:05 PM Andrew Helwer <andrew.helwer@xxxxxxxxx> wrote:

I do think intuitively <>[]<>P is equivalent to []<>P although I tried for about an hour to prove so without success. A good sign that I really need to work on my proof skills!Andrew--On Monday, May 20, 2024 at 1:53:12 PM UTC-4 Hillel Wayne wrote:Expert mode: find a use-case for <>[]<>P (or prove it's just []<>P or something)

H

On 5/19/2024 8:47 AM, Andrew Helwer wrote:

Oh I figured out the difference myself. []<>P can of course be true or false of a specific behavior. <>P is true if P is true at least once at any point in the behavior. []<>P is only true when, if P becomes false after becoming true, it eventually becomes true again.

Andrew

--On Sunday, May 19, 2024 at 9:36:27 AM UTC-4 Andrew Helwer wrote:

Examples of constant-level expressions:- 5 + 15

- 0 .. 10- {1, 2, 3, 4, 5}- "foobar"

- op, where op was declared as op == (constant _expression_)- x, where x was declared as CONSTANT x

Examples of state-level expressions:- n + 5, where n was declared as VARIABLE n- op, where op was declared as op == (state-level _expression_)

Examples of action-level expressions:- z' = z + 5, where z was declared as VARIABLE z- op, where op was declared as op == (action-level _expression_)

Examples of temporal-level expressions:- <>[](x > 5), where x was declared as VARIABLE x- P ~> Q, where P and Q are action-level expressions or below (I believe)

There is additional related terminology outside of this:- State: an assignment of values to variables; variables are accessed with no prime, like x

- Step: A pair of successive states, where variables are addressed by being primed or not, like x' or x

- Behavior: An infinite sequence of states- Spec: A set of behaviors comprising the possible executions of the system you are modeling- Formula: a bit of an imprecise term but is usually used to refer to temporal formulas, so either specs or temporal-level expressions

Constant-level expressions are just that, they can be evaluated without reference to any state or anything by just looking at them. State-level expressions can only be evaluated within the context of a specific state. Action-level expressions can only be evaluated within the context of a specific step. Temporal-level expressions can only be evaluated within the context of a specific behavior, or spec.

Actually I'm a bit confused about the last one. It would seem to me that <>P and []<>P are two different levels of formulas, since <>P can be true or false of a specific behavior whereas []<>P seems to be a statement over multiple behaviors. Can anybody help me out here?

Anyway how this all helped.

Andrew Helwer

On Sunday, May 19, 2024 at 9:18:13 AM UTC-4 marta zhango wrote:

Systems are specified as formulas. I also see functions described using logical connectives such as

implication (=>), conjunction (∧), disjunction (V) and quantification (\A, \E).

Is TLA+ specified as formulas or functions ? Or something else ?

On Sunday, May 19, 2024 at 11:08:42 PM UTC+12 marta zhango wrote:

Actually, it is for TLA+ itself. You have mentioned: constant, state, action, temporal. Any importantothers? Would you be so kind to show a general syntax for each ?

On Sunday, May 19, 2024 at 11:01:36 PM UTC+12 Stephan Merz wrote:

I don’t know documentation you looked at.

From a user’s perspective, Leslie Lamport’s video lectures [1] and/or Hillel Wayne’s Web site and book [2] are probably the best introduction (with the latter focusing on PlusCal, but this includes TLA+ expressions).

If you are looking for more mathematical descriptions covering the language and its semantics, Specifying Systems [3], the original paper introducing TLA (but not the specification language TLA+) [4] or an old paper of mine [5] may be helpful.

Hope this helps,Stephan

On 19 May 2024, at 12:44, marta zhango <marta...@xxxxxxxxx> wrote:

I actually need some nitpicking. TLA is a scheme for precise and clear description,

whereas the documentation is not.

What are the basic constructs then ? As this is what I would like to neatly summarise.

On Sunday, May 19, 2024 at 9:38:51 PM UTC+12 Stephan Merz wrote:

In fact, there is no such thing as "statements" in TLA+, only formulas of different levels (constant, state, action, temporal). This is not nitpicking, but quite a fundamental distinction.

Stephan

On 19 May 2024, at 11:24, marta zhango <marta...@xxxxxxxxx> wrote:

Have seen that statements in TLA are of the form [A]_p, where A is an action and p is a property.

But what are things without action formalism like

Cardinality(assignments[t])

and expressions such as

/\ assignments \in [Tasks -> SUBSET CPUs]

and

IsSorted(seq) == \A i, j \in 1..Len(seq): i < j => seq[i] <= seq[j]

What are the latter ? Because they do not look like TLA statements

in the form of [A]_p.

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**Follow-Ups**:**Re: [tlaplus] Statements in TLA***From:*Andrew Helwer

**References**:**[tlaplus] Statements in TLA***From:*marta zhango

**Re: [tlaplus] Statements in TLA***From:*Stephan Merz

**Re: [tlaplus] Statements in TLA***From:*marta zhango

**Re: [tlaplus] Statements in TLA***From:*Stephan Merz

**Re: [tlaplus] Statements in TLA***From:*marta zhango

**Re: [tlaplus] Statements in TLA***From:*marta zhango

**Re: [tlaplus] Statements in TLA***From:*Andrew Helwer

**Re: [tlaplus] Statements in TLA***From:*Andrew Helwer

**Re: [tlaplus] Statements in TLA***From:*Hillel Wayne

**Re: [tlaplus] Statements in TLA***From:*Andrew Helwer

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