Re: [tlaplus] Defining Cardinality with TLA

[Felipe Oliveira Carvalho <felipekde@xxxxxxxxx>]

That's not currently possible because the TLA+ doesn't support
user-defined syntax constructs this advanced.

--
Felipe

On Fri, Apr 26, 2024 at 8:54 AM marta zhango <martazhango@xxxxxxxxx> wrote:
>
> How can I declare or define a symbol to mean Cardinality such as |S|
>
> Something like this maybe, to say that |S| means or in equivalent to Cardinality(S)
>
> |S| == Cardinality (S)
>
> Does one also use the keyword LET or something else ?
>
> On Friday, April 26, 2024 at 11:17:46 PM UTC+12 Lee wrote:
>>
>> Hi Marta,
>>
>> If you want to know more about Cardinality please see this page by Hillel Wayne (https://learntla.com/core/operators.html?highlight=cardinality) . Since you said you're new, I can also recommend reading his entire tutorial page and blog posts in addition to his book (https://www.amazon.se/-/en/Hillel-Wayne/dp/1484238281). Other resources when you're done working these are:
>>
>> - Specifying Systems by Leslie Lamport (which is only TLA+)
>> - http://lamport.azurewebsites.net/tla/learning.html - great way to get into how to think about this
>>
>> Regards
>> Lee
>>
>> On Friday, April 26, 2024 at 10:11:55 AM UTC+2 marta zhango wrote:
>>>
>>> That is what I needed to see as I am new to all this, with no idea where to start.
>>>
>>> On Friday, April 26, 2024 at 4:39:07 PM UTC+12 Stephan Merz wrote:
>>>>
>>>> P.S.: Proofs of these theorems checked by TLAPS are given in https://github.com/tlaplus/tlapm/blob/main/library/FiniteSetTheorems_proofs.tla.
>>>>
>>>>
>>>> On 26 Apr 2024, at 06:37, Stephan Merz <Stepha...@xxxxxxxxx> wrote:
>>>>
>>>> As Markus pointed out, cardinality of finite sets is defined in a standard module of TLA+. A collection of lemmas about finite sets and cardinality, useful for actually reasoning about these notions, is available at https://github.com/tlaplus/tlapm/blob/main/library/FiniteSetTheorems.tla (included in the distribution of TLAPS).
>>>>
>>>> Stephan
>>>>
>>>> On 26 Apr 2024, at 02:22, marta zhango <marta...@xxxxxxxxx> wrote:
>>>>
>>>> Is the line
>>>>
>>>> IN  CS[S]
>>>>
>>>> part of the definition of cardinality ?
>>>>
>>>> On Friday, April 26, 2024 at 11:55:57 AM UTC+12 Markus Kuppe wrote:
>>>>>
>>>>> https://github.com/tlaplus/tlaplus/blob/03c7bf4f35ccf1217ac2c53e5bf60d1220c8b0d8/tlatools/org.lamport.tlatools/src/tla2sany/StandardModules/FiniteSets.tla#L21-L27
>>>>>
>>>>> > On Apr 25, 2024, at 4:53 PM, marta zhango <marta...@xxxxxxxxx> wrote:
>>>>> >
>>>>> > Have thought something like this too
>>>>> >
>>>>> > Cardinality(set) == (+ e \in DOMAIN set: IF set[e] THEN 1 ELSE 0)
>>>>> >
>>>>> > On Friday, April 26, 2024 at 9:17:00 AM UTC+12 marta zhango wrote:
>>>>> > Like this for instance ?
>>>>> >
>>>>> > Cardinality (S) = |S| == Count ( e \in S )
>>>>> >
>>>>> >
>>>>> > On Friday, April 26, 2024 at 8:36:13 AM UTC+12 marta zhango wrote:
>>>>> > How can I define the cardinality of a set as the number of elements in a set S
>>>>> > using the notation |S| using TLA.
>>>>>
>>>>
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>>>>
>>>>
>>>>
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