[tlaplus] composing specifications

[ns <nedsri1988@xxxxxxxxx>]

I have a question from reading Sec. 10.4.1 of the S.S. book There it talks about composition in the presence of shared updatable state. The example is of a  Sender and Receiver system communicating using a shared buf. I understand that if you have a monolithic spec then it would be written InitSR /\ [][NextSR]_<<s,r,buf>> (ignoring fairness for now), where NextSR == Sndr \/ Rcvr, defined in the book, specifically Sndr mentions r and Rcvr mentions s where s and r are the sender and receiver state vars resp. He then (I assume) wants to defines the system as the composition of two components Cs /\ Cr, where Cs = Init_S /\ [][NS]_<<s,buf>> and Cr == Init_R /\ [][NR]_<<r,buf>>. So  Cs /\ Cr ==  Init_S /\ Init_R /\ [][NS]_<<s,buf>> /\ [][NR]_<<r,buf>>. The form of say NS is given as Sndr \/ (sigma /\ (s'=s)), where sigma is calculated. The problem is that this still requires the component Cs know about r (and correspondingly Cr knows about s) How is this possible if Cs and Cr are two separate components? Does r represent the "environment" in an assume-guarantee setting?

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