Re: [tlaplus] How to generate all possible linear extensions (i.e., topological sortings) of a partial order?

 Hello,I am not trying to understand your definition but simply suggest how to make it syntactically legal. In the syntactic form  { e : x \in S, y \in T }the identifier x is not allowed to occur in S or T (cf. Specifying Systems, section 16.1.6). You must therefore use a nested set comprehension as in...ELSE LET Extend(m) == { <> \o l : l \in LinearExtensionsUtil(...) }     IN  UNION { Extend(m) : m \in Minimal(...) }(Of course, you do not actually need to use a LET but can also replace the use of Extend in the body by its definition. However, I find it easier to read in this way.)StephanOn 6 Apr 2021, at 11:20, hengx...@gmail.com wrote:Hi All,I am writing a TLA+ specification of a consistency model which is defined based on relations. I need to generate all possible linear extensions (i.e., topological sortings) of a partial order.The following TLA+ code can be found at https://github.com/hengxin/tla-causal-consistency/blob/main/RelationUtils.tla.I am able to generate an arbitrary linear extension of a partial order as follows (I use this algorithm: https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm):where Minimal(R, S) returns the set of minimal elements of S given relation R,and LeftRestriction(R, m) returns the set of pairs whose first element is m.However, I failed to generate all possible linear extensions of a partial order:TLC reports an error: Unknown operator 'm'.So how to generate all possible linear extensions of a partial order?Best regards,Hengfeng Wei (hengxin) -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/52111fcc-e8df-469e-8894-c113ae398056n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "tlaplus" group. To unsubscribe from this group and stop receiving emails from it, send an email to tlaplus+unsubscribe@xxxxxxxxxxxxxxxx. To view this discussion on the web visit https://groups.google.com/d/msgid/tlaplus/555B8BE7-2060-4E6F-B2DE-F609ABD05E62%40gmail.com.

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