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*From*: Mariusz Ryndzionek <mryndzionek@xxxxxxxxx>*Date*: Tue, 20 Oct 2020 11:26:21 -0700 (PDT)*References*: <777d286f-858b-42c2-ac89-1d2eac77f01en@googlegroups.com> <B6601963-34E5-412A-BAB2-3CBEEEC0B736@gmail.com> <8e33ff4b-097b-43a8-b58a-e35010782ae2n@googlegroups.com> <D6B92ECC-5325-4ADA-99BA-59CC601B9260@gmail.com>

Thanks Stephan and Markus!

wtorek, 20 października 2020 o 18:57:00 UTC+2 Stephan Merz napisał(a):

Thanks for the explanations. This operator (I renamed it to Shuffle for lack of a better name) could be defined as follows.Range(f) == {f[x] : x \in DOMAIN f}(***************************************************************************)(* If Sets is a set of (non-empty) sets then Choice(Sets) is the set of *)(* all choice functions over Sets, that is, functions that associate some *)(* with every set in Sets. *)(***************************************************************************)Choice(Sets) == { f \in [Sets -> UNION Sets] : \A S \in Sets : f[S] \in S }(***************************************************************************)(* Compute all sets that contain one element from each of the input sets: *)(* Shuffle({{1,2}, {3,4}, {5}}) = {{1,3,5}, {1,4,5}, {2,3,5}, {2,4,5}} *)(***************************************************************************)Shuffle(Sets) == { Range(f) : f \in Choice(Sets) }Regards,StephanOn 20 Oct 2020, at 14:09, Mariusz Ryndzionek <mrynd...@xxxxxxxxx> wrote:Okay, so I wasn't specific enough. I know that \X in TLA+ is not commutative and in fact not even associative.I wanted something that would give me:Cartesian({{1, 2}, {3, 4}, {5}}) = {{1, 3, 5}, {1, 4, 5}, {2, 3, 5}, {2, 4, 5}}Your last definition works in TLC. Thanks Stephan!Is the `Range` operator defined somewhere in official/builtin modules?Range(f) == { f[x] : x \in DOMAIN f }Regarding overriding in Java, is it recommended only for to performance reasons?wtorek, 20 października 2020 o 13:41:38 UTC+2 Stephan Merz napisał(a):Hello,your problem is not well specified because {S1, S2} = {S2, S1} but S1 \X S2 is different from S2 \X S1. Also, I don't understand your remark about the output: the cartesian product is a set, but its elements are sequences.Assuming that your operator takes a *sequence* of sets, i.e. Cartesian(<<S1, S2, ..., Sn>>), you can write the following in TLA+.Range(S) == { S[i] : i \in 1 .. Len(S) }Cartesian(S) ==LET U == UNION Range(S)IN {s \in Seq(U) : /\ Len(s) = Len(S)/\ \A i \in 1 .. Len(s) : s[i] \in S[i]}However, TLC will not be available to interpret this because of the quantification over the infinite set Set(U). The following should work in principle (I haven't actually tried):Cartesian(S) ==LET U == UNION Range(S)FSeq == [ (1 .. Len(s)) -> U ]IN {s \in FSeq : \A i \in 1 .. Len(s) : s[i] \in S[i]}However, you probably want to override this operator definition by a Java method.StephanOn 20 Oct 2020, at 13:27, Mariusz Ryndzionek <mrynd...@xxxxxxxxx> wrote:Hello,I need n-ary Cartesian product operator. Something that would do:Cartesian({S1, S2, .., Sn}) = S1 \X S2 \X .. SnThe output shouldn't necessarily be sequences. Sets will do.Is there already something like this in TLA+?Regards,Mariusz--

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**Follow-Ups**:**Re: [tlaplus] n-ary Cartesian product***From:*JosEdu Solsona

**References**:**[tlaplus] n-ary Cartesian product***From:*Mariusz Ryndzionek

**Re: [tlaplus] n-ary Cartesian product***From:*Stephan Merz

**Re: [tlaplus] n-ary Cartesian product***From:*Mariusz Ryndzionek

**Re: [tlaplus] n-ary Cartesian product***From:*Stephan Merz

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