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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 16th 2013

    I gave the entry logical relation an Idea-section, blindly stolen from a pdf by Ghani that I found on the web. Please improve, I still don’t know what a “logical relation” in this sense actually is.

    Also, I cross-linked with polymorphism. I hope its right that “parametricity” may redirect there?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014
    • (edited Feb 28th 2014)

    added an actual explanation to logical relation:

    A logical relation between sets/types equipped with extra (algebraic) structure is a relation that preserves this structure in the appropropriate way. Hence logical relations are to relations as homomorphisms between (algebraic) structures are to functions of the underlying sets/types. See for instance (Hermida 13, section 2) for a quick survey.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeFeb 28th 2014

    Never heard of that term before. (Doesn’t seem particularly well-chosen; I think I’d just call it an algebraic relation or an internal relation, i.e., a relation interpreted internally in the regular category of algebras. Wonder where Ghani had heard it.)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014

    The term is apparently due to Reynolds in 1983.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 28th 2014

    Where did you get this explanation/definition? It’s not how I would have defined the notion.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014

    It’s all there cited in the entry: section 2 of http://www.cs.bham.ac.uk/~udr/papers/logical-relations-and-parametricity.pdf

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 28th 2014

    Huh. I wonder whether other people would agree with that definition.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeFeb 28th 2014

    Maybe to make this less mysterious you might state the definition that you think is right and which citations it is extracted from.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMar 1st 2014
    • (edited Mar 1st 2014)

    I see see

    with a contribution by one of the authors of the above article.

    Not sure what to make of it all…

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 6th 2018

    Added an introductory text:

    • Lau Skorstengaard, An Introduction to Logical Relations: Proving Program Properties Using Logical Relations, (pdf)

    diff, v9, current

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