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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?
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.
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.)
The term is apparently due to Reynolds in 1983.
Where did you get this explanation/definition? It’s not how I would have defined the notion.
It’s all there cited in the entry: section 2 of http://www.cs.bham.ac.uk/~udr/papers/logical-relations-and-parametricity.pdf
Huh. I wonder whether other people would agree with that definition.
Maybe to make this less mysterious you might state the definition that you think is right and which citations it is extracted from.
I see see
with a contribution by one of the authors of the above article.
Not sure what to make of it all…
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