[Haskell-cafe] (names for) invariants for Eq and Ord?

[Brandon Allbery]

One thing to consider is that, if you look at the Report specification for
derived Ord instances and of the default (compare), you'll find that it
explicitly depends on (==). So you don't actually need a "law" here.

On Tue, May 29, 2018 at 3:03 PM Johannes Waldmann <
johannes.waldmann at htwk-leipzig.de> wrote:

> Dear Cafe,
>
> I am somewhat surprised that the Haskell Standard (*)
>
> https://www.haskell.org/onlinereport/haskell2010/haskellch6.html#x13-1270006.3
> does not contain any
> notation for (intended) properties of Eq and Ord instances,
> and their relation. For Java (standard library),
> the API spec uses wording like "consistent with equals"
> https://docs.oracle.com/javase/10/docs/api/java/lang/Comparable.html
>
> I am well aware that semantics (transitivity, etc.)
> cannot be enforced statically, in either language.
> But both standards still speak of "total order".
> Do we (Haskell) need something similar to "consistent with equals"?
>
> It depends. E.g., looking at a (random) source in containers
> (Data.Map.Internal), it seems that it will always use the result of
> compare, never of (==), on keys. That's not obvious from the docs.
> I just checked -- I can make a type where (==) = undefined,
> but write a proper Ord instance, and use it as key type.
>
> I am asking this because I will be teaching type classes,
> with Eq and Ord as examples. I detected the funny situation
> that the Java specification looks "more mathematical"
> than the corresponding Haskell one. What will the students think ...
>
> - J.W.
>
> (*) The Haskell standard is what you find when you scroll
> down, down, down to the very bottom of
> https://www.haskell.org/documentation . So, probably not that important...
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-- 
brandon s allbery kf8nh                               sine nomine associates
allbery.b at gmail.com                                  ballbery at sinenomine.net
unix, openafs, kerberos, infrastructure, xmonad        http://sinenomine.net
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