[GHC] #15078: base: Customary type class laws (e.g. for Eq) and non-abiding instances (e.g. Float) should be documented

[GHC]

#15078: base: Customary type class laws (e.g. for Eq) and non-abiding instances
(e.g. Float) should be documented
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        Reporter:  sjakobi           |                Owner:  Azel
            Type:  feature request   |               Status:  patch
        Priority:  normal            |            Milestone:  8.6.1
       Component:  Core Libraries    |              Version:  8.4.2
      Resolution:                    |             Keywords:  newcomer
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):  Phab:D4736
       Wiki Page:                    |
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Comment (by dfeuer):

 Expanding a bit in another direction, I think it probably makes sense to
 note that `Num` instances are typically expected to form rings. In fact,
 the `signum` and `abs` functions suggest even more structure, although I
 don't personally know what sort of structure that ''is''. I'd be very
 hesitant to document any expectations beyond the ring laws, because there
 are a number of exotic `Num` instances in the wild.

 The best-behaved law-breaker here is `Natural`, which does not have a
 sensible `negate` or `(-)`; it's a perfectly good semiring (more
 specifically, a ''rig''), but we don't have a class corresponding to that.
 As usual, `Float` and `Double` are truly flagrant law-breakers.

 It might also be worth mentioning that types that are well-behaved
 instances of both `Num` and `Ord` are ''not'' necessarily ordered rings.
 In particular, `Int`, `Word`, `Int8`, `Word8`, etc., are not ordered
 rings. As far as I know, the only `Num`+`Ord` instances in `base` that
 implement ordered rings are `Integer` and `Rational`.

-- 
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/15078#comment:6>
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