[Haskell-beginners] incoherent instance question

[Graham Gill]

Please see the paste: https://pastebin.com/zBim7Zkx

I'm experimenting with defining UpperBounded and LowerBounded typeclasses.
An example type belonging to the latter that is not also Bounded would be
type Natural from Numeric.Natural.

I want to say that if a type is Bounded, then it is also UpperBounded and
LowerBounded. If a type is both UpperBounded and LowerBounded, then it is
also Bounded.

To express the constraints, I need FlexibleInstances and
UndecidableInstances extensions. These allow the module to load into ghci
(8.4.2) with only a warning, but, without the INCOHERENT pragmas, I get an
overlapping instance error if I try to evaluate minBound, maxBound,
upperBound or lowerBound instantiated to either of the types Foo or Bar.

A solution is to apply the INCOHERENT pragma to the instances at lines 11,
14 and 17. Reading over section 10.8.3.6. Overlapping instances in the GHC
User Guide, I believe I understand. (Is there a better solution?)

In the paste, I have INCOHERENT pragmas only at lines 11 and 17. This gives
me the following behaviour in ghci:

   1. minBound, maxBound, upperBound and lowerBound instantiated to type
   Foo all function as expected, evaluating to the appropriate lower or upper
   bound.
   2. upperBound and maxBound instantiated at Bar give overlapping instance
   errors for UpperBounded, as expected.
   3. lowerBound :: Bar evaluates to C, as expected.
   4. minBound :: Bar gives an overlapping instance error for UpperBounded:

*UpperLowerBounded> minBound :: Bar

<interactive>:141:1: error:
   • Overlapping instances for UpperBounded Bar
       arising from a use of ‘minBound’
     Matching instances:
       instance [safe] Bounded a => UpperBounded a
         -- Defined at UpperLowerBounded.hs:14:10
       instance [safe] UpperBounded Bar -- Defined at
UpperLowerBounded.hs:31:10
   • In the expression: minBound :: Bar
     In an equation for ‘it’: it = minBound :: Bar


It's #4 that I don't understand. An explanation would be very much
appreciated. (Also, what's a [safe] instance?)

Regards,
Graham
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