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

Seems reasonable
 
If a type is both UpperBounded and LowerBounded, then it is also Bounded.

Danger Will Robinson. Nothing stops modules (realistically, in two different library) from defining incompatible UpperBounded and LowerBounded instances; for example, I may want `lowerBound :: Bool` to be `True`, while you may want `upperBound :: Bool` to be `True`; when they are both imported, bad things can happen. In this case, requiring an Ord constraint and adding documentation on lawful instances would pretty much solve the problem, but in general, this is an unwise thing to do.

Specifically, it is usually a bad idea to have a type class that should have an instance for a type whenever that type has instances of some combination of other classes.

Three ways around it:
  • Use a newtype wrapper: define `newtype LowerUpperBounded` and have the instance be `(LowerBounded a, UpperBounded a) => Bounded (LowerUpperBounded a)`
  • Defer instance definition to concrete types: if you know that a specific type has both super-instances, you can explicitly instantiate it at the sub-instance
  • Define a constraint alias: (this requires some more advanced extensions, so I'm only mentioning it as an option for completeness' sake) Using `ConstraintKinds`, you can define `type Bounded a = (LowerBounded a, UpperBounded a)`; this makes the two definitions synonymous.

To your immediate question, I think what's happening is that when you're trying to do `minBound :: Bar` it looks for an instance `Bounded Bar` and finds the unique one; then it needs to satisfy the constraints, so it looks for `LowerBounded Bar` and `UpperBounded Bar`, the latter of which has two possible instances, neither of which is marked overlapping or incoherent.

You'll notice that if you use `-fdefer-type-errors` you will be able to get the `minBound` of `Bar` (though for some reason you need to bind it to a variable), but not the `maxBound`.

You should also note that if you use the `OVERLAPPABLE` pragma rather than the `INCOHERENT` one, you get the same results, and that is generally considered less risky.

On Sun, Jun 3, 2018 at 8:43 PM Graham Gill <math.simplex@gmail.com> wrote:
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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