[Haskell-beginners] incoherent instance question

[Alex Rozenshteyn]

>
> mathematical equivalences


Yeah... Unfortunately, type classes aren't good at those. They're good for
necessary conditions, and you can make them work for necessary and
sufficient conditions, but only if you control the class in question. One
major problem in your attempt is that you're not defining Bounded yourself,
so you can't define necessary conditions (since those would have to be part
of the class). If you controlled Bounded, you could do this:

class UpperBounded a where ...
class LowerBounded a where ...
class (UpperBounded a, LowerBounded a) => Bounded a -- This is the
"necessary" part; notice no "..."
instance (UpperBounded a, LowerBounded a) => Bounded a -- This is the
"sufficient" part

You'd need to turn on some extensions (UndecidableInstances and
FlexibleContexts, IIRC).

On Fri, Jun 8, 2018 at 6:24 PM, Graham Gill <math.simplex at gmail.com> wrote:

> Thanks for the explanation David. The problem is clear from your
> description, and when you *really* do want to do it anyway I guess that's
> what the INCOHERENT and OVERLAPS/OVERLAPPING pragmas are for, to help you
> control the types.
>
> Just remember that they are "typeclasses", not "classclasses".
>
>
> Actually I wasn't thinking in terms of "classclasses", instead, of
> mathematical equivalences. A set of reals is bounded iff it is both upper
> and lower bounded. I wanted to try to express that in types, and wondered
> if I could do it without resorting to asymmetrical syntax (the newtype
> suggestion).
>
> Regards,
> Graham
>
>
> On Mon, Jun 4, 2018 at 8:54 AM David McBride <toad3k at gmail.com> wrote:
>
>> This is a common thing that people try to do.  I want class A to apply to
>> any type in which class B already applies.  It seems to mimic what would
>> work in object oriented programming and it is hard to see at first why it
>> doesn't work in haskell.
>>
>> Just remember that they are "typeclasses", not "classclasses".  When you
>> write
>>
>> class Foo a where foo :: ...
>> instance Show a => Foo a where foo = something
>>
>> Everything seems fine, but then you could write additional classes like
>> this
>>
>> instance Read a => Foo a where foo = something_else
>>
>> And what if you had a type that is both a Read and Show, like Int?  Now
>> there are two different things it could do -- something and
>> something_else.  How to decide?  Based on order?  But then the behavior of
>> the program could dramatically change based on the import order.
>>
>> I would advise you to treat Bounded, UpperBounded, and LowerBounded to be
>> separate properties and define them on all types explicitly rather than
>> trying to obtain instances for free.
>>
>> On Sun, Jun 3, 2018 at 11:42 PM, Graham Gill <math.simplex at 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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