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<div class="m_8602359256493275747moz-cite-prefix">Thank you Alex for that comprehensive
answer. That's very helpful. I'd considered a newtype, but I really wondered what prevented me from using or was bad about the approach I described.</div><div class="m_8602359256493275747moz-cite-prefix"><br></div><div class="m_8602359256493275747moz-cite-prefix">Regards,</div><div class="m_8602359256493275747moz-cite-prefix">Graham<br>
<br>
On 04-Jun-2018 1:10 AM, Alex Rozenshteyn wrote:<br>
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<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">I
want to say that if a type is Bounded, then it is also
UpperBounded and LowerBounded.</blockquote>
<div><br>
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<div>Seems reasonable<br>
</div>
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<div> </div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">If a type is both
UpperBounded and LowerBounded, then it is also Bounded.</blockquote>
<div><br>
</div>
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<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>Three ways around it:</div>
<div>
<ul>
<li>Use a newtype wrapper: define `newtype
LowerUpperBounded` and have the instance be
`(LowerBounded a, UpperBounded a) => Bounded
(LowerUpperBounded a)`</li>
<li>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</li>
<li>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.</li>
</ul>
<p>To your immediate question, I <i>think</i> 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.</p>
<p>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`.<br>
</p>
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<div>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.<br>
</div>
<br>
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<div dir="ltr">On Sun, Jun 3, 2018 at 8:43 PM Graham Gill
<<a href="mailto:math.simplex@gmail.com" target="_blank">math.simplex@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<div>Please see the paste: <a href="https://pastebin.com/zBim7Zkx" target="_blank">https://pastebin.com/zBim7Zkx</a></div>
<div><br>
</div>
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.
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>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?)</div>
<div><br>
</div>
<div>In the paste, I have INCOHERENT pragmas only at
lines 11 and 17. This gives me the following behaviour
in ghci:</div>
<div>
<ol>
<li>minBound, maxBound, upperBound and lowerBound
instantiated to type Foo all function as expected,
evaluating to the appropriate lower or upper
bound.<br>
</li>
<li>upperBound and maxBound instantiated at Bar give
overlapping instance errors for UpperBounded, as
expected.</li>
<li>lowerBound :: Bar evaluates to C, as expected.</li>
<li>minBound :: Bar gives an overlapping instance
error for UpperBounded:</li>
</ol>
<div><span style="font-family:monospace"><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">*UpperLowerBounded>
minBound :: Bar
</span><br>
<br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)"><interactive>:141:1:
</span><span style="font-weight:bold;color:rgb(255,84,84);background-color:rgb(255,255,255)">error:</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
• Overlapping instances for UpperBounded Bar</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
arising from a use of ‘minBound’</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
Matching instances:</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
instance [safe] Bounded a =>
UpperBounded a</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
-- Defined at
UpperLowerBounded.hs:14:10</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
instance [safe] UpperBounded Bar --
Defined at UpperLowerBounded.hs:31:10</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
• In the expression: minBound :: Bar</span><span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
<span style="font-weight:bold;color:rgb(0,0,0);background-color:rgb(255,255,255)">
In an equation for ‘it’: it = minBound ::
Bar</span><br>
<span style="color:rgb(0,0,0);background-color:rgb(255,255,255)">
</span><br>
</span><br>
</div>
</div>
<div>It's #4 that I don't understand. An explanation
would be very much appreciated. (Also, what's a [safe]
instance?)</div>
<div><br>
</div>
<div>Regards,</div>
<div>Graham</div>
<div><br>
</div>
</div>
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