Tyepclasses and creating 'Num' instances
Hi, Many thanks to everyone who responded to my earlier question about hierarchies of typeclasses. I have a followup question regarding creating instances. Suppose I have this additive semigroup typeclass: class (Num a) => AddSemigroup a where (|+|) :: a -> a -> a (|+|) = (+) I'd like to make 2-element tuples instances of AddSemigroup, provided their elements are: instance (AddSemigroup a, AddSemigroup b) => AddSemigroup (a, b) GHC says it "Could not deduce (Num (a, b))" in this situation, which seems fair enough so I tried: instance (AddSemigroup a, Num a, AddSemigroup b, Num b) => AddSemigroup (a, b) With the same result. Separate instances seem to work though: instance (Num a, Num b) => Num (a, b) instance (AddSemigroup a, AddSemigroup b) => AddSemigroup (a, b) At this point I feel like I must be duplicating instances that are provided in a standard way in the prelude somewhere, or more likely I've misunderstood the ideas around creating instances? Any advice much appreciated, Stu
On 02/23/2015 03:46 PM, Stuart Hungerford wrote:
instance (AddSemigroup a, AddSemigroup b) => AddSemigroup (a, b)
GHC says it "Could not deduce (Num (a, b))" in this situation, which seems fair enough so I tried:
instance (AddSemigroup a, Num a, AddSemigroup b, Num b) => AddSemigroup (a, b)
Since you've defined the "AddSemigroup plus" to be the "Num plus", when you attempt to make (a,b) an instance of AddSemigroup, GHC tries to use the "Num plus" on them; i.e. (x1,y1) + (x2,y2) = ??? Since (a,b) isn't an instance of Num, it doesn't know what to do here. It's obvious that you want, (x1,y1) + (x2,y2) = (x1+x2, y1+y2) (which is fine, since both 'a' and 'b' are instance of Num), but you could just as well declare, (x1,y1) + (x2,y2) = (x1*x2, y1*y2) The compiler doesn't know, so declaring 'a' and 'b' as instances of Num isn't enough. You really have to tell it how to add the pair.
With the same result. Separate instances seem to work though:
instance (Num a, Num b) => Num (a, b)
instance (AddSemigroup a, AddSemigroup b) => AddSemigroup (a, b)
Now it knows how to add (x1,y1) and (x2,y2), since (a,b) is an instance of Num. The compiler won't infer the pair instance from the individual ones though.
Be careful with that. I seem to recall a StackOverflow post where a really
confusing bug was eventually tracked down to a declaration of
instance Num (Double,Double)
somewhere in an imported package.
On Mon, Feb 23, 2015 at 1:03 PM, Michael Orlitzky
On 02/23/2015 03:46 PM, Stuart Hungerford wrote:
instance (AddSemigroup a, AddSemigroup b) => AddSemigroup (a, b)
GHC says it "Could not deduce (Num (a, b))" in this situation, which seems fair enough so I tried:
instance (AddSemigroup a, Num a, AddSemigroup b, Num b) => AddSemigroup
(a, b)
Since you've defined the "AddSemigroup plus" to be the "Num plus", when you attempt to make (a,b) an instance of AddSemigroup, GHC tries to use the "Num plus" on them; i.e.
(x1,y1) + (x2,y2) = ???
Since (a,b) isn't an instance of Num, it doesn't know what to do here. It's obvious that you want,
(x1,y1) + (x2,y2) = (x1+x2, y1+y2)
(which is fine, since both 'a' and 'b' are instance of Num), but you could just as well declare,
(x1,y1) + (x2,y2) = (x1*x2, y1*y2)
The compiler doesn't know, so declaring 'a' and 'b' as instances of Num isn't enough. You really have to tell it how to add the pair.
With the same result. Separate instances seem to work though:
instance (Num a, Num b) => Num (a, b)
instance (AddSemigroup a, AddSemigroup b) => AddSemigroup (a, b)
Now it knows how to add (x1,y1) and (x2,y2), since (a,b) is an instance of Num. The compiler won't infer the pair instance from the individual ones though.
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participants (3)
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Alex Hammel -
Michael Orlitzky -
Stuart Hungerford