[Haskell-cafe] Eq source code?

Bob Ippolito bob at redivi.com
Fri Apr 2 15:54:22 UTC 2021

The equations you've posted are laws that the instances of the Eq typeclass
must satisfy. If someone creates an instance that does not satisfy all of
the laws then the behavior is undefined. Laws are generally not present in
the source code outside of the comments, and they typically can not be
proved in standard Haskell.

I don't know why the documentation links are broken (bug in hackage?) but
you can find the source links here:

Many instances are automatically derived by the compiler (which is usually
what you would do for your own data types) or are otherwise dependent on
built-in primitives (e.g. eqInt, eqWord, etc.).

On Fri, Apr 2, 2021 at 8:38 AM Galaxy Being <borgauf at gmail.com> wrote:

> While learning about type classes, I tried to find the actual source code
> for Eq. In my beginner books this much is typically given
> class Eq a where
>   (==), (/=) :: a -> a -> Bool
> -- Minimal completion definition:
>   x /= y = not (x == y)
>   x == y = not (x /= y)
> I then found this
> <https://hackage.haskell.org/package/base-> at
> hackage.haskell.org, but the "source" links are dead. On this page is a
> section of what I can't tell is either source code or just commentary on
> all the different mathematical ideas about equality, i.e.,
> Reflexivity
> x == x = True
> Symmetry
> x == y = y == x
> Transitivity
> if x == y && y == z = True, then x == z = True
> Substitutivity
> if x == y = True and f is a "public" function whose return type is an
> instance of Eq, then f x == f y = True
> Negation
> x /= y = not (x == y)
> I would like to know if this is indeed in the source code or if it's just
> a sort of commentary. It looks important. Where can I find the actual
> source for all these basic type classes?
> LB
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