[Haskell-cafe] Is (==) commutative?

Twan van Laarhoven twanvl at gmail.com
Tue Jul 24 12:30:07 CEST 2012

On 2012-07-24 10:10, Christian Sternagel wrote:
> Dear all,
> with respect to formal verification of Haskell code I was wondering whether (==)
> of the Eq class is intended to be commutative (for many classes such
> requirements are informally stated in their description, since Eq does not have
> such a statement, I'm asking here). Or are there any known cases where
> commutativity of (==) is violated (due to strictness issues)?

Strictness plays no role for Eq, since to test for equality both sides will have 
to be fully evaluated. I think (==) is supposed to be equivalence relation, 
which is symmetric (i.e. commutative); as well as reflexive and transitive.

There are some cases of (==) not being reflexive, Floats being the most notable 
one, but many people consider that to be a bug. I can't think of any instances 
that violate symmetry.


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