[Haskell-cafe] type classes and logic

[Sebastian Fischer]

> Daniel Fischer wrote:
>>> class BEING human  => HUMAN human where
>>> Sub-classing is logical implication BEING(human)  => HUMAN(human)
>>> All types t that make BEING(t) = true also make HUMAN(t)=true
>>
>> No, it's the other way round. Every HUMAN is also a BEING, hence
>>
>> HUMAN(t) => BEING(t)
>
> Could I say that HUMAN is a subset of BEING?

That depends on whether predicates are sets.. But yes, every instance  
of HUMAN is also an instance of BEING, hence, the set of HUMAN  
instances is a subset of the set of BEING instances.

> In the light of the above examples how should I interpret the
> class-to-subclass relation as logical implication? Is it
> a)  If BEING then HUMAN (sufficient condition): BEING => HUMAN
> b)  HUMAN is true only if BEING (necessary condition): HUMAN => BEING
> c) Neither?

b). Every HUMAN is a BEING.

Cheers,
Sebastian

-- 
Underestimating the novelty of the future is a time-honored tradition.
(D.G.)