[Haskell-cafe] Category Theory woes

[Hans Aberg]

On 18 Feb 2010, at 22:06, Daniel Fischer wrote:

>>> ...missing are
>>> - c(x) contains x
>>> - c(x) is minimal among the sets containing x with y = c(y).
>>
>> It suffices*) with a lattice L with relation <= (inclusion in the  
>> case
>> of sets) satifying
>>   i. x <= y implies c(x) <= c(y)
>>  ii. x <= c(x) for all x in L.
>> iii. c(c(x)) = x.
>
> Typo, iii. c(c(x)) = c(x), of course.

Sure.

> If we replace "set" by "lattice element" and "contains" by ">=", the
> definitions are equivalent.

Right.

> The one you quoted is better, though.

It is a powerful concept. I think of a function closure as what one  
gets when adding all an expression binds to, though I'm not sure that  
is why it is called a closure.

   Hans