On 8 May 2011 17:55, john skaller <skal...@users.sourceforge.net> wrote:
>
> On 08/05/2011, at 10:31 PM, Rhythmic Fistman wrote:
>
>> You take a function f:a->b and wrap a up to get a new function with no
>> arguments, like this:
>>
>> g:1->b?
>
> It's a closure, or a specialisation, or perhaps even a projection.
>
> Basically you're taking some domain a and a function
>
> k: c -> a
>
> and composing them:
>
> g (x) = f ( k (x) )
>
> or just
>
> g = f . k (in forward notation)
>
> In your case you picked
>
> k: 1 -> a
>
> so the composition is g: 1 -> b
Ok, cool. So when I'm implementing such a thing in c++, what the hell
do I call the class? Or classes, because I often derive these things
from an abstract base class. I can't bring myself to call them
"factories", but now I've got more creators than genesis. You must
have some insight into this because you generate this stuff.
class thing_that_returns_b : public things_that_return_b {
a A;
private:
// pure virtual in things_that_return_b
virtual b g() {
// use a to create a b
}
};
>
>>
>> Is that 1 standard notation?
>
> In category theory, yes. 1 is "unit", a canonical type with 1 value.
> In Felix that value is (), the empty tuple. In set theory, any set
>
> {x}
>
> is a unit (singleton). Note this is not the same as 0, aka void,
> the type with NO values, or the empty set.
In practice I don't see the difference. () seems like no values to me.
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