No this is a mistake. Can is not an Option. Indeed it is (almost)
impossible to write Can using Option (if you are familiar with Peano
Arithmetic you will understand the need to qualify with almost). There
is an arrow from forall A. Can[A] to Option[A] but not from forall A.
Option[A] to Can[A] (easily) - try it for yourself. To suggest that
Can is an Option (or "an Option with more features" or "an Either") is
a mistake of misintegration (Peikoff DIM Hypothesis). Indeed the Can
algebra has nothing to do with Option (except for the aforementioned
function). There is no isomorphism between Can and Option - they are
not the same, not even close.
Here is a bit of code for fun. Note the bijective function using
Either alone:
sealed trait T[+A] {
val e: Either[(String, T[Throwable], List[(String, Throwable)],
Either[A, Unit]]
// bijection to e
val c: Can[A] = e match {
case Left(m, e, c) => Failure(m, e,
// Can makes the mistake of using a data constructor as a type.
// Unfortunately Scala permits this.
c map toFailure)
case Right(e) => e match {
case Left(a) => Full(a)
case Right(_) => Empty
}
}
}
object T {
// construct with Either or Can
}
--
Tony Morris
http://tmorris.net/
S, K and I ought to be enough for anybody.
David Pollak wrote:
> It's an Option.
>
> It contains a value or it doesn't. In the case that it does not
> contain a value, it may contain out of band information. This is
> not any different from None which contains information. It
> contains the information that it lacks information.
>
> Sure, you can write Option[T] as Either[T, Nothing], but the value
> of only having on type is lost.
>
> On Tue, Jan 6, 2009 at 2:59 PM, Tony Morris <[email protected]
> <mailto:[email protected]>> wrote:
>
>
> Right, that's what Oliver said and I was reinforcing it with
> deductive reasoning. It is also not Option. It is something else
> altogether. Nevertheless, an isomorphism can easily be written with
> Either alone (ignoring bottoms). So in some loose sense "it is an
> Either".
>
> -- Tony Morris http://tmorris.net/
>
> S, K and I ought to be enough for anybody.
>
>
> David Pollak wrote:
>> Tony,
>>
>> Can (now Box) is not an Either.
>>
>> David
>>
>> On Tue, Jan 6, 2009 at 2:37 PM, Tony Morris
> <[email protected] <mailto:[email protected]>
>> <mailto:[email protected] <mailto:[email protected]>>>
> wrote:
>>
>>
>> Can is not an Option and to call it so in any way is an error of
>> misintegration. Indeed it would be an error to "replace Option
> with
>> Can" - they are completely different algebras. Either is kinded *
>> -> * -> * so cannot possible be isomorphic and cannot possibly
> have
>> map, flatMap etc (though it can have a bifunctor map being
>> covariant in both type arguments). However, Either.LeftProjection
>> and Either.RightProjection are kinded * -> * and are both
> covariant
>> functors and monads, hence map, flatMap etc. are available. e.g.
>> for(x <- either.left) ... is valid, try it.
>>
>> Of mild interest, it is possible to construct an isomorphism
> to Can
>> using both Either and Option. Indeed, it is possible to construct
>> an isomorphism to Option using Either e.g. forall A. Option[A] ≡
>> Either [Unit, A] so it is possible using Either alone. I'll
>> leave both as reader exercises.
>>
>>
>> On Dec 21 2008, 5:15 am, Oliver Lambert <[email protected]
> <mailto:[email protected]>
>> <mailto:[email protected] <mailto:[email protected]>>> wrote:
>>> Ok so Can is not either an Either or an Option, its a Can. I
>> kind of
>>> wondered when I first used Can, and it was described as an
>> enhanced
>>> Option, why it wasn't called something like Option+ with
>> None, Some
>>> and Failure.
>>>
>>> On 21/12/2008, at 5:47 AM, David Pollak wrote:
>>>
>>>> Can has map, flatMap, filter etc. So it can be used in a for
>>>> comphrension. I don't believe Either has those methods.
>> Further,
>>>> Can has a bunch of helpers to turn Empty into Failure
>>>
>>>> On Dec 20, 2008 10:33 AM, "Oliver Lambert" <[email protected]
> <mailto:[email protected]>
>> <mailto:[email protected] <mailto:[email protected]>>> wrote:
>>>
>>>> Is Can a little less like Option and more like scala.Either,
>> where
>>>> the left side is used to indicate failure? On 21/12/2008, at
>>>> 1:43 AM, David Pollak wrote: > Folks, > >
>> Over the
>>>> year that Lift has had Can[T...
>>
>>
>>
>>
>>
>> -- Lift, the simply functional web framework http://liftweb.net
>> Collaborative Task Management http://much4.us Follow me:
>> http://twitter.com/dpp Git some: http://github.com/dpp
>>
>>>
>
>
>
>
>
>
>
>
> -- Lift, the simply functional web framework http://liftweb.net
> Collaborative Task Management http://much4.us Follow me:
> http://twitter.com/dpp Git some: http://github.com/dpp
>
> >
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