When talking about data types "is" means "is congruent to" or "is isomorphic to". You are not free to use "is" arbitrarily, since if you are then Can "is" anything I want it to be. Since equivalence can be broken into an implication both ways e.g. A -> B and B -> A then it is quite easy to test if "Can is an Option".
def f[A](o: Option[A]): Can[A] // this should be total and bijective def g[A](c: Can[A]): Option[A] // this should be total and bijective The use of => in function signatures means logical implication. Does Can imply Option? Yes (you can complete the g function). Does Option imply Can? No (you cannot complete the f function). Therefore, Can is not an Option. It was not even close (lack of totality in this test is catastrophic). If you want to try to save this notion of "Well Can is a something", then I have already pointed out a suggestion. Try to think of others, but do not say that Can is an Option - it is not, not even close. Poor Oliver was all confuzzled when he popped this one to me the other day. -- Tony Morris http://tmorris.net/ S, K and I ought to be enough for anybody. Jorge Ortiz wrote: > It depends on what the meaning of "is" is. > > If Option were not sealed, "Can" could be "implemented" as an > Option... by adding Failure and Empty as subclasses of None. In > this (OO) sense, a Can is an option. > > In the algebraic sense, then you're probably right that a Can is > not an Option. > > --j > > On Tue, Jan 6, 2009 at 5:23 PM, Tony Morris <[email protected] > <mailto:[email protected]>> wrote: > > > 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]> >> <mailto:[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]>> >>> <mailto:[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]>> >>> <mailto:[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]>> >>> <mailto:[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 >> >>> > > > > > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Lift" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/liftweb?hl=en -~----------~----~----~----~------~----~------~--~---
