scala Either.RightProjection confusion (for comprehension de-sugaring) - scala

Question

I can use an = in a scala for-comprehension (as specified in section 6.19 of the SLS) as follows:
Option
Suppose I have some function String => Option[Int]:
scala> def intOpt(s: String) = try { Some(s.toInt) } catch { case _ => None }
intOpt: (s: String)Option[Int]
Then I can use it thus
scala> for {
| str <- Option("1")
| i <- intOpt(str)
| val j = i + 10 //Note use of = in generator
| }
| yield j
res18: Option[Int] = Some(11)
It was my understanding that this was essentially equivalent to:
scala> Option("1") flatMap { str => intOpt(str) } map { i => i + 10 } map { j => j }
res19: Option[Int] = Some(11)
That is, the embedded generator was a way of injecting a map into a sequence of flatMap calls. So far so good.
Either.RightProjection
What I actually want to do: use a similar for-comprehension as the previous example using the Either monad.
However, if we use it in a similar chain, but this time using the Either.RightProjection monad/functor, it doesn't work:
scala> def intEither(s: String): Either[Throwable, Int] =
| try { Right(s.toInt) } catch { case x => Left(x) }
intEither: (s: String)Either[Throwable,Int]
Then use:
scala> for {
| str <- Option("1").toRight(new Throwable()).right
| i <- intEither(str).right //note the "right" projection is used
| val j = i + 10
| }
| yield j
<console>:17: error: value map is not a member of Product with Serializable with Either[java.lang.Throwable,(Int, Int)]
i <- intEither(str).right
^
The issue has something to do with the function that a right-projection expects as an argument to its flatMap method (i.e. it expects an R => Either[L, R]). But modifying to not call right on the second generator, it still won't compile.
scala> for {
| str <- Option("1").toRight(new Throwable()).right
| i <- intEither(str) // no "right" projection
| val j = i + 10
| }
| yield j
<console>:17: error: value map is not a member of Either[Throwable,Int]
i <- intEither(str)
^
Mega-Confusion
But now I get doubly confused. The following works just fine:
scala> for {
| x <- Right[Throwable, String]("1").right
| y <- Right[Throwable, String](x).right //note the "right" here
| } yield y.toInt
res39: Either[Throwable,Int] = Right(1)
But this does not:
scala> Right[Throwable, String]("1").right flatMap { x => Right[Throwable, String](x).right } map { y => y.toInt }
<console>:14: error: type mismatch;
found : Either.RightProjection[Throwable,String]
required: Either[?,?]
Right[Throwable, String]("1").right flatMap { x => Right[Throwable, String](x).right } map { y => y.toInt }
^
I thought these were equivalent
What is going on?
How can I embed an = generator in a for comprehension across an Either?

Answer 1

The fact that you cannot embed the = in the for-comprehension is related to this issue reported by Jason Zaugg; the solution is to Right-bias Either (or create a new data type isomorphic to it).
For your mega-confusion, you expanded the for sugar incorrectly. The desugaring of
for {
b <- x(a)
c <- y(b)
} yield z(c)
is
x(a) flatMap { b =>
y(b) map { c =>
z(c) }}
and not
x(a) flatMap { b => y(b)} map { c => z(c) }
Hence you should have done this:
scala> Right[Throwable, String]("1").right flatMap { x => Right[Throwable, String](x).right map { y => y.toInt } }
res49: Either[Throwable,Int] = Right(1)
More fun about desugaring (the `j = i + 10` issue)
for {
b <- x(a)
c <- y(b)
x1 = f1(b)
x2 = f2(b, x1)
...
xn = fn(.....)
d <- z(c, xn)
} yield w(d)
is desugared into
x(a) flatMap { b =>
y(b) map { c =>
x1 = ..
...
xn = ..
(c, x1, .., xn)
} flatMap { (_c1, _x1, .., _xn) =>
z(_c1, _xn) map w }}
So in your case, y(b) has result type Either which doesn't have map defined.