Scala collection: totally unpredictable behaviours...

Question

Have been pretty frustrated by Scala 2.8 collection behaviours. Here's the problem: I'm creating a Sudoku board. I'm labelling the cells from A1 to I9 (the letters being the rows and the digits being the columns). I want to get a list of units on the board, which is the 9 rows, the night columns, and the night quadrants.

Here's my scala class:

class Square(val row:Char, val column:Int) extends Pair[Char, Int](row, column) {
    override def toString() = "" + row + column 
}

object Board {
    private val rows = "ABCDEFGHI"
    private val cols = 1 to 9
    private lazy val units = unitList(rows, cols)
    private def cross(rows:Iterable[Char], columns:Iterable[Int]):Iterable[Square] = {
        for (row <- rows; col <- columns)
            yield new Square(row, col)
    }

    private def unitList(rows:Iterable[Char], cols:Iterable[Int]) = {
        val u1 = (for (col <- cols) yield cross(rows, List(col)))
        val u2 = (for (row <- rows) yield cross(List(row), cols))
        val u3 = (for (cols <- List("ABC", "DEF", "GHI"); rows <- List(1 to 3, 4 to 6, 7 to 9)) yield cross(cols, rows))

        u1 :+ u2 :+ u3  // won't compile, reason: :+ is not a member of Iterable[Iterable[sudoku.Square]]
    }

    def run() {
        val u1 = (for (col <- cols) yield cross(rows, List(col)))
        val u2 = (for (row <- rows) yield cross(List(row), cols))
        val u3 = (for (cols <- List("ABC", "DEF", "GHI"); rows <- List(1 to 3, 4 to 6, 7 to 9)) yield cross(cols, rows))
        println(u1)
        println(u2)
        println(u3)
        val u4 = u1 :+ u2 :+ u3  // compiles
        println(u1 :+ u2 :+ u3)  // compiles and output correctly
    }
}

See the comments in the code. Specifically, why the same code won't compile in unitList but compiles and runs fine in run()?

Also, when I observe the output of the run method, it seems the collection returned by the yield keyword is randomly switching between Vector and List:

Vector(Vector(A1, B1, C1, D1, E1, F1, G1, H1, I1), Vector(A2, B2, C2, D2, E2, F2, G2, H2, I2), Vector(A3, B3, C3, D3, E3, F3, G3, H3, I3), Vector(A4, B4, C4, D4, E4, F4, G4, H4, I4), Vector(A5, B5, C5, D5, E5, F5, G5, H5, I5), Vector(A6, B6, C6, D6, E6, F6, G6, H6, I6), Vector(A7, B7, C7, D7, E7, F7, G7, H7, I7), Vector(A8, B8, C8, D8, E8, F8, G8, H8, I8), Vector(A9, B9, C9, D9, E9, F9, G9, H9, I9))

Vector(List(A1, A2, A3, A4, A5, A6, A7, A8, A9), List(B1, B2, B3, B4, B5, B6, B7, B8, B9), List(C1, C2, C3, C4, C5, C6, C7, C8, C9), List(D1, D2, D3, D4, D5, D6, D7, D8, D9), List(E1, E2, E3, E4, E5, E6, E7, E8, E9), List(F1, F2, F3, F4, F5, F6, F7, F8, F9), List(G1, G2, G3, G4, G5, G6, G7, G8, G9), List(H1, H2, H3, H4, H5, H6, H7, H8, H9), List(I1, I2, I3, I4, I5, I6, I7, I8, I9))

List(Vector(A1, A2, A3, B1, B2, B3, C1, C2, C3), Vector(A4, A5, A6, B4, B5, B6, C4, C5, C6), Vector(A7, A8, A9, B7, B8, B9, C7, C8, C9), Vector(D1, D2, D3, E1, E2, E3, F1, F2, F3), Vector(D4, D5, D6, E4, E5, E6, F4, F5, F6), Vector(D7, D8, D9, E7, E8, E9, F7, F8, F9), Vector(G1, G2, G3, H1, H2, H3, I1, I2, I3), Vector(G4, G5, G6, H4, H5, H6, I4, I5, I6), Vector(G7, G8, G9, H7, H8, H9, I7, I8, I9))

Vector(Vector(A1, B1, C1, D1, E1, F1, G1, H1, I1), Vector(A2, B2, C2, D2, E2, F2, G2, H2, I2), Vector(A3, B3, C3, D3, E3, F3, G3, H3, I3), Vector(A4, B4, C4, D4, E4, F4, G4, H4, I4), Vector(A5, B5, C5, D5, E5, F5, G5, H5, I5), Vector(A6, B6, C6, D6, E6, F6, G6, H6, I6), Vector(A7, B7, C7, D7, E7, F7, G7, H7, I7), Vector(A8, B8, C8, D8, E8, F8, G8, H8, I8), Vector(A9, B9, C9, D9, E9, F9, G9, H9, I9), Vector(List(A1, A2, A3, A4, A5, A6, A7, A8, A9), List(B1, B2, B3, B4, B5, B6, B7, B8, B9), List(C1, C2, C3, C4, C5, C6, C7, C8, C9), List(D1, D2, D3, D4, D5, D6, D7, D8, D9), List(E1, E2, E3, E4, E5, E6, E7, E8, E9), List(F1, F2, F3, F4, F5, F6, F7, F8, F9), List(G1, G2, G3, G4, G5, G6, G7, G8, G9), List(H1, H2, H3, H4, H5, H6, H7, H8, H9), List(I1, I2, I3, I4, I5, I6, I7, I8, I9)), List(Vector(A1, A2, A3, B1, B2, B3, C1, C2, C3), Vector(A4, A5, A6, B4, B5, B6, C4, C5, C6), Vector(A7, A8, A9, B7, B8, B9, C7, C8, C9), Vector(D1, D2, D3, E1, E2, E3, F1, F2, F3), Vector(D4, D5, D6, E4, E5, E6, F4, F5, F6), Vector(D7, D8, D9, E7, E8, E9, F7, F8, F9), Vector(G1, G2, G3, H1, H2, H3, I1, I2, I3), Vector(G4, G5, G6, H4, H5, H6, I4, I5, I6), Vector(G7, G8, G9, H7, H8, H9, I7, I8, I9)))

I'm totally at lost here.

Answer 1

The result of the yield in the for comprehension is derived from the type of the first generator, in you method, you're constraining the types of your parameters so far you lose your :+ methods.

//The type of 1 to 9 is show below
scala> 1 to 9
res0: scala.collection.immutable.Range.Inclusive with scala.collection.immutable.Range.ByOne = Range(1, 2, 3, 4, 5, 6, 7, 8, 9)


//If you cast it to Iterable[Int] it doens't have the :+ method
scala> (res0:Iterable[Int]) :+ 1
<console>:7: error: value :+ is not a member of Iterable[Int]
       (res0:Iterable[Int]) :+ 1
       ^

//But if you don't, you have it
scala> res0 :+ 1                
res6: scala.collection.immutable.IndexedSeq[Int] = Vector(1, 2, 3, 4, 5, 6, 7, 8, 9, 1)

//And to prove that for comprehensions yield derives the type of the first generator:

scala> for(a <- res0) yield a
res7: scala.collection.immutable.IndexedSeq[Int] = Vector(1, 2, 3, 4, 5, 6, 7, 8, 9)

scala> for(a <- (res0:Iterable[Int])) yield a
res8: Iterable[Int] = Vector(1, 2, 3, 4, 5, 6, 7, 8, 9)

Answer 2

The compiler error occurs because :+ is a member of IndexedSeq (and thus List) but not of Iterable. If you change the return value of unitList from

u1 :+ u2 :+ u3

to

List(u1) :+ u2 :+ u3

it compiles just fine.

Answer 3

Notwithstanding the really weird behavior, :+ cannot possibly be the operator you want. Since you did not annotate the return type of unitList, I don't know what you expected. I assume you wanted to return either Iterable[Square] or Iterable[Iterable[Square]]. So let's see how you can get them, and why :+ is incorrect.

First of all, u1, u2 and u3 are all Iterable[Iterable[Square]], though the exact subtype varies. This should be easy to understand: cross returns Iterable[Square], so yielding cross in a for-comprehension results in an Iterable[Iterable[Square]].

Next, Let's consider :+. This method adds an element to a collection, so, if u1 is Iterable(a, b, c), where a, b and c are Iterable[Square], then u1 :+ u2 is Iterable(a, b, c, u2), and its type becomes Iterable[X], where X is the unification of Iterable[Square] (the type of a, b and c) and Iterable[Iterable[Square]] (the type of u2). The end result is an Iterable[Iterable[AnyRef]].

Since the type of u1, u2 and u3 are essentially the same, the correct operation in all likelyhood is this:

u1 ++ u2 ++ u3

Which will return Iterable[Iterable[Square]]. Now, if you want to remove the nesting and return Iterable[Square], you can flatten this:

(u1 ++ u2 ++ u3).flatten

One of these two things is probably what you want.

Now, as for the "random" switching, there's nothing random about it. In each case, there are two for-comprehensions, and the actual implementation of the resulting collection depends on the implementation of the original collection. So, let's consider it:

• u1: outer type derives from Range, inner type from String (first parameter to cross)
• u2: outer type derives from String, inner type from List (first parameter to cross)
• u3: outer type derives from List, inner type derives from String (first parameter to cross)

So it can be easily deduced that for-comprehensions over String (WrappedString, actually) and Range result in Vector, while for-comprehensions over List result in List.