Programming in Scala”

Chapter notes 16
This may seem like it shouldn’t work. The stream is referencing itself in its own tail! But the trick
is that the #:: constructor is non-strict in its second argument. The evaluation of cyclic will stop
without expanding the expression 1 #:: cyclic. It’s not until somebody takes the tail of the tail
of cyclic that the recursive reference is expanded, and again it expands only one element at a time,
allowing for an infinite, cyclic stream.
Note that the cyclic stream is reusing its own structure. cyclic.tail.tail is not a new stream
that looks like cyclic. It really is the same object as cyclic in every sense:
scala> cyclic.tail.tail eq cyclic
res0: Boolean = true
This technique is sometimes called “Tying the Knot”. For more information see the Haskell.org
article⁷¹.
However, be careful of creating such structures using the Scala standard library’s Stream. They can
be quite fragile. The reason is that scala.Stream is is strict in the head element and it will also
memoize⁷² the computed contents, which can lead to memory leaks.
Stream.apply
Be careful using Stream.apply, both in the standard library and in the exercises: they are constructed
using repeated parameters, which are always strict. This means that e.g.
Stream({println("One"); 1}, {println("Two"); 2}, {println("Three"); 3})
will immediately print One, Two, Three. Although the Stream will be constructed lazily, the contents
have already been evaluated.
For truly lazily constructed Streams you can always resort to #:: (which still evaluates the head
value strictly!) or nested cons(..,cons(..,..)) operators in the exercises.
Notes on chapter 6: Purely functional state
State in Scalaz
The Scalaz library⁷³ supplies a State data type⁷⁴ that is a specialization of a more general type
IndexedStateT⁷⁵, where State[S,A] = IndexedStateT[Id, S, S, A] and Id[A] = A.
⁷¹http://www.haskell.org/haskellwiki/Tying_the_Knot
⁷²http://en.wikipedia.org/wiki/Memoization
⁷³http://github.com/scalaz/scalaz
⁷⁴http://docs.typelevel.org/api/scalaz/stable/7.1.0-M3/doc/#scalaz.package\protect\char”0024\relax\protect\char”0024\relaxState\protect\
char”0024\relax
⁷⁵http://docs.typelevel.org/api/scalaz/stable/7.1.0-M3/doc/#scalaz.IndexedStateT