Scala For-Comprehensions

A for-comprehension is syntactic sugar for map, flatMap and filter operations on collections.

• The general form is for (s) yield e
• s is a sequence of generators and filters
• p <- e is a generator
• if f is a filter
• If there are several generators (equivalent of a nested loop), the last generator varies faster than the first
• You can use { s } instead of ( s ) if you want to use multiple lines without requiring semicolons
• e is an element of the resulting collection

Example 1

// list all combinations of numbers x and y where x is drawn from
// 1 to M and y is drawn from 1 to N
for (x <- 1 to M; y <- 1 to N)
  yield (x,y)

is equivalent to

(1 to M) flatMap (x => (1 to N) map (y => (x, y)))

Translation Rules

• A for-expression looks like a traditional for loop but works differently internally
• for (x <- e1) yield e2 is translated to e1.map(x => e2)
• for (x <- e1 if f) yield e2 is translated to for (x <- e1.filter(x => f)) yield e2
• for (x <- e1; y <- e2) yield e3 is translated to e1.flatMap(x => for (y <- e2) yield e3)
• This means you can use a for-comprehension for your own type, as long as you define map, flatMap and filter.

Example 2

for {  
  i <- 1 until n  
  j <- 1 until i  
  if isPrime(i + j)  
} yield (i, j)  

is equivalent to

for (i <- 1 until n; j <- 1 until i if isPrime(i + j))
    yield (i, j)  

is equivalent to

(1 until n).flatMap(i => (1 until i).filter(j => isPrime(i + j)).map(j => (i, j)))