Reduction operators

The associative operators :: (concatenation), &, |, ^, +, * and merge may be applied to vectors as ``reduction'' operators . For example,

        &[w,x,y,z]

is equivalent to

        (w & x & y & z)

and so on. Reduction operators may be combined with the iterated vector constructor. For example, to compute the sum of the first five squares, we could write:

        +[ i*i : i = 1..5]

Note that for the non-commutative operator ::, the order of the range specification matters. For example

        ::[ i*i : i = 1..5]

produces [1,4,9,16,25], while

        ::[ i*i : i = 5..1]

produces [25,16,9,4,1]. Also note that using :: as a reduction operator makes it possible to construct a vector by repeating a pattern. For example,

        ::[ [0,1] : i = 1..3]

is equivalent to [0,1,0,1,0,1].

Reduction operators do not coerce their arguments to vectors. A reduction operator applied to a scalar operand has no effect. Thus, +3 = 3 (and not 2, fortunately!).