Functional languages often have functional abstractions for iteration and
recursion. For example, Scheme has a mapping (iteration abstraction) function named map which applies
a function to each item of a list.
(map (lambda(x) (* x x x)) '(2 3 4 5))
produces the result
(8 27 64 125)
This same example is easily expressed using J. In J, the power function, expressed as
^, may be used as the argument of the bond conjunction, &, producing
the cube function ^&3. This monad may be applied as:
(^&3) 2 3 4 5
producing the result
8 27 64 125
The J programming notation has a rich collection of abstractions for
dealing with iteration over the items in lists and arrays. For example,
the insert adverb, /, allows a dyad to be inserted between
the items of a list or array.
+/ 1 2 3 4 5
evaluates the expression
1 + 2 + 3 + 4 + 5
while
*/ 1 2 3 4 5 6
evaluates the expression
1 * 2 * 3 * 4 * 5 * 6
Scheme and J both support an extensive family of abstractions for recursion and iteration which are beyond the scope of this paper. Such features are important in the exposition of a more advanced treatment of recursion and iteration. For example, Iverson [Iv 95] shows extensive use of J to construct mathematical proofs of correctness of algorithms.