fork (thing)

In the J programming language, a fork is the special name given to a composite verb made by concatenating three verbs. The general format for a monadic fork follows (f and h are monadic, while g is dyadic, and v is some noun):

(f g h) v is identical to (f v) g (h v)

For example:

• (+/ % #) v is equivalent to (+/v) % (#v) (the sum of v divided by the count of v)...also known as the arithmetic mean or the average of v.
• (sin % cos) v is equivalent to (sin v) % (cos v) (the sine of v divided by the cosine of v)...also known as the tangent v.
• (] g h) v is equivalent to (] v) g (h v) (the identity of v combined with h v), which is the schema for the monadic hook (g h) v.

The concept of a fork also generalizes to dyadic verbs in a train:

x (f g h) v is identical to (x f v) g (x h v)

Again, an example:

• u (+ , -) v is equivalent to (u+v) , (u-v) (the sum of u and v with the difference of u and v appended), or ``u plus or minus v.'' (This example taken from Learning J by Roger Stokes).

The most important thing to note about the concept of a fork is that it allows extended chaining of verbs in a meaningful way, because a fork can also be a component of a fork (or a hook, which, as noted above, is just a special case of a fork).

For example, to find the distance of each element from the mean (an important step in finding the variance and standard deviation) we just do it:

(- +/ % #) v is
(] - (+/ % #)) v is
(] - (+/ % #)) v is
v - ((+/ % #) v) is
v - ((+/v) % (#v)) is
the pairwise subtraction of elements in v with their mean.

More information on extended chaining of J verbs can be found at train.