Tacit Programming

One of distinct features of J is its brevity and to facilitate it tacit or point-free programming is often used 1. In short it is a style of programming where arguments are omitted. In J this is particularly easy to achieve since each function takes up to two argument, so it is easy to imagine them on both sides.

If we go back to our plus example, previously we defined it via what is called direct definition (using {{ }}) and referred to our arguments as x and y for left and right argument respectively.

   plus =: {{ x + y }}

However this can be reduced to tacit form, leveraging the fact that x is always coming from the left and y - from the right.

   plus =: +

This definition now becomes trivial so our plus function is just a plus + primitive which we can inline.

Being able to do this for a single primitive is not very useful on its own, so let's look at the definition of a function that is finding average of an array.

   mean =: {{ (+/ y) % (# y) }}

We have some new primitives here, let's go over them one-by-one.

• / is another function that is taking a function on its left, similar to \, this primitive is called reduce or fold, when called on y it will compute sum of ys elements.
• # is just a simple function that is computing length of y, it is called tally.
• % is division sign, since both slashes forward and backward are already used for other purposes, J reserves % for division.

Given this, if we read the original mean definition we should be able to interpret it as something like compute sum of the argument and then divide it by its length, the very definition of average.

However in J you can write this in its tacit form, omitting the argument to get +/ % #, let's breakdown how it works.