Split composition

Split-compose is a tacit construct, used to pre-process its argument(s) with the left and right-most operand before applying the middle operand between the result. Given functions,  , and  , the split composition on arguments   and   is defined as.

The name was introduced by the I|I language, where it is represented with, a higher-order function that applies first to the middle function and then the two outer functions (  also represents the Over operator). It doesn't appear as a primitive in any APL, nor can it, because it is a composition of three functions, while a compositional operator can take no more than two operands. This situation is identical to that of the fork. Both split-compose and fork can be constructed using two companion operators, tying together the three involved functions.

In Extended Dyalog APL and dzaima/APL, the construct can be formed using Reverse Compose and Compose. In this example, we multiply the interval (integers up until) of the left argument, with the Magnitude of the right: This is evaluated as. A further example concatenates the reciprocal of the left argument with the negation of the right: This is evaluated as.

Alternatives
In dialects that lack Reverse Compose (and even Compose), split-compose can be written either by defining the missing operator(s), or as a single derived function or fork, if this is supported. For example, in Dyalog APL the expression can be formed with Compose and Commute as  : Note that  applies   before   which can matter for functions with side effects. For example, consider the following where  would print  : The equivalent fork is, for example: