Scalar function

A scalar function is one of a class of primitive functions that apply to arguments one element at a time. Dyadic scalar functions pair elements of their arguments based on conformability rules, and thus are subject to scalar extension. In nested array languages, scalar functions pervade any nested arrays by recursively descending into them until reaching simple scalars; in flat array languages they usually do not apply inside boxes. Functions which are not scalar, are called mixed functions.

Only a particular valence of a function is labelled "scalar". The scalar monad Not usually shares the glyph  with non-scalar dyad Without, and similarly scalar Roll and non-scalar Deal are both written.

Standard scalar functions
Most APLs use a set of scalar functions that was worked out fairly early in APL's development. These are listed in this section.

Additional scalar functions
Very few additional scalar functions have been added later in various dialects: