Function-level

In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming.

In his 1977 Turing award lecture, Backus set forth what he considered to be the need to switch to a different philosophy in programming language design:

Programming languages appear to be in trouble. Each successive language incorporates, with a little cleaning up, all the features of its predecessors plus a few more. [...] Each new language claims new and fashionable features... but the plain fact is that few languages make programming sufficiently cheaper or more reliable to justify the cost of producing and learning to use them.

He designed FP to be the first programming language to specifically support the function-level programming style.

A function-level program is variable-free (cf. point-free programming), since program variables, which are essential in value-level definitions, are not needed in function-level programs.

In the function-level style of programming, a program is built directly from programs that are given at the outset, by combining them with program-forming operations or functionals. Thus, in contrast with the value-level approach that applies the given programs to values to form a succession of values culminating in the desired result value, the function-level approach applies program-forming operations to the given programs to form a succession of programs culminating in the desired result program.

As a result, the function-level approach to programming invites study of the space of programs under program-forming operations, looking to derive useful algebraic properties of these program-forming operations. The function-level approach offers the possibility of making the set of programs a mathematical space by emphasizing the algebraic properties of the program-forming operations over the space of programs.

Another potential advantage of the function-level view is the ability to use only strict functions and thereby have bottom-up semantics, which are the simplest kind of all. Yet another is the existence of function level definitions that are not the lifted (that is, lifted from a lower value-level to a higher function-level) image of any existing value-level one: these (often terse) function-level definitions represent a more powerful style of programming not available at the value-level and, arguably, are often easier to understand and reason about.

...
Wikipedia