Editing Function-level programming (section)

== Introduction ==
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 [[Programs as mathematical objects|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 function]]s 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.