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.
When Backus studied and publicized his function-level style of programming, his message was mostly misunderstood[2] as supporting the traditional functional programming style languages instead of his own FP and its successor FL.
In fact, Backus would not have disagreed with the 'restrictive' accusation: he argued that it was precisely due to such restrictions that a well-formed mathematical space could arise, in a manner analogous to the way structured programming limits programming to a restricted version of all the control-flow possibilities available in plain, unrestricted unstructured programs.
The value-free style of FP is closely related to the equational logic of a cartesian-closed category.