Contrast To Functional Programming
When Backus studied and publicized his function-level style of programming, his message was mostly misunderstood, giving boost to the traditional functional programming style languages instead of his own FP and its successor FL.
Backus calls functional programming applicative programming; his function-level programming is a particular, constrained type of applicative programming.
A key distinction from functional languages is that Backus' language has the following hierarchy of types:
- atoms
- functions, which take atoms to atoms
- Higher-order functions (which he calls "functional forms"), which take one or two functions to functions
...and the only way to generate new functions is to use one of the functional forms, which are fixed: you cannot build your own functional form (at least not within FP; you can within FFP (Formal FP)).
This restriction means that functions in FP are a module (generated by the built-in functions) over the algebra of functional forms, and are thus algebraically tractable. For instance, the general question of equality of two functions is equivalent to the halting problem, and is undecidable, but equality of two functions in FP is just equality in the algebra, and thus (Backus imagines) easier.
Even today, many users of lambda style languages often misinterpret Backus' function-level approach as a restrictive variant of the lambda style, which is a de facto value-level style. 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.
Read more about this topic: Function-level Programming
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