I’ve been reading Backus among other things, attempting to grasp the differences between first-order predicate logic, function-level, and variable-level combinatory logic. One area that has stood out for me in reading Backus was the notion that function-level may be more efficient to reason about than the more user-friendly variable-level.

[rant] In some circles I understand function-level is also known as pointfree (or pointless) while the most common variable-level usages appears to be lambda calculus based. Talk about my brain having a lexical meltdown. Reading Backus is bad enough… but trying to understand just what pure functional programming is ain’t easy either when there appears to be no consensus on exactly what that means. [/rant]

Backus goes on after his efficiency claim to discuss the notion of using primitive functions to compose functional forms and type hierarchies from composing those functional forms in succession. This immediately piqued my interest because in the back of my mind it had been nagging me why someone could possibly continue along the function-level line of thought when the mainstream had moved on to the more popular get-things-done lambda calculus way of doing things.

Then something struck me. Something I’ve thought about with regard to intelligence and that of the realm of referential transparency and the way in which we all operate in life. I began to draw parallels between the notion of type hierarchies, atoms, elements, molecules, proteins, enzymes, cells and organisms. The composition of primitive functions into these functional forms. The hierarchies these then build based upon the physical properties (quantum mechanics?) of those primitive functions and the unique ways in which functions may apply to others creating yet more uniquely propertied functional forms. The complexity of properties of these functions meaning some will be more inherently stable than others (potentially the types). That these unique properties could themselves be derived from evolutionary encapsulation. In other words; turtles all the way down.

Months back I set out to model my own theory of encapsulation. Initially known as my Principal of Rational Dynamic Complexity. Later I prefixed Robust. Then after finding that difficult to remember it became the Law of Encapsulation with each of those elements becimong principles. My The Law of Encapsulation states that; for any complex system to evolve in a constrained environment(eg. the earth) it must be dynamic yet rational in order to be robust.

So while others may prefer the variable world of the lambda calculus to get things done today, tomorrow is a new day, one I believe may yet see the rise of function-level. Only your likely to never know it because it will come naturally to you. In other words… an interface abstraction. Just as our bodies are for our brains.