Composition and Diamonds

Whilst streams, filter and cons/car/cdr are good examples, their context of functional programming might be seen as already rather detached from the realities of physical machines; however, another good example is Unix programs. The abstractions offered by programs like grep, sed, find, cat, cp, etc. are all quite small, and whilst bug-fixes, optimisations and even new features may still be added to the implementations, they've been essentially "finished" for decades.

The point is that these applications were not created to solve some real-world problem. Instead, it is assumed that real-world problems will be solved by scripts (or one-liners in a terminal), that users will be writing their own scripts, that each problem will require a new script and such scripts will churn as the requirements/practicalities change. Hence the job of Unix tools is to make scripts simple and easy to write. By decoupling the tools from any particular problem, they can provide small, reliable abstractions; if requirements change such that an abstraction doesn't quite fit, the solution is to change the script to use something else, rather than changing the contract of the tools.

This works well when the tools are small, and the user is assumed to have some competence or willingness to learn in order to solve their problems. It doesn't work so well when the tools are large (e.g. a modern Web browser) and the users are assumed to only be capable of e.g. clicking a "Go" button.

A trivial diamond of computation would be a custom purpose machine, e.g. [0].

Inter-operation between decoupled "small abstractions" and their composed descendants requires either a pre-existing mutual interchange form, or a set of wrappers that provide the same. This is equivalent to simply building on top of that common normal form, which exists, at varying levels of specificity and accessibility, whether one explicitly considers it or not [1]. This, combined with the ultimate CNF still being natural language, because computational semantics are still ultimately evaluated in the context of the human brain, argues for intentionally clarifying and improving that least common computational denominator, in the same way that if one entirely lapses in their recollection of higher synthetic geometry, "begin by assuming a compass and straightedge" is at the least never incorrect.

[0] https://news.ycombinator.com/item?id=13669033

[1] E.g. the cons example in the article is a small abstraction that composes well, at the abstract level, with the cond abstraction for destructuring quoted symbol lists when writing interpreters, but as noted by the author leaks too much of the underlying machine primitives, and thus is an impedance mismatch when seeking performance optimizations, as in a compiler.