A Love Letter to Composition

on November 7 2019, 6:07AM

Using composition gives you superpowers. It is by far the most practical experimentation tool I know.

The dot (.) operator is my favorite infix operator in Haskell. Statically typed languages help ensure that function composition is structurally sound before anything is run. Composition of two functions means the type of the output of the first function must equal the type of the input of the next function. Many languages now have a pipe operator which is the composition operator in reverse. Some even use pipe or dot to write flow of execution top-to-bottom or bottom-to-top, given how you can stack the calls.

This isn't just an article about the usefulness and specifics around function composition itself. Composition as a concept forms a basis of for problem solving and systems of proof. By decomposing a system or problem into parts we can scrutinize and, thus, verify them for use in constructing the same or potentially different solutions, proofs, and so on. Having solid building blocks means we can play around with different arrangements. Playing around with these building blocks and assumptions is how mathematics and experimentation works at its core.

Composition also forms part of the basis of a fascinating branch of mathematics known as category theory. Envision a type of mathematics that encodes any arbitrary concept as a graph-like diagram to explore general structures and relationships. Having a mechanism for encoding general topics empowers you with the ability to play with structure and assumptions and study the structure and implications of those arrangements. Caveat emptor; I am not saying composition requires category theory to be useful! In fact, having too complicated a system defeats the purpose of having a lightweight guide.

Architecturally, the common phrase that "systems are the sum of their parts" is a farce. If systems were some linear combination then removing individual elements would merely reduce the size of the system, but removal can mean total system failure, no change whatsoever, and possibly improvement in the system as a whole!

It is rare to find a mental tool so broadly applicable and yet so uncomplicated in nature. I'll reiterate strongly here; you don't necessarily need to be pedantic about the shape of things to reap these benefits. Nor do you need to understand category theory to its highest levels of complexity to piece together solutions. In my mind the broad steps are always the same:

  1. Take, or produce, components
  2. Scrutinize the components as you may be able to i. break things down further (1) ii. see how things connect iii. or verify the parts are sound
  3. Experiment with arrangements of components

I see composition as a framework for experimentation with no added consequence of increased complexity from the use of the framework itself. Experimentation allows us to explore new connections. Exploring new connections means finding solutions to problems in any domain. Discoveries are the bedrock of learning. Rapid experimentation increases rate of knowledge acquisitions as well as improved retention of knowledge. This is why composition is a superpower.