The Wiert Corner – irregular stream of stuff

Slowly but steadily, I’m now ready to continue reading [WayBack] From design patterns to category theory.

I found it two years ago after stumbling into [WayBack] Semigroups accumulate and [WayBack] Monoids accumulate. Both articles indicate they are part of two distinct series: [WayBack] Semigroups and [WayBack] Monoids which both in turn indicate the same super-series: [WayBack] Monoids, semigroups, and friends.

That intrigued me, as from a casual interest in Semigroups I got into a really structured coverage of many related topics leading all the way to design patterns. How cool is that!

Back than, I lacked some of the vocabulary I needed to fully grasp this, as part of the posts use the functional programming perspective which – for geeks like me that grew up in the procedural, object-oriented, and interface-polymorphism eras – takes some time to wrap their head around.

I did learn a thing or two back then, for instance the series taught me that some semigroups are not monoids. The diagram on the right shows how the various groups are related. But I could not replicate that knowledge, clearly lacking the words to explain it to myself.

What I really liked is the humble way in which the author – Mark Seeman – indicated that when he first thought about these topics himself, he too had still a lot of things to learn, including acquiring the vocabulary:

My first attempt at answering these questions was in 2010, but while I had the experience that certain abstractions composed better than others, I lacked the vocabulary. I’ve been wanting to write a better treatment of the topic ever since, but I’ve been constantly learning as I’ve grappled with the concepts.

Like me, he is on a life long quest in learning new things every day.

Now that I’ve done more functional programming (mainly from object-oriented code bases), I think I’m more equipped to digest his writings, better understand them and maybe even explain them.

By now there also should be more topics than these ones:

• [WayBack] Monoids, semigroups, and friends
  • [WayBack] Monoids
    • [WayBack] Strings, lists, and sequences as a monoid
    • [WayBack] Money monoid
    • [WayBack] Convex hull monoid
    • [WayBack] Tuple monoids
    • [WayBack] Function monoids
    • [WayBack] Endomorphism monoid
    • [WayBack] Monoids accumulate
  • [WayBack] Semigroups
    • [WayBack] Bounding box semigroup
    • [WayBack] Semigroups accumulate
  • Quasigroups
  • Magmas
    • Rock Paper Scissors magma
    • Colour-mixing magma
• Software design isomorphisms
  • Unit isomorphisms
  • Function isomorphisms
  • Argument list isomorphisms
  • Uncurry isomorphisms
  • Object isomorphisms
  • Abstract class isomorphism
  • Inheritance-composition isomorphism
• From structural patterns to category theory
  • Composite as a monoid
  • Coalescing Composite as a monoid
  • Endomorphic Composite as a monoid
  • Null Object as identity

Time to do some reading over the next weeks…

–jeroen