So recently I have become one of those jerks that has sailed through Read A Couple Of Chapters Of A Book About Haskell, by way of Snuck Maybe Types Into My Work Project to arrive at full-blown Good Morning Sir/Madam, Have You Got A Spare Moment To Talk About Monads™?. That is to say, by selfishly forcing these concepts upon my colleagues I have ended up spending a lot of my working life explaining them and why I think they are good to stop everybody hating me for making their lives unnecessary complicated. In doing so, I think I have come across one of the main conceptual stumbling blocks, which I hope to make less-stumble-able.
So the problem, as I see it, isn’t grasping what a Monad is (it’s a burrito, it’s a poster tube, it’s a snobby waste of time, easy!), or even what a Functor is (it’s mappable, right?), but whether they are even “things” at all. It’s one thing to see words like Monad, Functor, Monoid or Traversable around the place but it’s a little unclear how to make, or god forbid, actually use one in something approaching real life code. Are they objects? Do I make a new Monad object just like I’d make a new Promise?
const response = new Monad(ajaxUrl)Is is a Functor a method I can run on something to increase the amount of maths?
const makeProgramFaster = response.Functor("MAXIMISE DATA")The short answer is “no”, and the long answer, well, that’s also “no”, followed by “ok, let me tell you what typeclasses are and hopefully the other stuff will sort of get cleared up along the way.”
Maths is sadness
Reading about type theory, particularly materials written from a very mathematical perspective, can often make it feel even worse, with explanations that feel so broad and simple that they feel either a) meaningless or b) like they must contain some unseen trap we mere mortals do not understand.
Anyhow, I thought perhaps a better approach here is to explain what these things are not and work from there. Because the aim here is to end up with some real life knowledge we can use to write real code, instead of using examples from the world of computers, let’s use them from the world of crime dramas, because I have been watching a lot of those recently.
Time for a tenuous analogy
So we have a police officer. In this case, it’s Detective Sergeant Kate Fleming from Jed Mercurio’s surprisingly gripping Line Of Duty series (I too struggled with the series title’s almost Clancy-ian levels of Really Must We Spell This Out, do persevere with it though, it really is OK, you probably only need to watch the first couple of seasons to follow this article)
DS Kate Fleming is a Police Officer in AC-12, a unit in the police force somewhere in London that investigates Bent Coppers and makes sure there is no Dodgy Dealings or Underhand Business. DS Kate Fleming was not born a police officer, but certainly displays all the characteristics of one - she Catches Criminals, Likes A Pint, and Her Marriage Is In Tatters because of course she is Married To The Job.
Here is another Police Officer - in this case Detective Constable Nigel “Nige” Morton, played by 90s lad hero and renowned bounding frown Neil Morrissey. “Nige” was also not born a copper, but he is certainly one now as he Likes A Pint and also, to some extent, Catches Criminals. “Nige”, however, is a bit of a sneaky prick, and has been known from time to time to take a few backhanders in exchange for leaking information to the press and to other criminals. Therefore, to some extent, as well being a Police Officer, “Nige” is a Bent Copper because of his Underhand Business and Dodgy Dealings.
How does this relate to typeclasses then?
DS Kate Fleming is not a typeclass.
DC Nigel “Nige” Morton is also not a typeclass.
Liking A Pint is not a typeclass.
Neither is Underhand Business.
Typeclass examples
So what are?
Human Person
Both DS Kate Fleming and DC Nigel “Nige” Morton can have instances of the typeclass Human Person, because they Breath, Eat and Poo. They are ‘lawful’ instances of Human Person because I am too lazy to think of a reason that they are not.
Police Officer
DS Kate Fleming can be an instance of the typeclass of Police Officer because she Catches Criminals and Likes A Pint. She is also a ‘lawful’ instance, we can say, because as well as this, she does no Underhand Business or Dodgy Dealings.
DC Nigel “Nige” Morton is, to the innocent eye, an instance of the typeclass Police Officer. He also Likes A Pint, Catches Criminals, and although he is seen to have a marriage earlier in the show, later he is seen to be mowing his lawn in a solitary fashion shot through a lens tinged with regret. However, he is not a ‘lawful’ instance of the typeclass Police Officer, because of his Underhand Business or Dodgy Dealings.
Bent Copper
DS Kate Fleming is not in the typeclass Bent Copper, because (spoiler alert!) throughout the show she is seen to behave in a moral fashion befitting an officer working for AC-12, the anti-corruption unit at the centre of the whole show.
DC Nigel “Nige” Morton however is in the typeclass Bent Copper, exactly because of his Underhand Business, Dodgy Dealings and Perhaps Not Really Needing That Walking Stick But Claiming Disability Benefits Regardless. He is probably also a lawful instance of Bent Copper (although I understand at this juncture that this makes the whole analogy somewhat confusing) - simply because Bent Coppers Don’t Really Have Rules, And If They Did, Playing By Them Would Somewhat Defeat The Point.
Anti-Corruption Police Officer
DS Kate Fleming is also in this typeclass because she Nicks Bent Coppers, whilst DC Nigel “Nige” Morton is not because he wouldn’t Dob In One Of Our Own. Clear? As mud? Great.
Back to stupid code
So how does this relate to computers and showing our colleagues how incredibly intellectual we are?
Let’s take an array. That’s a thing you have probably used.
const arr = [1, 2, 2, 4, 65, 7]arr is not a typeclass, it is an object (or more broadly, a value).
A Functor is a typeclass though, and arr can be an instance of Functor.
The rules of a ‘lawful’ Functor is that we can run a Map function over the contents of the array and afterward The Length Of The Array Remains The Same and It’s Still An Array and Basically Nothing Really Weird Has Happened.
arr.map(x => x)
// arr == [1, 2, 2, 4, 65, 7]As you see here, our array is the same length and the function has been applied to each item without any Funny Business. To tie it back to our police-based analogy - if DS Kate Fleming was given some important evidence to take back to the station, this result constitutes the evidence arriving at the station untampered for some forensic analysis that will pull the case together in the final nail-biting moments of the series.
However, what if DC Nigel “Nige” Morton was given that same evidence? That’s a nice 65 value in there, surely nobody would notice if he snuck it for himself? Surely he’s Done His Bit Over The Years And Deserves It, after all.
var nigesFilthyPocket = []
arr.map(x => {
if (x < 65) {
return x
} else {
nigesFilthyPocket.push(x)
return 0
}
})
// arr == [1, 2, 2, 4, 0, 7]If you can follow this code (and forgive the use of a mutable variable in an article that is, despite severely beating around the bush about the fact, written about the subject of functional programming) I think we can all agree that “Nige” here is a bit of a swine.
“Nige”’s horrible law-breaking evidence-stealing map function does not make a ‘lawful’ Functor, as it breaks the Basically Nothing Really Weird Has Happened rule above by doing a massive side-effect and mutating an outside variable when it should just be doing nothing outside of the arr. However, if there is a TotallyAwfulFunctor typeclass, this would make an excellent instance of it.
OK, I’m exhausted, please, tell me, what is a typeclass?
Sure.
Objects and datatypes can be made instances of the typeclass Functor, provided they implement map without any funny business. These could be arrays, tree structure, Maybe and Either, and loads more. You can map over them all and expect the same behaviour.
People are instances of the typeclass Human Being, as in general they implement the Breath, Eat and Poo functions. (todo: add javascript example)
Anything that can be compared to another thing to check whether it is the same or not can be an instance of the typeclass Eq.
Many objects and datatypes can be made instances of the typeclass Monad, if they are also lawful Functors and Applicative Functors and implement bind and return functions. (What? Not now…)
Therefore…
A typeclass is a way of categorising things based not on what they are but what they can and can’t do.
(Thanks Riku for helping me put that more succinctly. You may find it hard to believe that I have a tendency to ramble).
Make sense? If not, why not get in touch?
Further reading: