A monad? Probably not what you need...

Published by Karol Majta on 2nd Jan 2015

Tiny Endian

This morning my friend messaged me with a question if he should "use monads" to solve his problem. I was just writing a short explanation for him, but in some mysterious ways it grew longer and longer, to finally become this beast. I've decided to put it online but first spread a sefty net by placing a disclaimer paragraph.

So here it goes: my understanding of monads is fully intuitive and this article may contain errors, or just plain nonsense. Yet I am insolent enough to see it as a good thing (the intuition, not errors). I am an average developer tackling day-to-day problems, and most of newcomers to monads will be too. This article is also an obvious ripoff, but if you're a self-learned programmer you have to learn somewhere. If you're curious enough to care, links to some resources that I found informative/fun are at the end of this article. To conclude, this thing is more anecdotal than informative.

Getting a "monad" in Python

"Monads" in Python don't make much sense, so dont take any of this very seriously:

def operator(lambda_and_arg, how_many=0):
    """
    Get lambda and arg from `lambda_and_arg` and call lambda with arg.
    In addition return incremented value of how_many (it denotes how_many
    times `operator` was called already.
    """
    _lambda, arg = lambda_and_arg
    return _lambda(arg), how_many+1

Now we can roll with it like this:

>>> operator((math.sqrt, 4))
(2.0, 1)
>>> operator((math.cos, 0), how_many=3)
(1.0, 4)
>>> operator((lambda x: x+1, 10), how_many=2)
(11, 3)

Well, operator is beautiful, it's pure, so it's output depends solely on its input, unittestable, etc, but nobody in the company wants to use it because it actually needs manual bookkeeping of how_many:

>>> x1, n = operator((lambda x: x>0, -3))
>>> # (False, 1)
>>> x2, n = operator((math.sin, 0), how_many=n)
>>> # (0.0, 2)

Aint noboty got time for that... So we can make our operator stateful, in a weird way...

class Op(object):

def __init__(self, val):
    self.transformed = False
    self.call_count = val.call_count if isinstance(val, Op) else 1
    self.value = val.value if isinstance(val, Op) else val

def __repr__(self):
    return repr((self.value, self.call_count))

def op(self, transformation):
    cc = 1 if not self.transformed else self.call_count + 1
    res = transformation(self.value)
    cc += 1 if res.transformed else 0
    res.transformed = True
    res.call_count = cc
    return res

This is how the usage mightt look:

>>> Op(10).op(lambda x: Op(x > 0)).op(lambda x: Op("YUP!" if x else "NAH..."))
("YUP!", 3)
>>> Op([1, 2, 3])
([1, 2, 3], 1)
>>> Op(Op(20))
(20, 1)

I've explicitly omitted getting self.value in shell, as by default monads are not obligated to povide any facility to "pull the value out". They can, but dont have to. And if they do, its because they're nice to you, not because they're monads.

Now let's have a look at Haskells monad typeclass. It is required to define two functions:

  • return which roughly translates to 'take my value and wrap it in a context (in our usecase take our value and add some implicit state)'
  • bind which roughly translates to 'take my value and do some extra stuff' and return something that i can bind to again

At this point it should be clear, that Op is return and op is bind. At this point we should also check that Op conforms to so-called monad laws.

Op(x).op(y) should be same as y(x).

>>> Op([1, 2, 3]).op(lambda x: Op(len(x)))
(3, 1)
>>> (lambda x: Op(len(x)))([1, 2, 3])
(3, 1)

Op(x).op(Op) should be the same as Op(x).

>>> Op("hello")
("hello", 1)
>>> Op("hello").op(Op)
("hello", 1)

Op(x).op(f).op(g) should be the same as Op(x).op(lambda x: f(x).op(g))`:

>>> # this one is much more clear if we define some helper functions
>>> def f(x): return Op(x.strip())
>>> def g(x): return Op(x.trim())
>>> Op('  hello  ').op(f).op(g)
('HELLO', 2)
>>> Op(' hello  ').op(lambda x: f(x).op(g))
('HELLO', 2)

What's in it for me?

Alright, back to the point. What do "monads" give you? The answer is... It depends. If yo do OOP, the answer is probably... not very much If you program in dynamically typed language the answer is... not very much If you program in imperative language the answer is... not very much

Let's elaborate on point 3 for a while as it yields some interesting afterthougths. Imperative programming languages have strict order of operations, so the flow of such thing in python is obvious:

a(b(), c())

Both b and c need to be evaluated, because a needs them. The order of operations is left-to-right, so b is evaluated first, c second, and then, with their return values, a is evaluated. This means, that if a, b or c hit stdio, they do it in particular order.

Haskell is a lazily evaluated language, which means, that if we never use the value of a in IO context (which commonly means one of: print em, store em, or send em over a wire) they will never execute their side effect.

Haskell compiler does arbitrary reordering of expressions according to some rules, so if we call a(b(), c()) there is no guarantee on the order of calls to b and c (and while there is no memoization by default, there is also no guarantee to the number of calls).

So basically, Haskells IO monad does two things. It says "execute this stuff, I need it for side effects" and also takes care about the order of execution (the order of execution seems to be the perk that actually sprouts from the mathematical definition of monad).

If you're programming in imperative language you probably don't need to care for any of these things (most of the time).

So, what's the deal with with dynamically typed languages? Well... I've seen monads done in in perl, ruby, python, javascript and my only thought was... seriously, give yourself a break. I mean, yes - you can do that, but if your return is expected to return something you can bind to, but the runtime allows you to return null, 32, or any random stuff, than you have more serious problems to worry about. So stop bragging about your understanding of monads and go write some unittests. Oh, and btw, yes I do most of development in dynamically typed languages.

Just to stop ranting for a while. As I've stated in the second python example, once you "put something into a monad" you can "do stuff to it" but you can never "pull it out", this is like the number one rule of monads (or more likely the n-th rule of monads, I don't know them that well). So, in our python example, naming Op "a monad" is quite pointless.

>>> a = Op(10).op(lambda x: Op(x+1)).op(lambda x: Op(2*x))
(22, 2)
>>> print a.value
22
>>> a.call_count = 10
>>> a.op(lambda x: Op(0))
(0, 11)

We've just messed internals of our "monad", so calling it "a monad" is just introducing abstraction/complexity while gaining nothing. It's like having a girlfriend with no benefits.

Don't do it. You will just confuse your coworkers.

It's my private opinion, but to have a proper monad you need at least "private" member protection in your runtime. And to squeeze it to the max you need a static type system.

Alright, so back to point 1. What can you get from monads if you're doing OOP instead of functional-style programming? Our python example uses "a monad" to manage state, but if you have a language that supports stateful objects, then just use them (in a smart way). The State monad in Haskell is there just to mitigate the fact, that the language has no variable state.

Some may argue this is a good thing. You are free to pick sides.

Of course there are some benefits of using monadic style with OOP. Most of them relate to the "can't pull it out" rule and ordering of operations.

If you're doing scala you probably know something called Option. This is like the most awesome and simple monad I've seen. It's super useful to mitigate null return values in your code. You returne Some(thing) or Nothing instead. While it might not seem like much, it guarantees that functions that use this value will take Option as argument, and handle it explicitly. By the way... You can exploit this behavior having no clue that Option actually is a monad.

The other thing are futures/deferreds/promises. I will give example in JS because I feel most comfortable with kriskowal's Q deferred API. If you feel uncomfortable reading this after I've criticized dynamic languages you are free to stop here.

var d = Q.defer();
jQuery.get("http://google.com", {}, function (resp) { d.resolve(resp); });

// yeah, i know jquery ajax calls return promises by themselves, just
// wanted to be more explicit
//
// now watch the magic...
//

var initialUppercased = d.promise
  .then(function (resp) { return resp.toUpperCase(); })
  .then(function (uppercased) { return uppercased.slice(100); });

We can say initialUppercased is a promise of some text See the typeclass analogy? initialUppercased is actually Promise(String)

The nice thing about promises is the fact that they show monads both in context of "operation ordering" and "cant pull the value out". (The Option/Maybe example above shows only the latter). While the first one seems obvious (or should i make another http request inside one of then calls?) the second one needs to be elaborated upon. Once you get a promise, you can only "bind" to it by calling then. There is no way to get resp or uppercased. In your code somewhere we would probably see.

initialUppercased.then(function (val) { jQuery('body').text(val); });

The fact that you can use the actual value (you could have as well assigned it to window.property instead of modifying DOM) is the fact that JS allows arbitrary state mutations. What you definately don't want in your code is:

var d = Q.defer();
var result = undefined;
jQuery.get("http://google.com", {}, function (resp) { result = resp; });
console.log(result);

The only way you can access the response is by "binding" with then. The fact that at some point you can store the raw value in global for reuse is just a peculiarity of JS runtime.

Alright, so what comes out of this?

Basically I see monads fit for doing four things:

  • Making sure that things "are done" in some context and cannot be "pulled out of it" (for some languages the compiler will take care of it, for others you have to depend on developer's good will, so the benefit can be easily lost)
  • Assuring order of operations (in imperative programming useful in async contexts)
  • Implicit state handling (in OOP you probably have other means that are simple and easier to understand for most people).
  • Assuring that operations will happen at all (important with Haskell and it's lazy IO)

Of course monads (presumably) can do much more, but (please don't hate me on me) I still cannot figure out how to use the fact that List are monads in a productive way.

Isn't the right question a key to right answer?

It might be useful to know what monads are, but wouldn't it be even better to know when to use them?

Let's ask a more perverse question: "When are monads developed?".

Well, for most of the time, people just solve problems, and notice that the solution they came to is "monadic", which basically means:

Hey Mike, method thing we call here looks like `return` and the second
one looks like `bind`. It seems oure JavaScript promise API is monadic.

This is cool.

There is a sweet spot for monads in Haskell, but as I've stated before, I see the IO and State as prosthesis. It's not a bad thing. Haskell has its ways and is a super-interesting programming language, which compiles to machine code, is garbage-collected yet fast, lazy and overally seems awesome. You must expect a price to pay for this.

This is cool too.

And there is a camp of "monadistas", who will try to create monadic style for assembly language while bragging about their PhD in mathematics (just kidding, math people are usually super-nice and helpful, and rarely know assembly).

The best you can do is just ignore the noise.

The links, and the disclaimer after disclaimer

Ok, here go the links to interesting stuff:

The last thing I want to add is the fact that our Op is the most dull monad example. If I were to write this from scratch I would probably come up with a more interesting one.

Oh and one more notion. I honestly think that the fact, that "hello world" in Haskell requires using an IO monad is responsible for most of confustion and hype around them!