Functional Programming Aha! Moments

In the past couple of years, I've dedicated a fair amount of time to closet-functional-programming. Although I haven't gotten an opportunity to use a more purist functional programming language (e.g. not FrameWorkOfTheDay.JS) in my day-to-day day, industry work, I believe some of the values of functional programming have bled into my daily practice, for the better.

Industry aside, I want to share some of the "Aha! moments" I've had while learning about functional programming. These are moments where something just clicked for me; some part of me almost can't help but share them.

Lets Can Be Described by Anonymous Functions

Although "functional programming" is one of those things were if you ask five people for a definition you are likely to get six different definitions, one general consensus seems to hold: assignment should be reduced, minimally scoped or eliminated entirely in functional programming.

The let macro/expression/sugar is basically a means of reducing assignments into minimally scoped, (generally) non-mutative expressions with a set of bindings. Here's a contrived example of what this might look like in Clojure

Here we're saying, let's bind `x` to `35` then `y` to a value calculated from `x`, then we'll use `y` to calculate some result. This entire expression is just that, it's an expression. This `let` is evaluated as a whole, and the result is simply `42`.

So, here comes the first "Aha!" This same kind of scoped assignment can be done through applying anonymous functions! Here's what that looks like for the above example

Basically the pattern here is just, for each bound symbol (in this case `x` and `y`) nest and call an anonymous function, passing the bound value down (`35` and `(- x 14)`)! I found this discovery exceptionally cool because it further emphasized the power of these functional languages: something as simple as anonymous functions can be combined to form powerful abstractions. 

Monadic Bind Is Like Method Chaining

Monads, in general, have provided many an "Aha" for me. They're definitely one of those constructs where, once you get passed the initial "this is slightly out of my comfort zone" feeling, you are ready to embrace an overwhelming amount of power.`bind` (looks like `>>=`) is one of the crucial operations implementable by a monad, it has the following type signature

Ignoring currying and some other subtleties, if I'm thinking in an "object oriented mindset" I might reason about this as follows:

• `bind` is a function that take 2 arguments
• a generic wrapper around some type `a`
• a function which takes some `a` and returns some generic wrapper around type `b` (where `b` may be the same type as `a`)
• `bind` returns some generic wrapper around type `b`

To me, this sounds exactly like a single call that enables method chaining! Think a la calling `bind` to transform from monad to monad to monad... In my mind, `bind` is an enabling feature, that allows Haskell code to be elegant, expressive and powerful without lacking type safety (see `do` notation).

To visualize how this is kind of like method chaining, observe the following Ruby code

We can imagine these calls (with the exception of `count`) being like a type-not-so-safe version of Haskell's `bind` applied a couple of times (2 to be exact). Here are what the steps might look like

1. `m a` is a range of `Fixnum` (e.g. `Range Fixnum`)
2. `map` applies a block that takes the `Range Fixnum` and returns an `Array Fixnum`
3. `select`, with its block, takes an `Array Fixnum` and returns an `Array Fixnum`
4. Finally, `count` is simply applied to the `Array Fixnum`

Message Passing (OOP Style) Can Be Achieved via Closures

Disclaimer/Plug: this last "Aha" is shamelessly ripped off from The Structure and Interpretation of Computer Programs (SICP). I am over half way through this book, it is wonderful, please consider showing the authors your support by buying it.

The authors of SICP take the reader through a fantastic journey in which the powers of LISP and functional programming are clearly displayed through examples in the Scheme dialect. One piece of this journey that recently blew my mind was when the authors used closures to define a mutable bank account that responds to different messages. Here's the code (again shamelessly ripped)

What you're seeing here is basically a constructor that builds objects, given a beginning balance, that respond to the `'withdraw` and `'deposit` messages.

Frankly, I don't really know what I can say about this that the authors haven't already said (1) more articulately, (2) more clearly and (3) in a more inspirational manner.

In conclusion, these are just a few of the awesome concepts I've picked up in my pursuit of functional programming. If you have any thoughts on these, or my description of them, don't hesitate to comment.

What Is A Monad?

Being a hobbyist Haskell programmer, I have heard the term "monad" a lot. In my experience playing with Haskell I have used monads plenty of times, however, it was not until recently that I have come to a digestible understanding of what they really are.

Think Method Chaining

Some of the prominent phrases which I hear being used to describe monads are "they're ways to fake state" and "they are really just a form of method chaining." Although, in my (perhaps nieve) understanding of monads, both of these statements are true, the latter has been far more useful in helping me arrive at a useful understanding of "the m word." So I encourage anyone who may be struggling with the definition of a monad to do the same: think method chaining.

Method Chaining You Say?

Yes method chaining. In the object oriented world this may mean something like this:

someObject.someMethod(1)
          .otherMethod("Pizza")
          .finalMethod()

So, in OOP, the objects returned by each of these methods would encapsulate state. Now, in Haskell, there is not really a concept of state, things are what they are. The sequential mutilation of objects is not something Haskell supports naturally, so it uses the monad as a slick way to sort of "fake state."

What It Looks Like

Disclaimer: this is my current understand of Haskellian monads, and not the similar but slightly different, mathematically definition of monads

To build a monad, two main functions are necessary as well as a monadic type. First I'll discuss a monadic type.

Monadic Type

A monad's type can be whatever it needs to be. Perhaps one of the most famous ones in the Haskell world it the Maybe monad, which is defined simply as:

data Maybe a = Nothing | Just a

Maybe is one of the most beautiful aspects of Haskell. It is very similar to null or nil in other languages, but what makes it different is the fact that (as I understand it) in Haskell's pure, functional model, Maybe cannot go unhandled or pop up in unexpected places. In my mind, it is a kind of a neat and precise example of a monadic type.

The return Function

Another thing a monad needs is a return function whose signature looks like:

return :: a -> m a

return is simply a function whose purpose is to construct the monadic type. Pretty simple, eh? So for Maybe, this might be as simple as:

return n = Just n

The Bind Function

The other function needed by a monad, the function that truly brings out the magic, is the bind function which is usually denoted as (>>=) in the Haskell world. In the OOP example above, the bind function is kind of like the periods in between the different calls, but oh so much more magical. Bind's signature looks like:

(>>=) :: m a -> (a -> m b) -> m b

So, let's break this down.

The first thing that bind takes is a monadic type. So, this could be something as simple as Just 5 or whatever monadic type you are operating on. The second parameter is a function that takes the type boxed by the first parameter (the monadic type) and returns a monadic type boxing b (which could be the same type as a but by no means must be). In the end, bind returns another monadic type, as returned by the middle parameter.

All in all, this seems like a lot to swallow, and, uh, what does this have to do with method chaining or our return function?

Remember, bind is really one of those strange infix operators, so if I may make some simplifications, it kind of looks like:

a thing >>= function that returns another thing

In this simplification, "thing" is substituted for "monadic type" to make bind easier to swallow. The point is, all this whole mess does is return another monadic type! So, there's nothing keeping me from implementing another bind operator (or reusing the same one, if applicable) like such:

a thing >>= function that returns another thing >>= function that returns yet another thing ...

See what I mean about this being like the "period between" in that above OOP example? All bind really does is take some value (wrapped in a monad) and apply some function to it, and re-wrap the output!

return is pretty cool because a lot of the time it comes at the end of all the binding (wow, a return at the end? Sounds like some other paradigms out there). return is really the end game, the termination of the "chaining."

Parting Words

In conclusion, I hope I have shed some light on what can be a very difficult topic to understand. If you would like to learn more, the Haskell community has a great article on monads also there are some really awesome answers to the question of "what is a monad" on SO.