The reply by louthy is great, but it doesn't answer your first question:
> What is referential transparency?
A function reference that can be replaced at all call sites in a program with its body with all of the references to its arguments replaced with references to the call site arguments without the observable behavior of the program changing is referentially transparent.
In practice, it means that you can safely refactor lines of code into a function reference without worrying about breaking your program.
It is trivial to ensure that a function that does no side effects, like `addTwoNumbers(a, b)` is referentially transperent, and we do it all the time, and we have very little trouble reasoning about what functions like that will behave like at runtime, so we do it as much as possible anyway. We call it things like "single responsibility principle" and KISS, and it leads to more maintainable programs.
However, it isn't as easy to do with a function like `printStringLine(aMessage)` or `divideTwoNumbers(a, b)`. Obviously, if you move your print statements and the state of a program changes, you'll get different output depending on where you moved them to. And the behavior of divideTwoNumbers when the dividend is 0 is problematic. As is making a network call --> depending on when it is called, you might get a different answer. All of those things are things the programmer has little to no control over.
The monad interface provides a way to make those things referentially transparent, often storing the transformations made in a sequence of bind calls in a data structure, then interpreting that data structure via a method called `unsafeRun`. Since the return of bind is now a data structure containing the transformations to be applied, it is possible to test that the network calls, console output, and error raising and throwing logic outputs in the correct order by substituting a "logging" implementation of the monad in tests rather than an "executing" monad in tests. Then you can test the "executing" monad by sequencing two operations that produce output and checking that that output matches your expectations, rather than checking that all of the network calls in your application actually work at test time.
Additionally, since we can usually unit test our non-side-effecting functions easily, using a monad method is a type-safe, code-level indicator in code that "trouble out of our control at runtime may happen HERE." So if you have trouble, and you are making a network call in your bind/flatMap, you know where to look: in your NetworkCallMonad implementation.
Referential transparency allows us to reason about a program's behavior by just looking at the body of the function, rather than anything else around it. It's the ultimate form of encapsulation, and has the same benefits. So, now that we have a way to define referentially transparent side effects that encapsulate problems that can only happen when the stars align incorrectly, we can reason locally and test locally around all the things in the program, which means the program is simpler to reason about.
There are some consequences, though. ANY 2 Monads won't compose. List>.bind((i) => i + 1) won't compile, or work. You need a MonadListTransformer that knows which order the monads are composed (Does Option contain lists, or does the list contain options?) in order to do the extraction and flattening in the correct order. Of course, this adds runtime execution overhead, and in the case of two nested monads is not too difficult to acheive.
But often, when you encode a program's effects into monads, you end up with monstrosities: >>>>. That can get to be a mouthful, and our simple little bind definition is now several layers deep. All that means is that you need to add some methods to your Monad interface, and give them new names, so that you have a type that is a Monad and a IO and a Monoid and a ApplicativeError. Those may sound like gobbledygook names, but they are the names chosen by mathemeticians and the FP community, so to Google them you have to use the names.
Monads, and `TypeClasses` are not the only way to achieve RT programs, but they are pretty widespread, well-defined, well-tested, and well-documented interfaces that will work. In languages without higher-kinded-generics (Generics that can hold other generics), you can simulate them in any language with generics using `Box` and `Unbox` -- typescript does this in its fp lib, for example -- so that you can still get the code reuse out of defining simple instances that can be derived from things higher in the dependency tree.
Anyway, they have value for simplifying programs, but all of their value is derived by maintaining referential transparency throughout the entire codebase as much as possible, and by staying within a context unless there is a safe way to exit the monadic context (This is called a `Comonad` -- at allows you to get a value out of a Monad without risking behavioral changes in your application, and not all `Monads` have a corresponding `Comonad`) until the very last line of your main file. Organizing many custom monadic effects is a common concern, and a really good solution for that is to use a single monadic type that can handle all of your effect needs -- like the IO monad in haskell -- and using the good `ol interpreter pattern to implement methods that delegate to the one base monad to do their effectful work. This is called tagless final style.
One consequence is that you do a lot of wrapping and unwrapping in your code with monads. It gets tedious to call the same constructor over and over again. Haskell, and other languages with extension methods, make this easier by automatically lifting call sites into the currently used Monad context type implicitly. Otherwise, you have to call
new Monad(new Monad(new MyNetworkCall("myApiAddress")).map((networkCaller) => networkCaller.callGet(1))).flatMap((result) => new MyNetworkCall("myOtherApiAddress").map((netWorkCaller) => networkCaller.post(result.user)))
a lot, which is safe, but tedious to write and read. If you have to do this because of language limitations, refactor and extract as much as possible so that your code is readable AND safe.
Obviously, if your language or a library in your language doesn't define the standard typeclasses, of which Monad is only one interface, defining them and using them can be a real pain. Using them is kind of like using any framework --> trivial programs that are small should not use monads unless screwing up at runtime is VERY expensive. A lot of business applications are neither small nor trivial, and screwing up can have dire consequences, so a lot of programs can benefit from this level of encapsulation. It's just another tool, a proven (in the mathematical sense) tool, in your toolbox that can help code quality. Referential transparency isn't a magic silver bullet or a panacea. You still have to think.
> I'm not sure I follow. Is this like saying I have a function:
> let myFunc = (arg1: SomeType): NewType => {}
Not quite.
let myFunc = (arg1: SomeType): SomeType => {}
The `SomeType` wrapping the `A` is returned as a new instance of `SomeType` that now contains a `B` and not an `A`. The argument `arg1` is not mutated. The `A` it holds is extracted, transformed through user code into a `B`, and then placed back within a new instance of `SomeType`.
This obviously happens a lot in any language with generics. Like, all the time. And, every generic will implement the way it does the extraction differently, but the transformation always gets applied to the extracted value(s) in the same way, by calling the user function on the extracted value(s), then ensuring that if multiple instances are created (because multiple values were extracted) that only one instance of the generic that contains all the transformed values is returned.
Here's a simple example of it in use:
let getCharsFromStrings(strings: List): List = bind(strings)((s: String) => s.map((c:Char) => c)))
getCharsFromStrings(List("one","two")) // outputs List('o','n','e','t','w','o')
Since each string is broken into a list of its characters, you might have expected the return to be a list of two lists of characters. A Monad does the flattening for you. In fact, in some languages it is called `flatMap`, because it applies you function to each element that is extracted and flattens the nested structure by one level, turning your list of lists of chars into a list of chars via concatenation.