# Hello, monad!

# Intro

In this chapter we’re going to write a hello world program. Doing so in Haskell requires monads, a concept from category theory. You might think this is overly complicated for something as simple as printing some output, but you’d be wrong, printing output is not simple at all. Just think about buffers, encoding, concurrency… If you judge a language by the ease with which you can write helloworld, you’re going to pick a language that hides important “details”.

We’re first going to look at pure functions, i.e. functions without any side-effects, and their types. Purity is the default in Haskell, but does not allow writing output, which is a (side) effect.

We will then cover the IO monad, which is how Haskell handles necessary effects. This will allow us to finally write helloworld.

This chapter is probably the hardest part of this tutorial and what makes it *for madmen*.

# Pure functions

In essence, every function in Haskell has exactly 1 input and 1 output. We can still use “multiple” inputs by making that output itself a function. Let’s look at how this works with addition:

`+) 3 7 (`

Writing two values separated by a space is function application, `f a`

is applying argument `a`

to function `f`

.

Function application in Haskell is left-associative, so the code above is equivalent to:

`+) 3) 7 ((`

Here, we have a function `(+)`

, to which we apply `3`

. The result is a new function that takes a number and adds 3 to it. To this new function we then apply `7`

.

Now it’s time to talk about types. As mentioned, a function only has one input and one output, and we type it using an arrow. A function that takes some type `a`

as input and outputs some `b`

has type `a -> b`

. Consequently, a function that takes an `a`

and produces a second function with type `b -> c`

, has type `a -> (b -> c)`

. For our function `(+)`

, that means the type must be:

`(+) :: Int -> (Int -> Int)`

*(Note: in Haskell,* `::`

*indicates a type declaration)*

Since arrows in type declarations are right-associative, the parentheses are superfluous in this case, and we can also write:

`(+) :: Int -> Int -> Int`

Because we know functions cannot have side-effects, the type declaration tells us pretty much exactly what the function is going to do: it will compute an `Int`

given two other `Int`

s. Nothing else will happen, and it won’t matter when we evaluate this function.

We don’t have to apply all arguments at once. The following is perfectly valid:

```
add3 :: Int -> Int
= (+) 3
add3
ten :: Int
= add3 7 ten
```

The `(+)`

function is a bit special. Using symbols in parentheses as a function names turns it into an infix operator. We can therefore also write a much more natural looking sum:

```
ten :: Int
= 3 + 7 ten
```

Finally, a note about lazy evaluation. In the above examples, `ten`

does not have the value `10`

, rather it is an expression that will result in the value `10`

. Thanks to referential transparency, the compiler can decide not to compute the value of `ten`

right away, but just pass (a reference to) its body (`3 + 7`

) and postpone evaluation to whenever it’s actually needed. Not only does this let us avoid unnecessary computations, but it also lets us use infinite data structures. An example:

```
infiniteListOf1s :: [Int]
= 1 : infiniteListOf1s infiniteListOf1s
```

*(Note:* `:`

*is a “prepend” operator with type* `a -> [a] -> [a]`

*, e.g.* `1 : [2,3]`

*=* `[1, 2, 3]`

*)*

This list is infinite! Because Haskell is non-strict, this is fine. The compiler will make sure we only compute the part of the list we actually need by using lazy evaluation. So as long as we don’t try to *read* the whole list, it won’t enter an infinite loop.

# Effects

Let us now, armed with the above knowledge, look at the project generated by the command `stack new`

.

In `app/Main.hs`

we find the following:

```
module Main where
import Lib
main :: IO ()
= someFunc main
```

This should confuse you. So let’s look at the individual parts.

`module Main where`

declares the name of the module. “Main” is a special name, as you probably expect.

`import Lib`

imports the Lib module and *adds all the symbols Lib exports to the current namespace*. This includes

`someFunc`

, but we can’t tell from the import statement, we will be changing this line to something more informative in a bit.`main :: IO ()`

declares that the type of the value called `main`

is `IO ()`

. This would quite rightly confuse you about now. Why isn’t this a function? What are these mysterious parentheses? What is an `IO`

?

Why isn’t `main`

a function? As mentioned, functions compute one value from another, but this isn’t really the nature of computer programs. Rather, we want a program that does stuff, whereas a function is just an inert formula. `main`

should be a list of actions / effects, such as writing to stdout or listening for http requests.

Then what is `()`

? This is a special type called *unit*. Every type has one or more *inhabitants*, a boolean has inhabitants `True`

and `False`

, an unsigned 8-bit integer is inhabited by numbers \(0\) through \(2^8\). Unit has only 1 inhabitant, the unit. This entails that a value with type unit carries no information. Having a pure function that outputs a unit would be pointless, because we could simply substitute the answer without ever needing to evaluate said function. However, the unit type acts a lot like the number 1, and has a lot of uses when combined with other types. One of those is as used here. Both the type and the inhabitant of unit are written as `()`

in Haskell.

`IO`

, if you’re particularly observant, you may have noticed we seem to have applied it just like a function, but in the type declaration. Just like values have types, types have kinds. The kind of `Int`

, `()`

, `String`

, `Char`

, etc. is `*`

, the kind of `IO`

is `* -> *`

. Just as with function application, the kind of `IO ()`

, that is `()`

applied to `IO`

, is therefore `*`

. As for the “meaning” of `IO`

, it turns a type that is computed with pure functions, into one that is computed using effects. We will see how to use impure functions in a bit.

Putting all that together, `main`

, by its type `IO ()`

is a unit computed using side effects. Since `()`

contains no information, `IO ()`

is just a series of effects / instructions “without” output. That is pretty much what we generally look for in a program!

# Fixing the import statement

After all that stuff about the type of `main`

, we turn to look at the next line, the *term* of main: `main = someFunc`

. This is rather disappointing, as it merely references a single other value. `someFunc`

is exported by the `Lib`

module. We pretty much have to guess that, because with the current import notation, it is not explicit. This becomes a problem once you have more modules. So let’s get ahead of ourselves and change that import to the following:

`import Lib (someFunc)`

this will expose *only* `someFunc`

from `Lib`

, and tells us exactly where symbols are coming from. We can also make the import qualified, which forces us to mention the module name explicitly:

```
import qualified Lib
= Lib.someFunc main
```

plus it’s totally valid to do both:

```
import qualified Lib
import Lib (someFunc)
```

Which will expose `someFunc`

, but allows you to access other symbols through the explicit notation from above.

# Combining effects with monads

Now it’s time to look at what is happening in `someFunc`

. But where can we find the `Lib`

module that defines it? If you haven’t changed anything, it should be `src/Lib.hs`

(modules names must match relative path names). You can change which directory are part of your project in `package.yaml`

.

The file should look like this:

```
module Lib
( someFuncwhere
)
someFunc :: IO ()
= putStrLn "someFunc" someFunc
```

We’ve seen the module declaration before. This one also specifies which symbols to export, `someFunc`

in this case.

`someFunc`

is apparently defined as the application of the `String`

`"someFunc"`

applied to `putStrLn`

. `putStrLn`

is part of the standard *prelude*, which is implicitly imported in every file. It’s type is `String -> IO ()`

and, as you might expect, what it does is write a string to stdout (without flushing buffers).

But how can we have multiple effects? Is there some function with type `IO () -> IO () -> IO ()`

that combines the effects in both arguments and that we have to tediously add everywhere? Well, such a function exists but there’s better ways to go about it.

As we’ve seen, `IO`

has kind `* -> *`

. When a type of kind `* -> *`

follows certain rules, we say that it is a monad. In particular, for any monad `m`

, the following functions must exist:

```
return :: a -> m a
fmap :: (a -> b) -> m a -> m b
(>>=) :: m a -> (a -> m b) -> m b
```

`IO`

is a monad. Substituting `IO`

for `m`

, we know that we have at least the following functions:

```
return :: a -> IO a
fmap :: (a -> b) -> IO a -> IO b
(>>=) :: IO a -> (a -> IO b) -> IO b
```

`return`

simply pretends a pure computation is impure. Similarly, `fmap`

turns a function over pure values into one over impure values. If, for instance, we read some input string, that string has type `IO String`

, but our pure functions only work for `String`

! `fmap`

remedies that problem by *lifting* functions to IO. `(>>=)`

is a bit more complicated. You can think of it a bit like unix pipes. It takes some impurely computed value, and feeds that value to the next impure computation.

Let’s look at a few examples, take the time to let this sink in:

```
computeHelloWorld :: IO String
= return "Hello, World!"
computeHelloWorld
computeHelloWorldLength :: IO Int
= fmap length computeHelloWorld
computeHelloWorldLength
greetTheWorld :: IO ()
= computeHelloWorld >>= putStrLn greetTheWorld
```

(`putStrLn`

is the output-writing function with type `String -> IO ()`

)

For a slightly more useful example we’ll use `getLine`

from the prelude. It has type `IO String`

and will get a line from stdin. We can now do:

```
nameToGreeting :: String -> String
= "Hello " ++ name ++ ", I am monad."
nameToGreeting name
greetPerson :: IO ()
=
greetPerson fmap nameToGreeting getLine >>= putStrLn
```

This is not very easy to read, and it would get a lot worse if we were to also write to stdout before reading from stdin. Luckily, Haskell has some syntactic sugar for monads in the form of do-blocks.

```
greetPerson :: IO ()
=
greetPerson do
putStrLn "I am monad, what is your name?"
<- getLine
personName putStrLn ("Hello, " ++ personName ++ "! What shall we *do* together?")
```

The type of a do-block will be the type of its last element.

## Side-note

Suppose we have the type `IO (IO a)`

. By `(>>=)`

, we know that it is equivalent to `IO ()`

. Because for any `foo :: IO (IO a)`

we can do `bar = foo >>= id`

, resulting in a `bar :: IO a`

. But by `return bar`

we get `foo`

again! In other words, it doesn’t matter how often you apply a monad to a type, it will be equivalent (technically, *isomorphic*) to a single application of that monad. This is what the famous phrase “monads are just monoids in the category of endofunctors” means (sort-of). A monoid being something that stays the same (type) under repeated application of a certain operation.

# Conclusion

You’ve learned how effects can be represented in a functionally pure language by using monads. It is usually better to avoid using `IO`

monads when possible. Trivially, we could write our entire program using monads, but we would lose many advantages of programming in Haskell.

I would personally argue that an IO monad is not a good way to represent effects, but it’s the current standard for generic functionally pure programming languages. Some interesting alternatives include uniqueness types (used in Clean), free monads (Haskell) and model-update systems (Elm).

You’ve also been introduced to lazy evaluation. There are both advantages and disadvantages to it, but that is outside the scope of this chapter.