Syntax in Functions

Pattern matching

This chapter will cover some of Elm’s cool syntactic constructs and we’ll start with pattern matching. Pattern matching consists of specifying patterns to which some data should conform and then checking to see if it does and deconstructing the data according to those patterns.

Many imperative languages (C, C++, Java, etc.) have case syntax and if you’ve ever programmed in them, you probably know what it’s about. It’s about taking a variable and then executing blocks of code for specific values of that variable and then maybe including a catch-all block of code in case the variable has some value for which we didn’t set up a case.

Elm takes that concept and one-ups it. Like the name implies, case expressions are, well, expressions. Not only can we evaluate expressions based on the possible cases of the value of a variable, we can also do pattern matching. This leads to really neat code that’s simple and readable. You can pattern match on any data type — numbers, characters, lists, tuples, etc. Let’s make a really trivial function that checks if the number we supplied to it is a seven or not.

lucky : number -> String
lucky x =
    case x of
        7 -> "LUCKY NUMBER SEVEN!"
        _ -> "Sorry, you're out of luck, pal!"

When you call lucky, the patterns will be checked from top to bottom and when it conforms to a pattern, the corresponding function body will be used. The only way a number can conform to the first pattern here is if it is 7. If it’s not, it falls through to the second pattern, which matches anything and discards it. The _ is a wildcard that’s used when we don’t care what the specific value is. If you do care what the value is, you can write any variable name in this place and the value will be bound to that variable, like this:

lucky : number -> String
lucky x =
    case x of
        7 -> "LUCKY NUMBER SEVEN!"
        n -> "Sorry, you're out of luck, pal! You had " ++ toString n

This function could have also been implemented by using an if statement. But what if we wanted a function that says the numbers from 1 to 5 and says "Not between 1 and 5" for any other number? Without pattern matching, we’d have to make a pretty convoluted if then else tree. However, with it:

sayMe : number -> String
sayMe x = 
    case x of
        1 -> "One!"
        2 -> "Two!"
        3 -> "Three!"
        4 -> "Four!"
        5 -> "Five!"
        _ -> "Not between 1 and 5"

Note that if we moved the last pattern (the catch-all one) to the top, it would always say "Not between 1 and 5", because it would catch all the numbers and they wouldn’t have a chance to fall through and be checked for any other patterns.

We could use pattern matching to define a factorial function recursively, the way it is usually defined in mathematics. We start by saying that the factorial of 0 is 1. Then we state that the factorial of any positive integer is that integer multiplied by the factorial of its predecessor. Here’s how that looks like translated in Elm terms.

factorial : number -> number
factorial n =
    case n of
        0 -> 1
        _ -> n * factorial (n - 1)

This is the first time we’ve defined a function recursively. Recursion is important in functional languages and we’ll take a closer look at it later. But in a nutshell, this is what happens if we try to get the factorial of, say,

1. It tries to compute 3 * factorial 2. The factorial of 2 is 2 * factorial 1, so for now we have 3 * (2 * factorial 1). factorial 1 is 1 * factorial 0, so we have 3 * (2 * (1 * factorial 0)). Now here comes the trick — we’ve defined the factorial of 0 to be just 1 and because it encounters that pattern before the catch-all one, it just returns 1. So the final result is equivalent to 3 * (2 * (1 * 1)). Had we written the second pattern on top of the first one, it would catch all numbers, including 0 and our calculation would never terminate. That’s why order is important when specifying patterns and it’s always best to specify the most specific ones first and then the more general ones later.

Pattern matching must be complete. If we define a function like this:

charName : Char -> String
charName c = 
    case c of
        'a' -> "Albert"
        'b' -> "Broseph"
        'c' -> "Cecil"

The compiler will notice that we haven’t accounted for all possibilites, either by specifying a pattern for every possible value of c, or by including a wildcard that matches on every value. It will say:

This `case` does not have branches for all possibilities.
3|     case c of
4|         'a' -> "Albert"
5|         'b' -> "Broseph"
6|         'c' -> "Cecil"

You need to account for the following values:

    <values besides 'a', 'b', and 'c'>

Add a branch to cover this pattern!

It complains that we have missing patterns, and rightfully so. When making patterns, we should always include a catch-all pattern so that our program doesn’t crash if we get some unexpected input. Features like this are why Elm can all but guarantee no runtime errors in your code.

As you can see, the syntax for case expressions is pretty simple:

case expression of 
    pattern -> result
    pattern -> result
    pattern -> result
    ...

expression is matched against the patterns. The pattern matching action is the same as expected: the first pattern that matches the expression is used. If it falls through the whole case expression and no suitable pattern is found, a compilation error occurs.

Pattern matching can also be used in the declared parameters of functions, and on tuples. What if we wanted to make a function that takes two vectors in a 2D space (that are in the form of pairs) and adds them together? To add together two vectors, we add their x components separately and then their y components separately. Here’s how we would have done it if we didn’t know about pattern matching:

addVectors : (Float, Float) -> (Float, Float) -> (Float, Float)
addVectors a b = 
    (Tuple.first a + Tuple.first b, Tuple.second a + Tuple.second b)

Well, that works, but there’s a better way to do it. Let’s modify the function so that it uses pattern matching.

addVectors : (Float, Float) -> (Float, Float) -> (Float, Float)
addVectors (x1, y1) (x2, y2) = 
    (x1 + x2, y1 + y2)

There we go! Much better. Note that this is already a catch-all pattern. The type of addVectors (in both cases) is addVectors : (Float, Float) -> (Float, Float) - > (Float, Float), so we are guaranteed to get two pairs as parameters.

first and second extract the components of pairs. But what about triples? Well, there are no provided functions that do that but we can make our own.

first : (a, b, c) -> a
first (x, _, _) = x

second : (a, b, c) -> b
second (_, y, _) = y

third : (a, b, c) -> c
third (_, _, z) = z

As a reminder, the _ means that we really don’t care what that part is, so we just write a _.

Lists themselves can also be used in pattern matching. You can match with the empty list [] or any pattern that involves :: and the empty list. But since [1,2,3] is just syntactic sugar for 1::2::3::[], you can also use the former pattern. A pattern like x::xs will bind the head of the list to x and the rest of it to xs, even if there’s only one element so xs ends up being an empty list.

Note: The x::xs pattern is used a lot, especially with recursive functions. But patterns that have :: in them only match against lists of length 1 or more.

Note: xs is not some special “pattern matching” variable. It’s just like any other variable. x::y would bind the head of the list to x and the rest of it to y. The s on the end is just used by convention.

If you want to bind, say, the first three elements to variables and the rest of the list to another variable, you can use something like x::y::z::zs. It will only match against lists that have three elements or more.

Now that we know how to pattern match against list, let’s make our own implementation of the List.member function, which checks if a value is present in a list, using

member : a -> List a -> Bool
member value list =
    case list of
        [] -> False
        (x::xs) ->
            if x == value then
                True
            else 
                member value xs

Checking if it works:

toPrint = member 1 [1,2,3,4]
True
toPrint = member 1 [2,3,4,5]
False

Nice! Notice that if you want to bind to several variables (even if one of them is just _ and doesn’t actually bind at all), we have to surround them in parentheses. Also notice the if then else expression we used. It’s very similar to if statements in other languages, except it’s an expression instead of a statement. That means it evaluates to a specific value, so we can’t ignore the else.

Let’s make a trivial function that tells us some of the first elements of the list in (in)convenient English form.

tell : List a -> String
tell list =
    case list of
        [] -> "The list is empty"
        (x::[]) -> "The list has one element: " ++ toString x
        (x::y::[]) -> "The list has two elements: " ++ toString x ++ " and " ++ toString y
        (x::y::_) -> "This list is long. The first two elements are: " ++ toString x ++ " and " ++ toString y

This function is safe because it takes care of the empty list, a singleton list, a list with two elements and a list with more than two elements. Note that (x::[]) and (x::y::[]) could be rewriten as [x] and [x,y] (because its syntatic sugar, we don’t need the parentheses). We can’t rewrite (x::y::_) with square brackets because it matches any list of length 2 or more.

This type of function construction is very common in Elm. Let’s get some more practice by using pattern matching and a little recursion to implement our own List.length function:

length : List a -> Int
length list =
    case list of
        [] -> 0
        (_::xs) -> 1 + length xs

This is similar to the factorial and member functions we wrote earlier. First we defined the result of a known input — the empty list. This is also known as the edge condition. Then in the second pattern we take the list apart by splitting it into a head and a tail. We say that the length is equal to 1 plus the length of the tail. We use _ to match the head because we don’t actually care what it is. Also note that we’ve taken care of all possible patterns of a list. The first pattern matches an empty list and the second one matches anything that isn’t an empty list.

Let’s see what happens if we call length on ['h','a','m']. First, it will check if it’s an empty list. Because it isn’t, it falls through to the second pattern. It matches on the second pattern and there it says that the length is 1 + length ['a','m'], because we broke it into a head and a tail and discarded the head. O-kay. The length of ['a','m'] is, similarly, 1 + length ['m']. So right now we have 1 + (1 + length ['m']). length ['m'] is 1 + length []. And we’ve defined length [] to be 0. So in the end we have 1 + (1 + (1 + 0)).

Let’s implement List.sum. We know that the sum of an empty list is 0. We write that down as a pattern. And we also know that the sum of a list is the head plus the sum of the rest of the list. So if we write that down, we get:

sum : List number -> number
sum list =
    case list of
        [] -> 0
        (x::xs) -> x + sum xs

One more thing — you can’t use ++ in pattern matches. If you tried to pattern match against (xs ++ ys), what would be in the first and what would be in the second list? It doesn’t make much sense. It would make sense to match stuff against (xs ++ [x,y,z]) or just (xs ++ [x]), but because of the nature of lists, you can’t do that.

Let it be

Let bindings let you bind to variables anywhere and are expressions themselves, so they are very useful for naming the results of more complicated expressions. Just like any construct in Elm that is used to bind values to names, let bindings can be used for pattern matching. Let’s see them in action! This is how we could define a function that gives us a cylinder’s surface area based on its height and radius:

cylinder : Float -> Float -> Float
cylinder r h =
    let 
        sideArea = 2 * pi * r * h
        topArea = pi * r ^2
    in  
        sideArea + 2 * topArea

The form is let <bindings> in <expression>. The names that you define in the let part are accessible to the expression after the in part. Notice that the names are also aligned in a single column.

Let bindings are expressions themselves. Remember when we did the if statement and it was explained that an if then else statement is an expression? That means you can cram it in almost anywhere.

toPrint = [if 5 > 3 then "Woo" else "Boo", if 'a' > 'b' then "Foo" else "Bar"]
["Woo", "Bar"]
toPrint = 4 * (if 10 > 5 then 10 else 0) + 2
42

You can also do that with let bindings.

toPrint = 4 * (let a = 9 in a + 1) + 2
42

They can also be used to introduce functions in a local scope:

toPrint = [let square x = x * x in (square 5, square 3, square 2)]
[(25,9,4)]

Like we said before, you can pattern match with let bindings. They’re very useful for quickly dismantling a tuple into components and binding them to names and such.

toPrint = (let (a,b,c) = (1,2,3) in a+b+c) * 100
600