What is 'Pattern Matching' in functional languages?

Question

I\'m reading about functional programming and I\'ve noticed that Pattern Matching is mentioned in many articles as one of the core features of functional languages.

Answer 1

Short answer: Pattern matching arises because functional languages treat the equals sign as an assertion of equivalence instead of assignment.

Long answer: Pattern matching is a form of dispatch based on the “shape” of the value that it's given. In a functional language, the datatypes that you define are usually what are known as discriminated unions or algebraic data types. For instance, what's a (linked) list? A linked list List of things of some type a is either the empty list Nil or some element of type a Consed onto a List a (a list of as). In Haskell (the functional language I'm most familiar with), we write this

data List a = Nil
            | Cons a (List a)

All discriminated unions are defined this way: a single type has a fixed number of different ways to create it; the creators, like Nil and Cons here, are called constructors. This means that a value of the type List a could have been created with two different constructors—it could have two different shapes. So suppose we want to write a head function to get the first element of the list. In Haskell, we would write this as

-- `head` is a function from a `List a` to an `a`.
head :: List a -> a
-- An empty list has no first item, so we raise an error.
head Nil        = error "empty list"
-- If we are given a `Cons`, we only want the first part; that's the list's head.
head (Cons h _) = h

Since List a values can be of two different kinds, we need to handle each one separately; this is the pattern matching. In head x, if x matches the pattern Nil, then we run the first case; if it matches the pattern Cons h _, we run the second.

Short answer, explained: I think one of the best ways to think about this behavior is by changing how you think of the equals sign. In the curly-bracket languages, by and large, = denotes assignment: a = b means “make a into b.” In a lot of functional languages, however, = denotes an assertion of equality: let Cons a (Cons b Nil) = frob x asserts that the thing on the left, Cons a (Cons b Nil), is equivalent to the thing on the right, frob x; in addition, all variables used on the left become visible. This is also what's happening with function arguments: we assert that the first argument looks like Nil, and if it doesn't, we keep checking.