Pattern matching

Pattern matching is a language feature that makes it easy to both test and decompose structured data into its constituent parts. While most programming languages provide familiar ways to build structured data, pattern matching enables you to take apart structured data and bring its fragments into scope by binding them to the names you specify. Syntactically, the patterns resemble the construction of structured data, but generally appear in input-direction positions, such as in function argument positions, after the case keyword in switch expressions, and after let or var declarations.

Consider the following function call:

let name : Text = fullName({ first = "Jane"; mid = "M"; last = "Doe" });

This code constructs a record with three fields and passes it to the function fullName. The result of the call is named and brought into scope by binding it to the identifier name. The last, binding step is called pattern matching, and name : Text is one of the simplest forms of pattern. For instance, in the following implementation of the callee:

func fullName({ first : Text; mid : Text; last : Text }) : Text {  first # " " # mid # " " # last};

The input is an (anonymous) object, which is destructured into its three Text fields, whose values are bound to the identifiers first, mid and last. They can be freely used in the block that forms the body of the function. Above we have resorted to name punning (a form of aliasing) for object field patterns, using the name of a field to also name its contents. A more general form of field pattern allows the content to be named separately from the field, as in …​; mid = m : Text; …​. Here mid determines which field to match, and m names the content of that field within the scope of the pattern.

You can also use pattern matching to declare literal patterns, which look just like literal constants. Literal patterns are especially useful in switch expressions because they can cause the current pattern match to fail, and thus start to match the next pattern. For example:

switch ("Adrienne", #female) {  case (name, #female) { name # " is a girl!" };  case (name, #male) { name # " is a boy!" };  case (name, _) { name # ", is a human!" };}
1. will match the first case clause (because binding to the identifier name cannot fail and the shorthand variant literal #Female compares as equal), and evaluate to "Adrienne is a girl!". The last clause showcases the wildcard pattern _. It cannot fail, but won’t bind any identifier.

The last kind of pattern is the or pattern. As its name suggests, these are two or more patterns that are separated by the keyword or. Each of the sub-patterns must bind to the same set of identifiers, and is matched from left-to-right. An or pattern fails when its rightmost sub-pattern fails.

pattern kindexample(s)contextcan failremarks
literalnull, 42, (), "Hi"everywherewhen the type has more than one value
namedage, xeverywherenointroduces identifiers into a new scope
wildcard_everywhereno
typedage : Nateverywhereconditional
option?0, ?valeverywhereyes
tuple( component0, component1, …​ )everywhereconditionalmust have at least two components
object{ fieldA; fieldB; …​ }everywhereconditionalallowed to mention a subset of fields
fieldage, count = 0objectconditionalage is short for age = age
variant#celsius deg, #sundayeverywhereyes#sunday is short form for #sunday ()
alternative (or-pattern)0 or 1everywheredependsno alternative may bind an identifier

The following table summarises the different ways of pattern matching.

Since pattern matching has a rich history and interesting mechanics, a few additional comments are justified.

terminology
The (usually structured) expression that is being matched is frequently called the scrutinee and the patterns appearing behind the keyword case are the alternatives. When every possible scrutinee is matched by (at least one) alternative, then we say that the scrutinee is covered. The patterns are tried in top-down fashion and thus in case of overlapping patterns the one higher-up is selected. An alternative is considered dead (or inactive), if for every value that it matches there is higher-up alternative that is also matched.

booleans
The data type Bool can be regarded as two disjointed altenatives (true and false) and Motoko’s built-in if construct will eliminate the data and turn it into control flow. if expressions are a form of pattern matching that abbreviates the general switch expression for the special case of boolean scrutinees.

variant patterns
Motoko’s variant types are a form of disjoint union (sometimes also called a sum type). A value of variant type always has exactly one discriminator and a payload which can vary from discriminator to discriminator. When matching a variant pattern with a variant value, the discriminators must be the same (in order to select the alternative) and if so, the payload gets exposed for further matching.

enumerated types
Other programming languages — for example C, but not Motoko — often use a keyword enum to introduce enumerations. These are impoverished relatives of Motoko’s variant types, as the alternatives are not allowed to carry any payload. Correspondingly, in those languages the switch-like statements lack the full power of pattern matching. Motoko provides the short-hand syntax (as in type Weekday = { #mon; #tue; …​ }) to define basic enumerations, for which no payloads are required.

error handling
Error handling can be considered a use-case for pattern matching. When a function returns a value that has an alternative for success and one for failure (for example, an option value or a variant), pattern matching can be used to distinguish between the two as discussed in Error handling.

irrefutable matching
Some types contain just a single value. We call these singleton types. Examples of these are the unit type (also known as an empty tuple) or tuples of singleton types. Variants with a single tag and no (or singleton-typed) payload are singleton types too. Pattern matching on singleton types is particularly straightforward, as it only has one possible outcome: a successful match.

exhaustiveness (coverage) checking
When a pattern check alternative has the potential to fail, then it becomes important to find out whether the whole switch expression can fail. If this can happen the execution of the program can trap for certain inputs, posing an operational threat. To this end, the compiler checks for the exhaustiveness of pattern matching by keeping track of the covered shape of the scrutinee. The compiler issues a warning for any non-covered scrutinees (Motoko even constructs a helpful example of a scrutinee that is not matched). A useful by-product of the exhaustiveness check is that it identifies and warns about dead alternatives that can never be matched.

In summary, pattern checking is a great tool with several use-cases. By statically analyzing patterns, the compiler assists the programmer by pointing out unhandled cases and unreachable code, both of which often indicate programmer error. The static, compile-time nature of coverage checking reliably rules out runtime failures.