Case expressions

We can use “case expressions” to choose among multiple alternatives.

Basic case expressions with conditions

The basic form of a case expression is as follows:

{? alternative1   if  condition1,
   alternative2   if  condition2,
   alternativeN   otherwise

This will try each condition, starting with the first, until finding the first condition that is true. Then the value of the entire case expression will be equal to the corresponding alternative. The otherwise case will always be chosen if it is reached. Each condition must be an expression of type Bool; the alternatives can have any type (though they must all have the same type, whatever it is).

For example, consider the definition of the caseExample function below:

caseExample : N -> N
caseExample(n) =
  {? n + 2    if n < 10 \/ n > 20,
     0        if n == 13,
     77n^3    if n == 23,
     n^2      otherwise

Here are a few sample inputs and outputs for caseExample, with an explanation of each:

  • caseExample(5) == 7: the first condition is true (since 5 < 10), so the result is 5 + 2.
  • caseExample(23) == 25: the first condition is again true (since 23 > 20), so the result is 23 + 2. Note that the first true condition is always chosen, so it does not matter that the later condition n == 23 would also be true.
  • caseExample(13) == 0: the first condition is false (13 is neither < 10 nor > 20, but the second condition (13 == 13) is true.
  • caseExample(12) == 144: the first three conditions are all false, so the otherwise case is used, with the result 12^2.

If none of the conditions in a case expression are true, it is an error: see Value did not match any of the branches in a case expression.

Case expressions with conditions and patterns

More generally, case expressions can use pattern matching in addition to Boolean conditions, and each alternative in a case expression can have multiple conditions. The most general form of a case expression is as follows:

{? alternative1   guard11 guard12 ...,
   alternative2   guard21 guard22 ...,

where each guard has one of two forms:

  • if <condition>. This guard succeeds if the condition is true.
  • if <expression> is <pattern>. This guard succeeds if the given expression matches the pattern; furthermore, any variables in the pattern will be defined locally within the corresponding alternative as well as any subsequent guards in the same clause.

The keyword when can also be used as a synonym for if.