# Case

The basic syntax of case expressions looks like this:

```
\case e_1, ... e_n \with {
| p_1^1, ... p_n^1 => d_1
...
| p_1^k, ... p_n^k => d_k
}
```

where e_1, … e_n and d_1, … d_k are expressions and p_1^1, … p_n^k are patterns. Such an expression reduces in the same way as functions defined by pattern matching (see Functions). If the typechecker does not know the type of a case expression, it must be specified explicitly:

`\case e_1, ... e_n \return T \with { ... }`

The general syntax of case expressions looks like this:

`\case e_1 \as x_1 : E_1, ... e_n \as x_n : E_n \return T \with { ... }`

where x_1, … x_n are variables and E_1, … E_n are expressions. The parts \as x_i and : E_i can be omitted. Expressions E_i can refer to x_1, … x_{i-1} and expression T can refer to x_1, … x_n. In this case, e_i must have type E_i[e_1/x_1, … e_{i-1}/x_{i-1}]. The type of the case expression is T[e_1/x_1, … e_n/x_n].

## \scase

Expression \scase is related to \case in the same way as \sfunc is related to \func. That is, expressions of the form \scase e_1, … e_n \with { … } never evaluate. To evaluate such an expression, you need to use keyword \eval before it. Similarly, \peval \scase e_1, … e_n \with { … } has type \scase e_1, … e_n \with { … } = \eval \scase e_1, … e_n \with { … }.

## \elim in \case

If one of the expressions e_1, … e_n is a variable, keyword \elim can be specified before it. This variable will be evaluated from the context in the clauses. More importantly, it will be substituted in the types of other arguments and the result type of the case expression. Thus, the following two snippets are equivalent if e : E and the result type of the case expression is A.

```
\case \elim x, e \with {
| pat, pat' => result
}
```

```
\case x \as x, e : E \return A \with {
| pat, pat' => result
}
```