# Section 4Conditional Expressions and Functions

## 4.1  Booleans and Relations

Like the arithmetic operations, the test operations can take more than two arguments. For example, `(< 1 2 3)` is legal Scheme notation for ``1 < 2 and 2 < 3.'' The `and` and `or` operators also take any number of arguments. The `not` operation always takes one argument. The `and`, `or`, and `not` operators work on Boolean values only.

## 4.2  Functions that Test Conditions

Exercise Notes

Exercise 3.3.1 The `=` operator works on numbers, only, so trying to test a Boolean function using the pattern

```(= (in-interval-1? 0)
false)
```

will not succeed. If a test is supposed to produce `false`, you can create a test claim using `not`, instead:
```(not (in-interval-1? 0))
```

Of course, if a test is supposed to produce `true`, it needs no wrapper.

## 4.3  Conditionals and Conditional Functions

A `cond` expression must contain a sequence of condition lines, where each line has exactly two parts:

```(cond
...)
```

(We're using square brackets to surround condition-answer pairs. You can use round parentheses if you prefer.) When a poorly-formed `cond` expression is typed into DrScheme, DrScheme highlights the incorrect part of the expression as a syntax error. If an individual condition line is highlighted, then only that line is incorrect. If multiple lines are highlighted, then the parentheses are not balanced in an individual line (so DrScheme thinks that multiple lines are a single line).

Just like an expression in a definition, no extra parentheses can be added around the condition or answer expressions in a `cond`-line. Parentheses cannot be placed around `else`.

Beyond Syntax

The rules concerning the shape of a `cond` expression do not specify the kind of condition expressions that are allowed. In fact, a condition expression must have a Boolean value. For example, according to the syntax for forming a `cond` expression, the following is a legal expression:

```(cond
[1 2])
```

If you enter this expression in DrScheme, DrScheme tentatively accepts the expression, but then checks whether the condition `1` is `true` or `false`. It is neither, so DrScheme highlights the `1` and prints an error message. This is a run-time error.

The following is another legal expression according to the syntax rules:

```(cond
[true 5]
[1 2])
```

In this case, DrScheme evaluates the expression and returns `5`. Although `1` would be an illegal condition value if the second condition is ever tested, DrScheme never tests it since the first condition is always `true`.

When a `cond` expression is evaluated, at least one of the conditions must be `true`. If no condition is `true`, then DrScheme prints the run-time error ``no matching cond case.'' For example, the following expression generates the ``no matching cond clause'' error, since there is only one condition and it is `false`:

```(cond
[false 0])
```

A `cond` expression with an `else` clause never generates the ``no matching case'' error because the `else` clause always matches.

Automatic Parenthesis Correction

When you type an close parenthesis `)` where an open bracket `[` needs to be closed, DrScheme automtically changes `)` to `]` to close the bracket. For example, typing `)` after

```(define (positive? n)
(cond
[(> n 0) true
```

produces `]`, instead of `)`. Similarly, `]` may be automatically converted to `)`. Automatic parenthesis correction is handy, but if it bothers you, turn it off via the Edit|Preferences menu item.

## 4.4  Designing Conditional Functions - no notes

No DrScheme notes for this section.