Conditional expressions are evaluated as follows. The predicate $\langle p_1 \rangle$ is evaluated first. If its value is false, then $\langle p_2 \rangle$ is evaluated. If $\langle p_2 \rangle$'s value is also false, then $\langle p_3 \rangle$ is evaluated. This process continues until a predicate is found whose value is true, in which case the interpreter returns the value of the corresponding consequent expression $\langle e \rangle$ of the clause as the value of the conditional expression. If none of the $\langle p \rangle$'s is found to be true, the value of the cond is undefined.

To evaluate a conditional expression, the interpreter starts by evaluating the $predicate$ of the expression. If the $predicate$ evaluates to true, the interpreter evaluates the $consequent$-$expression$ and returns its value as the value of the conditional. If the $predicate$ evaluates to false, it evaluates the $alternative$-$expression$ and returns its value as the value of the conditional.[3]

The word predicate is used for procedures that return true or false, as well as for expressions that evaluate to true or false. The absolute-value procedure abs makes use of the primitive predicates >, <, and =.[4] These take two numbers as arguments and test whether the first number is, respectively, greater than, less than, or equal to the second number, returning true or false accordingly.

The word predicate is used for operators and functions that return true or false, as well as for expressions that evaluate to true or false. The absolute-value function abs makes use of the primitive predicate >=, an operator that takes two numbers as arguments and tests whether the first number is greater than or equal to the second number, returning true or false accordingly.

Another way to write the absolute-value procedure is (define (abs x) (cond ((< x 0) (- x)) (else x))) which could be expressed in English as If $x$ is less than zero return $- x$; otherwise return $x$. Else is a special symbol that can be used in place of the $\langle p \rangle$ in the final clause of a cond. This causes the cond to return as its value the value of the corresponding $\langle e \rangle$ whenever all previous clauses have been bypassed. In fact, any expression that always evaluates to a true value could be used as the $\langle p \rangle$ here.

Here is yet another way to write the absolute-value procedure: (define (abs x) (if (< x 0) (- x) x)) This uses the special form if, a restricted type of conditional that can be used when there are precisely two cases in the case analysis. The general form of an if expression is (if $\langle \textit{predicate} \rangle$ $\langle \textit{consequent}\rangle$ $\langle \textit{alternative}\rangle$) To evaluate an if expression, the interpreter starts by evaluating the $\langle \textit{predicate}\rangle$ part of the expression. If the $\langle \textit{predicate}\rangle$ evaluates to a true value, the interpreter then evaluates the $\langle \textit{consequent}\rangle$ and returns its value. Otherwise it evaluates the $\langle \textit{alternative}\rangle$ and returns its value.[5]

If we prefer to handle the zero case separately, we can specify the function that computes the absolute value of a number by writing \[\begin{array}{lll} |x| &=& \left\{ \begin{array}{rl} x & \mbox{if $x > 0$} \\ 0 & \mbox{if $x = 0$} \\ -x & \mbox{otherwise} \end{array} \right. \end{array}\] In Python, we express a case analysis with multiple cases by nesting conditional expressions as alternative expressions inside other conditional expressions: def abs(x): return x if x > 0 else 0 if x == 0 else - x Parentheses are not needed around the alternative expression 0 if x == 0 else - x, because the conditional-expression syntactic form is right-associative. The general form of a case analysis is $e$$_1$ if $p$$_1$ else $e$$_2$ if $p$$_2$ $\cdots$ $e$$_n$ if $p$$_n$ else $final$-$alternative$-$expression$ We call a consequent expression $e_i$ together with its predicate $p_i$ a clause. A case analysis can be seen as a sequence of clauses, followed by a final alternative expression. According to the evaluation of conditional expressions, a case analysis is evaluated by first evaluating the predicate $p$$_1$. If its value is false, then $p$$_2$ is evaluated. If $p$$_2$'s value is also false, then $p$$_3$ is evaluated. This process continues until a predicate is found whose value is true, in which case the interpreter returns the value of the corresponding consequent expression $e$ of the clause as the value of the case analysis. If none of the $p$'s is found to be true, the value of the case analysis is the value of the final alternative expression.

In addition to primitive predicates such as <, =, and >, there are logical composition operations, which enable us to construct compound predicates. The three most frequently used are these:

• (and $\langle e_1\rangle \ldots \langle e_n \rangle$ )
  The interpreter evaluates the expressions $\langle e \rangle$ one at a time, in left-to-right order. If any $\langle e \rangle$ evaluates to false, the value of the and expression is false, and the rest of the $\langle e \rangle$'s are not evaluated. If all $\langle e \rangle$'s evaluate to true values, the value of the and expression is the value of the last one.
• (or $\langle e_1 \rangle\ldots \langle e_n \rangle$)
  The interpreter evaluates the expressions $\langle e \rangle$ one at a time, in left-to-right order. If any $\langle e \rangle$ evaluates to a true value, that value is returned as the value of the or expression, and the rest of the $\langle e \rangle$'s are not evaluated. If all $\langle e \rangle$'s evaluate to false, the value of the or expression is false.
• (not $\langle e \rangle$)
  The value of a not expression is true when the expression $\langle e \rangle$ evaluates to false, and false otherwise.

Notice that and and or are special forms, not procedures, because the subexpressions are not necessarily all evaluated. Not is an ordinary procedure.

In addition to primitive predicates such as >=, >, <, <=, ==, and != that are applied to numbers,[6] there are logical composition operations, which enable us to construct compound predicates. The three most frequently used are these:

• $expression$$_1$ and $expression$$_2$
  This operation expresses logical conjunction, meaning roughly the same as the English word and. We assume[7] this syntactic form to be syntactic sugar[8] for
  $expression$$_2$ if $expression$$_1$ else False.
• $expression$$_1$ or $expression$$_2$
  This operation expresses logical disjunction, meaning roughly the same as the English word or. We assume this syntactic form to be syntactic sugar for
  True if $expression$$_1$ else $expression$$_2$.
• not $expression$
  This operation expresses logical negation, meaning roughly the same as the English word not. The value of the expression is true when $expression$ evaluates to false, and false when $expression$ evaluates to true.

Notice that and and or are syntactic forms, not operators; their right-hand expression is not always evaluated. The operator not, on the other hand, follows the evaluation rule of section 1.1.3. It is a unary operator, which means that it takes only one argument, whereas the arithmetic operators and primitive predicates discussed so far are binary, taking two arguments. The operator not precedes its argument; we call it a prefix operator. Another prefix operator is the numeric negation operator, an example of which is the expression - x in the abs functions above.

As an example of how these are used, the condition that a number $x$ be in the range $5 < x < 10$ may be expressed as (and (> x 5) (< x 10))

As an example of how these predicates are used, the condition that a number $x$ be in the range $5 < x < 10$ may be expressed as x > 5 and x < 10 The syntactic form and has lower precedence than the comparison operators > and <, and the conditional-expression syntactic form $\cdots$if$\cdots$else$\cdots$ has lower precedence than any other operator we have encountered so far, a property we used in the abs functions above.