10.1 Booleans

The boolean objects are true and false. The boolean constant true is written as ‘#t’, and the boolean constant false is written as ‘#f’.

The primary use for boolean objects is in the conditional expressions if, cond, and, and or; the behavior of these expressions is determined by whether objects are true or false. These expressions count only #f as false. They count everything else, including #t, pairs, symbols, numbers, strings, vectors, and procedures as true (but see True and False).

Programmers accustomed to other dialects of Lisp should note that Scheme distinguishes #f and the empty list from the symbol nil. Similarly, #t is distinguished from the symbol t. In fact, the boolean objects (and the empty list) are not symbols at all.

Boolean constants evaluate to themselves, so you don’t need to quote them.

#t                                      ⇒  #t
#f                                      ⇒  #f
'#f                                     ⇒  #f
t                                       error→ Unbound variable

variable: false

variable: true

These variables are bound to the objects #f and #t respectively. The compiler, given the usual-integrations declaration, replaces references to these variables with their respective values.

Note that the symbol true is not equivalent to #t, and the symbol false is not equivalent to #f.

standard procedure: boolean? object

Returns #t if object is either #t or #f; otherwise returns #f.

(boolean? #f)                           ⇒  #t
(boolean? 0)                            ⇒  #f

standard procedure: not object

procedure: false? object

These procedures return #t if object is false; otherwise they return #f. In other words they invert boolean values. These two procedures have identical semantics; their names are different to give different connotations to the test.

(not #t)                                ⇒  #f
(not 3)                                 ⇒  #f
(not (list 3))                          ⇒  #f
(not #f)                                ⇒  #t

extended standard procedure: procedure boolean=? boolean1 boolean2 boolean3 …

This predicate is true iff the boolean args are either all true or all false.

Implementation note: The standard requires this procedure’s arguments to satisfy boolean?, but MIT/GNU Scheme allows any object to be an argument.

procedure: boolean/and object …

This procedure returns #t if none of its arguments are #f. Otherwise it returns #f.

procedure: boolean/or object …

This procedure returns #f if all of its arguments are #f. Otherwise it returns #t.