#### 3.1Booleans and Equality

True and false booleans are represented by the values #t and #f, respectively, though operations that depend on a boolean value typically treat anything other than #f as true. The #t value is always eq? to itself, and #f is always eq? to itself.

See Reading Booleans for information on reading booleans and Printing Booleans for information on printing booleans.

 procedure(boolean? v) → boolean? v : any/c
Returns #t if v is #t or #f, #f otherwise.

Examples:

 > (boolean? #f) #t > (boolean? #t) #t > (boolean? 'true) #f

 procedure(not v) → boolean? v : any/c
Returns #t if v is #f, #f otherwise.

Examples:

 > (not #f) #t > (not #t) #f > (not 'we-have-no-bananas) #f

 procedure(equal? v1 v2) → boolean? v1 : any/c v2 : any/c
Two values are equal? if and only if they are eqv?, unless otherwise specified for a particular datatype.

Datatypes with further specification of equal? include strings, byte strings, pairs, mutable pairs, vectors, boxes, hash tables, and inspectable structures. In the last six cases, equality is recursively defined; if both v1 and v2 contain reference cycles, they are equal when the infinite unfoldings of the values would be equal. See also gen:equal+hash and prop:impersonator-of.

Examples:

 > (equal? 'yes 'yes) #t > (equal? 'yes 'no) #f > (equal? (expt 2 100) (expt 2 100)) #t > (equal? 2 2.0) #f > (equal? (make-string 3 #\z) (make-string 3 #\z)) #t

 procedure(eqv? v1 v2) → boolean? v1 : any/c v2 : any/c
Two values are eqv? if and only if they are eq?, unless otherwise specified for a particular datatype.

The number and character datatypes are the only ones for which eqv? differs from eq?.

Examples:

 > (eqv? 'yes 'yes) #t > (eqv? 'yes 'no) #f > (eqv? (expt 2 100) (expt 2 100)) #t > (eqv? 2 2.0) #f > (eqv? (integer->char 955) (integer->char 955)) #t > (eqv? (make-string 3 #\z) (make-string 3 #\z)) #f

 procedure(eq? v1 v2) → boolean? v1 : any/c v2 : any/c
Return #t if v1 and v2 refer to the same object, #f otherwise. See also Object Identity and Comparisons.

Examples:

 > (eq? 'yes 'yes) #t > (eq? 'yes 'no) #f > (let ([v (mcons 1 2)]) (eq? v v)) #t > (eq? (mcons 1 2) (mcons 1 2)) #f > (eq? (make-string 3 #\z) (make-string 3 #\z)) #f

 procedure(equal?/recur v1 v2 recur-proc) → boolean? v1 : any/c v2 : any/c recur-proc : (any/c any/c -> any/c)
Like equal?, but using recur-proc for recursive comparisons (which means that reference cycles are not handled automatically). Non-#f results from recur-proc are converted to #t before being returned by equal?/recur.

Examples:

> (equal?/recur 1 1 (lambda (a b) #f))

#t

> (equal?/recur '(1) '(1) (lambda (a b) #f))

#f

 > (equal?/recur '#(1 1 1) '#(1 1.2 3/4) (lambda (a b) (<= (abs (- a b)) 0.25)))

#t

 procedure v : any/c
Returns #t if v is an immutable string, byte string, vector, hash table, or box, #f otherwise.

Note that immutable? is not a general predicate for immutability (despite its name). It works only for a handful of datatypes for which a single predicate—string?, vector?, etc.recognizes both mutable and immutable variants of the datatype. In particular, immutable? produces #f for a pair, even though pairs are immutable, since pair? implies immutability.

Examples:

 > (immutable? 'hello) #f > (immutable? "a string") #t > (immutable? (box 5)) #f > (immutable? #(0 1 2 3)) #t > (immutable? (make-hash)) #f > (immutable? (make-immutable-hash '([a b]))) #t

 value
A generic interface (see Generic Interfaces) that supplies an equality predicate and hashing functions for a structure type. The following methods must be implemented:

• equal-proc : (-> any/c any/c (-> any/c any/c boolean?) any/c) tests whether the first two arguments are equal, where both values are instances of the structure type to which the generic interface is associated (or a subtype of the structure type).

The third argument is an equal? predicate to use for recursive equality checks; use the given predicate instead of equal? to ensure that data cycles are handled properly and to work with equal?/recur (but beware that an arbitrary function can be provided to equal?/recur for recursive checks, which means that arguments provided to the predicate might be exposed to arbitrary code).

The equal-proc is called for a pair of structures only when they are not eq?, and only when they both have a gen:equal+hash value inherited from the same structure type. With this strategy, the order in which equal? receives two structures does not matter. It also means that, by default, a structure sub-type inherits the equality predicate of its parent, if any.

• hash-proc : (-> any/c (-> any/c exact-integer?) exact-integer?) computes a hash code for the given structure, like equal-hash-code. The first argument is an instance of the structure type (or one of its subtypes) to which the generic interface is associated.

The second argument is an equal-hash-code-like procedure to use for recursive hash-code computation; use the given procedure instead of equal-hash-code to ensure that data cycles are handled properly.

• hash2-proc : (-> any/c (-> any/c exact-integer?) exact-integer?) computes a secondary hash code for the given structure. This procedure is like hash-proc, but analogous to equal-secondary-hash-code.

Take care to ensure that hash-proc and hash2-proc are consistent with equal-proc. Specifically, hash-proc and hash2-proc should produce the same value for any two structures for which equal-proc produces a true value.

When a structure type has no gen:equal+hash implementation, then transparent structures (i.e., structures with an inspector that is controlled by the current inspector) are equal? when they are instances of the same structure type (not counting sub-types), and when they have equal? field values. For transparent structures, equal-hash-code and equal-secondary-hash-code derive hash code using the field values. For opaque structure types, equal? is the same as eq?, and equal-hash-code and equal-secondary-hash-code results are based only on eq-hash-code. If a structure has a prop:impersonator-of property, then the prop:impersonator-of property takes precedence over gen:equal+hash if the property value’s procedure returns a non-#f value when applied to the structure.

Examples:

 > (define (farm=? farm1 farm2 recursive-equal?) (and (= (farm-apples farm1) (farm-apples farm2)) (= (farm-oranges farm1) (farm-oranges farm2)) (= (farm-sheep farm1) (farm-sheep farm2))))
 > (define (farm-hash-1 farm recursive-equal-hash) (+ (* 10000 (farm-apples farm)) (* 100 (farm-oranges farm)) (* 1 (farm-sheep farm))))
 > (define (farm-hash-2 farm recursive-equal-hash) (+ (* 10000 (farm-sheep farm)) (* 100 (farm-apples farm)) (* 1 (farm-oranges farm))))
 > (define-struct farm (apples oranges sheep) #:methods gen:equal+hash [(define equal-proc farm=?) (define hash-proc  farm-hash-1) (define hash2-proc farm-hash-2)])
> (define east (make-farm 5 2 20))
> (define west (make-farm 18 6 14))
> (define north (make-farm 5 20 20))
> (define south (make-farm 18 6 14))
> (equal? east west)

#f

> (equal? east north)

#f

> (equal? west south)

#t

 value
A deprecated structure type property (see Structure Type Properties) that supplies an equality predicate and hashing functions for a structure type. gen:equal+hash should be used instead. Accepts a list of three procedures that correspond to the methods of gen:equal+hash.

##### 3.1.1Boolean Aliases

 (require racket/bool)
The bindings documented in this section are provided by the racket/bool and racket libraries, but not racket/base.

 value
An alias for #t.

 value
An alias for #f.

 procedure(symbol=? a b) → boolean? a : symbol? b : symbol?
Returns (equal? a b) (if a and b are symbols).

 procedure(boolean=? a b) → boolean? a : boolean? b : boolean?
Returns (equal? a b) (if a and b are booleans).

 procedure(false? v) → boolean? v : any/c
Returns (not v).

 syntax(nand expr ...)
Same as (not (and expr ...)).

Examples:

 > (nand #f #t) #t > (nand #f (error 'ack "we don't get here")) #t

 syntax(nor expr ...)
Same as (not (or expr ...)).

In the two argument case, returns #t if neither of the arguments is a true value.

Examples:

 > (nor #f #t) #f > (nor #t (error 'ack "we don't get here")) #f

 syntax(implies expr1 expr2)
Checks to be sure that the first expression implies the second.

Same as (if expr1 expr2 #t).

Examples:

 > (implies #f #t) #t > (implies #f #f) #t > (implies #t #f) #f > (implies #f (error 'ack "we don't get here")) #t

 procedure(xor b1 b2) → any b1 : any/c b2 : any/c
Returns the exclusive or of b1 and b2.

If exactly one of b1 and b2 is not #f, then return it. Otherwise, returns #f.

Examples:

 > (xor 11 #f) 11 > (xor #f 22) 22 > (xor 11 22) #f > (xor #f #f) #f