5 Advanced Student

An name or a variable is a sequence of characters not including a space or one of the following:

" , ' ` ( ) [ ] { } | ; #

A number is a number such as 123, 3/2, or 5.5.

A symbol is a quote character followed by a name. A symbol is a value, just like 0 or empty.

A string is enclosed by a pair of ". Unlike symbols, strings may be split into characters and manipulated by a variety of functions. For example, "abcdef", "This is a string", and "This is a string with \" inside" are all strings.

A character begins with #\ and has the name of the character. For example, #\a, #\b, and #\space are characters.

In function calls, the function appearing immediatly after the open parenthesis can be any functions defined with define or define-struct, or any one of the pre-defined functions.

5.1 Pre-Defined Variables

empty : empty?

The empty list.

true : boolean?

The true value.

false : boolean?

The false value.

5.2 Syntax for Advanced

In Advanced, set! can be used to mutate variables, and define-struct’s structures are mutatable. define and lambda can define functions of zero arguments, and function calls can invoke functions of zero arguments.

(lambda (variable ...) expression)

Creates a function that takes as many arguments as given variables, and whose body is expression.

(λ (variable ...) expression)

The Greek letter λ is a synonym for lambda.

(expression expression ...)

Calls the function that results from evaluating the first expression. The value of the call is the value of function’s body when every instance of name’s variables are replaced by the values of the corresponding expressions.

The function being called must come from either a definition appearing before the function call, or from a lambda expression. The number of argument expressions must be the same as the number of arguments expected by the function.

(define-datatype dataype-name [variant-name field-name ...] ...)

A short-hand for defining a group of related structures. The following define-datatype:

(define-datatype datatype-name
[variant-name field-name ...]
...)

is equivalent to:

(define (datatype-name? x)
(or (variant-name? x) ...))
(define-struct variant-name (field-name ...))
...

(begin expression expression ...)

Evaluates the expressions in order from left to right. The value of the begin expression is the value of the last expression.

(begin0 expression expression ...)

Evaluates the expressions in order from left to right. The value of the begin expression is the value of the first expression.

(set! variable expression)

Evaluates expression, and then mutates the variable to have expression’s value. The variable must be defined by define, letrec, let*, or let.

(delay expression)

Produces a “promise” to evaluate expression. The expression is not evaluated until the promise is forced with force; when the promise is forced, the result is recorded, so that any further force of the promise immediately produces the remembered value.

(shared ([name expression] ...) expression)

Like letrec, but when an expression next to an id is a cons, list, vector, quasiquoted expression, or make-struct-name from a define-struct, the expression can refer directly to any name, not just names defined earlier. Thus, shared can be used to create cyclic data structures.

(recur name ([name expression] ...) expression)

A short-hand syntax for recursive loops. The first name corresponds to the name of the recursive function. The names in the parenthesis are the function’s arguments, and each corresponding expression is a value supplied for that argument in an initial starting call of the function. The last expression is the body of the function.

More precisely, the following recur:

(recur func-name ([arg-name arg-expression] ...)
body-expression)

is equivalent to:

(local [(define (func-name arg-name ...) body-expression)]
(func-name arg-expression ...))

(let name ([name expression] ...) expression)

An alternate syntax for recur.

(case expression [(choice ...) expression] ... [(choice ...) expression])

A case form contains one or more clauses. Each clause contains a choices (in parentheses)—either numbers or names—and an answer expression. The initial expression is evaluated, and its value is compared to the choices in each clause, where the lines are considered in order. The first line that contains a matching choice provides an answer expression whose value is the result of the whole case expression. Numbers match with the numbers in the choices, and symbols match with the names. If none of the lines contains a matching choice, it is an error.

(case expression [(choice ...) expression] ... [else expression])

This form of case is similar to the prior one, except that the final else clause is taken if no clause contains a choice matching the value of the initial expression.

(match expression [pattern expression] ...)

A match form contains one or more clauses that are surrounded by square brackets. Each clause contains a pattern—a description of a value—and an answer expression. The initial expression is evaluated, and its value is matched against the pattern in each clause, where the clauses are considered in order. The first clause that contains a matching pattern provides an answer expression whose value is the result of the whole match expression. This expression may reference identifiers defined in the matching pattern. If none of the clauses contains a matching pattern, it is an error.

(when test-expression body-expression)

If test-expression evaluates to true, the result of the when expression is the result of evaluating the body-expression, otherwise the result is (void) and the body-expression is not evaluated. If the result of evaluating the test-expression is neither true nor false, it is an error.

(unless test-expression body-expression)

Like when, but the body-expression is evaluated when the test-expression produces false instead of true.

5.3 Common Syntaxes

The following syntaxes behave the same in the Advanced level as they did in the Intermediate Student with Lambda level.

(local [definition ...] expression)

Groups related definitions for use in expression. Each definition can be either a define or a define-struct.

When evaluating local, each definition is evaluated in order, and finally the body expression is evaluated. Only the expressions within the local (including the right-hand-sides of the definitions and the expression) may refer to the names defined by the definitions. If a name defined in the local is the same as a top-level binding, the inner one “shadows” the outer one. That is, inside the local, any references to that name refer to the inner one.

(letrec ([name expr-for-let] ...) expression)

Like local, but with a simpler syntax. Each name defines a variable (or a function) with the value of the corresponding expr-for-let. If expr-for-let is a lambda, letrec defines a function, otherwise it defines a variable.

(let* ([name expr-for-let] ...) expression)

Like letrec, but each name can only be used in expression, and in expr-for-lets occuring after that name.

(let ([name expr-for-let] ...) expression)

Like letrec, but the defined names can be used only in the last expression, not the expr-for-lets next to the names.

(time expression)

Measures the time taken to evaluate expression. After evaluating expression, time prints out the time taken by the evaluation (including real time, time taken by the CPU, and the time spent collecting free memory). The value of time is the same as that of expression.

(define (name variable variable ...) expression)

Defines a function named name. The expression is the body of the function. When the function is called, the values of the arguments are inserted into the body in place of the variables. The function returns the value of that new expression.

The function name’s cannot be the same as that of another function or variable.

(define name expression)

Defines a variable called name with the the value of expression. The variable name’s cannot be the same as that of another function or variable, and name itself must not appear in expression.

(define-struct structure-name (field-name ...))

Defines a new structure called structure-name. The structure’s fields are named by the field-names. After the define-struct, the following new functions are available:

make-structure-name : takes a number of arguments equal to the number of fields in the structure, and creates a new instance of that structure.
structure-name-field-name : takes an instance of the structure and returns the value in the field named by field-name.
structure-name? : takes any value, and returns true if the value is an instance of the structure.

The name of the new functions introduced by define-struct must not be the same as that of other functions or variables, otherwise define-struct reports an error.

In Advanced, define-struct introduces one additional function:

set-structure-name-field-name! : takes an instance of the structure and a value, and mutates the instance’s field to the given value.

(cond [question-expression answer-expression] ...)

(cond [question-expression answer-expression]

...

[else answer-expression])

Chooses a clause based on some condition. cond finds the first question-expression that evaluates to true, then evaluates the corresponding answer-expression.

If none of the question-expressions evaluates to true, cond’s value is the answer-expression of the else clause. If there is no else, cond reports an error. If the result of a question-expression is neither true nor false, cond also reports an error.

else cannot be used outside of cond.

(if test-expression then-expression else-expression)

When the value of the test-expression is true, if evaluates the then-expression. When the test is false, if evaluates the else-expression.

If the test-expression is neither true nor false, if reports an error.

(or expression expression expression ...)

Evaluates to true if all the expressions are true. If any expression is false, the or expression immediately evaluates to false (and the expressions to the right of that expression are not evaluated.)

If any of the expressions evaluate to a value other than true or false, or reports an error.

(and expression expression expression ...)

Evaluates to true as soon as one of the expressions is true (and the expressions to the right of that expression are not evaluated.) If all of the expressions are false, the and expression evaluates to false.

If any of the expressions evaluate to a value other than true or false, and reports an error.

(check-expect expression expected-expression)

Checks that the first expression evaluates to the same value as the expected-expression.

(check-within expression expected-expression delta-expression)

Checks that the first expression evaluates to a value within delta-expression of the expected-expression. If delta-expression is not a number, check-within reports an error.

(check-error expression match-expression)

(check-error expression)

Checks that the expression reports an error, where the error messages matches the value of matchexpression, if it is present.

(check-member-of expression expression expression ...)

Checks that the value of the first expression as that of one of the following expressions.

(check-range expression low-expression high-expression)

Checks that the value of the first expression is a number in between the value of the low-expression and the high-expression, inclusive.

(require string)

Makes the definitions of the module specified by string available in the current module (i.e., the current file), where string refers to a file relative to the current file.

The string is constrained in several ways to avoid problems with different path conventions on different platforms: a / is a directory separator, . always means the current directory, .. always means the parent directory, path elements can use only a through z (uppercase or lowercase), 0 through 9, -, _, and ., and the string cannot be empty or contain a leading or trailing /.

(require module-name)

Accesses a file in an installed library. The library name is an identifier with the same constraints as for a relative-path string (though without the quotes), with the additional constraint that it must not contain a ..

(require (lib string string ...))

Accesses a file in an installed library, making its definitions available in the current module (i.e., the current file). The first string names the library file, and the remaining strings name the collection (and sub-collection, and so on) where the file is installed. Each string is constrained in the same way as for the (require string) form.

(require (planet string (string string number number)))

Accesses a library that is distributed on the internet via the PLaneT server, making it definitions available in the current module (i.e., current file).

5.4 Pre-Defined Functions

5.4.1 Numbers: Integers, Rationals, Reals, Complex, Exacts, Inexacts

< : (real real real ... -> boolean)

Compares real numbers for less-than.

<= : (real real real ... -> boolean)

Compares real numbers for less-than or equality.

= : (number number number ... -> boolean)

Compares numbers for equality.

> : (real real real ... -> boolean)

Compares real numbers for greater-than.

>= : (real real ... -> boolean)

Compares real numbers for greater-than or equality.

abs : (real -> real)

Evaluates the absolute value of a real number.

acos : (number -> number)

Evaluates the arccosine (inverse of cos) of a number.

add1 : (number -> number)

Evaluates a number one larger than a given number.

angle : (number -> real)

Extracts the angle from a complex number.

asin : (number -> number)

Evaluates the arcsine (inverse of sin) of a number.

atan : (number (number) -> number)

Evaluates the arctan of the given number or the ratio of the two given numbers.

ceiling : (real -> integer)

Determines the closest integer (exact or inexact) above a real number.

complex? : (any -> boolean)

Determines whether some value is complex.

conjugate : (number -> number)

Evaluates the conjugate of a complex number.

cos : (number -> number)

Evaluates the cosine of a number (radians).

cosh : (number -> number)

Evaluates the hyperbolic cosine of a number.

current-seconds : (-> integer)

Evaluates the current time in seconds elapsed (since a platform-specific starting date).

denominator : (rat -> integer)

Evaluates the denominator of a rational.

e : real

Euler’s number.

even? : (integer -> boolean)

Determines if some integer (exact or inexact) is even or not.

exact->inexact : (number -> number)

Converts an exact number to an inexact one.

exact? : (number -> boolean)

Determines whether some number is exact.

exp : (number -> number)

Evaluates e raised to a number.

expt : (number number -> number)

Evaluates the power of the first to the second number.

floor : (real -> integer)

Determines the closest integer (exact or inexact) below a real number.

gcd : (integer integer ... -> integer)

Evaluates the greatest common divisior of two integers (exact or inexact).

imag-part : (number -> real)

Extracts the imaginary part from a complex number.

inexact->exact : (number -> number)

Approximates an inexact number by an exact one.

inexact? : (number -> boolean)

Determines whether some number is inexact.

integer->char : (integer -> char)

Lookups the character that corresponds to the given integer (exact only!) in the ASCII table (if any).

integer-sqrt : (number -> integer)

Evaluates the integer (exact or inexact) square root of a number.

integer? : (any -> boolean)

Determines whether some value is an integer (exact or inexact).

lcm : (integer integer ... -> integer)

Evaluates the least common multiple of two integers (exact or inexact).

log : (number -> number)

Evaluates the base-e logarithm of a number.

magnitude : (number -> real)

Determines the magnitude of a complex number.

make-polar : (real real -> number)

Creates a complex from a magnitude and angle.

make-rectangular : (real real -> number)

Creates a complex from a real and an imaginary part.

max : (real real ... -> real)

Determines the largest number.

min : (real real ... -> real)

Determines the smallest number.

modulo : (integer integer -> integer)

Finds the remainder of the division of the first number by the second; try (modulo 4 3) (modulo 4 -3).

negative? : (number -> boolean)

Determines if some value is strictly smaller than zero.

number->string : (number -> string)

Converts a number to a string.

number? : (any -> boolean)

Determines whether some value is a number.

numerator : (rat -> integer)

Evaluates the numerator of a rational.

odd? : (integer -> boolean)

Determines if some integer (exact or inexact) is odd or not.

pi : real

The ratio of a circle’s circumference to its diameter.

positive? : (number -> boolean)

Determines if some value is strictly larger than zero.

quotient : (integer integer -> integer)

Divides the first integer (exact or inexact) into the second; try (quotient 3 4) and (quotient 4 3).

random

(case->

(integer -> integer)

(-> (and/c real inexact? (>/c 0) (</c 1))))

Generates a random natural number less than some given integer, or to generate a random inexact number between 0.0 and 1.0 exclusive.

rational? : (any -> boolean)

Determines whether some value is a rational number.

real-part : (number -> real)

Extracts the real part from a complex number.

real? : (any -> boolean)

Determines whether some value is a real number.

remainder : (integer integer -> integer)

Determines the remainder of dividing the first by the second integer (exact or inexact).

round : (real -> integer)

Rounds a real number to an integer (rounds to even to break ties).

sgn : (real -> (union 1 1.0 0 0.0 -1 -1.0))

Evaluates the sign of a real number.

sin : (number -> number)

Evaluates the sine of a number (radians).

sinh : (number -> number)

Evaluates the hyperbolic sine of a number.

sqr : (number -> number)

Evaluates the square of a number.

sqrt : (number -> number)

Evaluates the square root of a number.

sub1 : (number -> number)

Evaluates a number one smaller than a given number.

tan : (number -> number)

Evaluates the tangent of a number (radians).

zero? : (number -> boolean)

Determines if some value is zero or not.

5.4.2 Booleans

boolean=? : (boolean boolean -> boolean)

Determines whether two booleans are equal.

boolean? : (any -> boolean)

Determines whether some value is a boolean.

false? : (any -> boolean)

Determines whether a value is false.

not : (boolean -> boolean)

Evaluates the negation of a boolean value.

5.4.3 Symbols

symbol->string : (symbol -> string)

Converts a symbol to a string.

symbol=? : (symbol symbol -> boolean)

Determines whether two symbols are equal.

symbol? : (any -> boolean)

Determines whether some value is a symbol.

5.4.4 Lists

append : ((listof any) ... -> (listof any))

Creates a single list from several.

assoc : (any (listof any) -> (listof any) or false)

Produces the first element on the list whose first is equal? to v; otherwise it produces false.

assq

(listof (cons X Y))

(union false (cons X Y)))

Determines whether some item is the first item of a pair in a list of pairs.

caaar

((cons

(cons (cons W (listof Z)) (listof Y))

(listof X))

Selects the first item of the first list in the first list of a list.

caadr

((cons

(cons (cons W (listof Z)) (listof Y))

(listof X))

(listof Z))

Selects the rest of the first list in the first list of a list.

caar : ((cons (cons Z (listof Y)) (listof X)) -> Z)

Selects the first item of the first list in a list.

cadar

((cons (cons W (cons Z (listof Y))) (listof X))

Selects the second item of the first list of a list.

cadddr : ((listof Y) -> Y)

Selects the fourth item of a non-empty list.

caddr : ((cons W (cons Z (cons Y (listof X)))) -> Y)

Selects the third item of a non-empty list.

cadr : ((cons Z (cons Y (listof X))) -> Y)

Selects the second item of a non-empty list.

car : ((cons Y (listof X)) -> Y)

Selects the first item of a non-empty list.

cdaar

((cons

(cons (cons W (listof Z)) (listof Y))

(listof X))

(listof Z))

Selects the rest of the first list in the first list of a list.

cdadr

((cons W (cons (cons Z (listof Y)) (listof X)))

(listof Y))

Selects the rest of the first list in the rest of a list.

cdar

((cons (cons Z (listof Y)) (listof X))

(listof Y))

Selects the rest of a non-empty list in a list.

cddar

((cons (cons W (cons Z (listof Y))) (listof X))

(listof Y))

Selects the rest of the rest of the first list of a list.

cdddr

((cons W (cons Z (cons Y (listof X))))

(listof X))

Selects the rest of the rest of the rest of a list.

cddr : ((cons Z (cons Y (listof X))) -> (listof X))

Selects the rest of the rest of a list.

cdr : ((cons Y (listof X)) -> (listof X))

Selects the rest of a non-empty list.

cons : (X (listof X) -> (listof X))

Constructs a list.

cons? : (any -> boolean)

Determines whether some value is a constructed list.

eighth : ((listof Y) -> Y)

Selects the eighth item of a non-empty list.

empty? : (any -> boolean)

Determines whether some value is the empty list.

fifth : ((listof Y) -> Y)

Selects the fifth item of a non-empty list.

first : ((cons Y (listof X)) -> Y)

Selects the first item of a non-empty list.

fourth : ((listof Y) -> Y)

Selects the fourth item of a non-empty list.

length : ((listof any) -> number)

Evaluates the number of items on a list.

list : (any ... -> (listof any))

Constructs a list of its arguments.

list* : (any ... (listof any) -> (listof any))

Constructs a list by adding multiple items to a list.

list-ref : ((listof X) natural-number -> X)

Extracts the indexed item from the list.

list? : (any -> boolean)

Determines whether some value is a list.

make-list : (natural-number any -> (listof any))

Constructs a list of k (the first argument) copies of x (the second argument).

member : (any (listof any) -> boolean)

Determines whether some value is on the list (comparing values with equal?).

member? : (any (listof any) -> boolean)

Determines whether some value is on the list (comparing values with equal?).

memq : (any (listof any) -> (union false list))

Determines whether some value is on some list if so, it produces the suffix of the list that starts with x if not, it produces false. (It compares values with the eq? predicate.)

memv : (any (listof any) -> (union false list))

Determines whether some value is on the list if so, it produces the suffix of the list that starts with x if not, it produces false. (It compares values with the eqv? predicate.)

null : empty

The empty list.

null? : (any -> boolean)

Determines whether some value is the empty list.

remove : (any (listof any) -> (listof any))

Constructs a list like the given one with the first occurrence of the given item removed (comparing values with equal?).

rest : ((cons Y (listof X)) -> (listof X))

Selects the rest of a non-empty list.

reverse : ((listof any) -> list)

Creates a reversed version of a list.

second : ((cons Z (cons Y (listof X))) -> Y)

Selects the second item of a non-empty list.

seventh : ((listof Y) -> Y)

Selects the seventh item of a non-empty list.

sixth : ((listof Y) -> Y)

Selects the sixth item of a non-empty list.

third : ((cons W (cons Z (cons Y (listof X)))) -> Y)

Selects the third item of a non-empty list.

5.4.5 Posns

make-posn : (number number -> posn)

Constructs a posn.

posn : signature

Signature for posns.

posn-x : (posn -> number)

Extracts the x component of a posn.

posn-y : (posn -> number)

Extracts the y component of a posn.

posn? : (anything -> boolean)

Determines if its input is a posn.

set-posn-x! : (posn number -> void)

Updates the x component of a posn.

set-posn-y! : (posn number -> void)

Updates the x component of a posn.

5.4.6 Characters

char->integer : (char -> integer)

Lookups the number that corresponds to the given character in the ASCII table (if any).

char-alphabetic? : (char -> boolean)

Determines whether a character represents an alphabetic character.

char-ci<=? : (char char char ... -> boolean)

Determines whether a character precedes another (or is equal to it) in a case-insensitive manner.

char-ci<? : (char char char ... -> boolean)

Determines whether a character precedes another in a case-insensitive manner.

char-ci=? : (char char char ... -> boolean)

Determines whether two characters are equal in a case-insensitive manner.

char-ci>=? : (char char char ... -> boolean)

Determines whether a character succeeds another (or is equal to it) in a case-insensitive manner.

char-ci>? : (char char char ... -> boolean)

Determines whether a character succeeds another in a case-insensitive manner.

char-downcase : (char -> char)

Determines the equivalent lower-case character.

char-lower-case? : (char -> boolean)

Determines whether a character is a lower-case character.

char-numeric? : (char -> boolean)

Determines whether a character represents a digit.

char-upcase : (char -> char)

Determines the equivalent upper-case character.

char-upper-case? : (char -> boolean)

Determines whether a character is an upper-case character.

char-whitespace? : (char -> boolean)

Determines whether a character represents space.

char<=? : (char char char ... -> boolean)

Determines whether a character precedes another (or is equal to it).

char<? : (char char char ... -> boolean)

Determines whether a character precedes another.

char=? : (char char char ... -> boolean)

Determines whether two characters are equal.

char>=? : (char char char ... -> boolean)

Determines whether a character succeeds another (or is equal to it).

char>? : (char char char ... -> boolean)

Determines whether a character succeeds another.

char? : (any -> boolean)

Determines whether a value is a character.

5.4.7 Strings

explode : (string -> (listof string))

Translates a string into a list of 1-letter strings.

format : (string any ... -> string)

Formats a string, possibly embedding values.

implode : ((listof string) -> string)

Concatenates the list of 1-letter strings into one string.

int->string : (integer -> string)

Converts an integer in [0,55295] or [57344 1114111] to a 1-letter string.

list->string : ((listof char) -> string)

Converts a s list of characters into a string.

make-string : (nat char -> string)

Produces a string of given length from a single given character.

replicate : (nat string -> string)

Replicates the given string.

string : (char ... -> string)

Builds a string of the given characters.

string->int : (string -> integer)

Converts a 1-letter string to an integer in [0,55295] or [57344, 1114111].

string->list : (string -> (listof char))

Converts a string into a list of characters.

string->number : (string -> (union number false))

Converts a string into a number, produce false if impossible.

string->symbol : (string -> symbol)

Converts a string into a symbol.

string-alphabetic? : (string -> boolean)

Determines whether all ’letters’ in the string are alphabetic.

string-append : (string ... -> string)

Juxtaposes the characters of several strings.

string-ci<=? : (string string string ... -> boolean)

Determines whether one string alphabetically precedes another (or is equal to it) in a case-insensitive manner.

string-ci<? : (string string string ... -> boolean)

Determines whether one string alphabetically precedes another in a case-insensitive manner.

string-ci=? : (string string string ... -> boolean)

Compares two strings character-wise in a case-insensitive manner.

string-ci>=? : (string string string ... -> boolean)

Determines whether one string alphabetically succeeds another (or is equal to it) in a case-insensitive manner.

string-ci>? : (string string string ... -> boolean)

Determines whether one string alphabetically succeeds another in a case-insensitive manner.

string-copy : (string -> string)

Copies a string.

string-ith : (string nat -> string)

Extracts the ith 1-letter substring from the given one.

string-length : (string -> nat)

Determines the length of a string.

string-lower-case? : (string -> boolean)

Determines whether all ’letters’ in the string are lower case.

string-numeric? : (string -> boolean)

Determines whether all ’letters’ in the string are numeric.

string-ref : (string nat -> char)

Extracts the i-the character from a string.

string-upper-case? : (string -> boolean)

Determines whether all ’letters’ in the string are upper case.

string-whitespace? : (string -> boolean)

Determines whether all ’letters’ in the string are white space.

string<=? : (string string string ... -> boolean)

Determines whether one string alphabetically precedes another (or is equal to it).

string<? : (string string string ... -> boolean)

Determines whether one string alphabetically precedes another.

string=? : (string string string ... -> boolean)

Compares two strings character-wise.

string>=? : (string string string ... -> boolean)

Determines whether one string alphabetically succeeds another (or is equal to it).

string>? : (string string string ... -> boolean)

Determines whether one string alphabetically succeeds another.

string? : (any -> boolean)

Determines whether a value is a string.

substring : (string nat nat -> string)

Extracts the substring starting at a 0-based index up to the second 0-based index (exclusive).

5.4.8 Images

image=? : (image image -> boolean)

Determines whether two images are equal.

image? : (any -> boolean)

Determines whether a value is an image.

5.4.9 Misc

=~ : (number number non-negative-real -> boolean)

Checks whether two numbers are within some amount (the third argument) of either other.

current-milliseconds : (-> exact-integer)

Returns the current “time” in fixnum milliseconds (possibly negative).

eof : eof

The end-of-file value.

eof-object? : (any -> boolean)

Determines whether some value is the end-of-file value.

eq? : (any any -> boolean)

Determines whether two values are equivalent from the computer’s perspective (intensional).

equal? : (any any -> boolean)

Determines whether two values are structurally equal where basic values are compared with the eqv? predicate.

equal~? : (any any non-negative-real -> boolean)

Compares like equal? on the first two arguments, except using =~ in the case of numbers.

eqv? : (any any -> boolean)

Determines whether two values are equivalent from the perspective of all functions that can be applied to it (extensional).

error : (any ... -> void)

signals an error, combining the given values into an error message. If any of the values’ printed representations is too long, it is truncated and “...” is put into the string. If the first value is a symbol, it is treated specially; it is suffixed with a colon and a space (the intention is that the symbol is the name of the function signalling the error).

exit : (-> void)

Exits the running program.

force : (delay -> any)

Finds the delayed value; see also delay.

gensym : (-> symbol?)

Generates a new symbol, different from all symbols in the program.

identity : (any -> any)

Returns the argument unchanged.

promise? : (any -> boolean)

Determines if a value is delayed.

sleep : (-> positive-number void)

Causes the program to sleep for the given number of seconds.

struct? : (any -> boolean)

Determines whether some value is a structure.

void : (-> void)

Produces a void value.

void? : (any -> boolean)

Determines if a value is void.

5.4.10 Numbers (relaxed conditions)

* : (number ... -> number)

Multiplys all given numbers.

+ : (number ... -> number)

Adds all given numbers.

- : (number ... -> number)

Subtracts from the first all remaining numbers.

/ : (number ... -> number)

Divides the first by all remaining numbers.

5.4.11 Higher-Order Functions

andmap : ((X -> boolean) (listof X) -> boolean)

(andmap p (list x-1 ... x-n)) = (and (p x-1) ... (p x-n))

apply

((X-1 ... X-N -> Y)

X-1

...

X-i

(list X-i+1 ... X-N)

Applies a function using items from a list as the arguments.

argmax : ((X -> real) (listof X) -> X)

Finds the (first) element of the list that maximizes the output of the function.

argmin : ((X -> real) (listof X) -> X)

Finds the (first) element of the list that minimizes the output of the function.

build-list : (nat (nat -> X) -> (listof X))

(build-list n f) = (list (f 0) ... (f (- n 1)))

build-string : (nat (nat -> char) -> string)

(build-string n f) = (string (f 0) ... (f (- n 1)))

compose

((Y-1 -> Z)

...

(Y-N -> Y-N-1)

(X-1 ... X-N -> Y-N)

(X-1 ... X-N -> Z))

Composes a sequence of procedures into a single procedure.

filter : ((X -> boolean) (listof X) -> (listof X))

Constructs a list from all those items on a list for which the predicate holds.

foldl : ((X Y -> Y) Y (listof X) -> Y)

(foldl f base (list x-1 ... x-n)) = (f x-n ... (f x-1 base))

foldr : ((X Y -> Y) Y (listof X) -> Y)

(foldr f base (list x-1 ... x-n)) = (f x-1 ... (f x-n base))

for-each : ((any ... -> any) (listof any) ... -> void)

Applies a function to each item on one or more lists for effect only.

map : ((X ... -> Z) (listof X) ... -> (listof Z))

Constructs a new list by applying a function to each item on one or more existing lists.

memf

((X -> any)

(listof X)

(union false (listof X)))

Produces true if the function given as the first argument produces a non-false value for any item in the second argument.

ormap : ((X -> boolean) (listof X) -> boolean)

(ormap p (list x-1 ... x-n)) = (or (p x-1) ... (p x-n))

procedure? : (any -> boolean)

Produces true if the value is a procedure.

quicksort : ((listof X) (X X -> boolean) -> (listof X))

Constructs a list from all items on a list in an order according to a predicate.

sort : ((listof X) (X X -> boolean) -> (listof X))

Constructs a list from all items on a list in an order according to a predicate.

5.4.12 Reading and Printing

display : (any -> void)

Prints the argument to stdout (without quotes on symbols and strings, etc.).

newline : (-> void)

Prints a newline to stdout.

pretty-print : (any -> void)

Like write, but with standard newlines and indentation.

print : (any -> void)

Prints the argument as a value to stdout.

printf : (string any ... -> void)

Formats the rest of the arguments according to the first argument and print it to stdout.

read : (-> sexp)

Reads input from the user.

with-input-from-file : (string (-> any) -> any)

Opens the named input file and to extract all input from there.

with-input-from-string : (string (-> any) -> any)

Turns the given string into input for read* operations.

with-output-to-file : (string (-> any) -> any)

Opens the named output file and to put all output there.

with-output-to-string : (string (-> any) -> any)

Produces a string from all write/display/print operations.

write : (any -> void)

Prints the argument to stdout (in a traditional style that is somewhere between print and display).

5.4.13 Vectors

build-vector : (nat (nat -> X) -> (vectorof X))

Constructs a vector.

make-vector : (number X -> (vectorof X))

Constructs a vector.

vector : (X ... -> (vector X ...))

Constructs a vector.

vector-length : ((vector X) -> nat)

Determines the length of a vector.

vector-ref : ((vector X) nat -> X)

Extracts an element from a vector.

vector-set! : ((vectorof X) nat X -> void)

Updates a vector.

vector? : (any -> boolean)

Determines if a value is a vector.

5.4.14 Boxes

box : (any -> box)

Constructs a box.

box? : (any -> boolean)

Determines if a value is a box.

set-box! : (box any -> void)

Updates a box.

unbox : (box -> any)

Extracts the boxed value.

5.4.15 Hash Tables

hash-copy : (hash -> hash)

Copies a hash table.

hash-count : (hash -> integer)

Determines the number of keys mapped by a hash table.

hash-eq? : (hash -> boolean)

Determines if a hash table uses eq? for comparisions.

hash-equal? : (hash -> boolean)

Determines if a hash table uses equal? for comparisions.

hash-eqv? : (hash -> boolean)

Determines if a hash table uses eqv? for comparisions.

hash-for-each : ((hash X Y) (X Y -> any) -> void)

Applies a function to each mapping of a hash table for effect only.

hash-has-key? : ((hash X Y) X -> boolean)

Determines if a key is associated with a value in a hash table.

hash-map : ((hash X Y) (X Y -> A) -> (listof A))

Constructs a new list by applying a function to each mapping of a hash table.

hash-ref

(case->

((hash X Y) X -> Y)

((hash X Y) X Y -> Y)

((hash X Y) X (-> Y) -> Y))

Extracts the value associated with a key from a hash table; the three argument case allows a default value or default value computation.

hash-ref!

(case->

((hash X Y) X Y -> Y)

((hash X Y) X (-> Y) -> Y))

Extracts the value associated with a key from a mutable hash table; if the key does not have an mapping, the third argument is used as the value (or used to compute the value) and is added to the hash table associated with the key.

hash-remove : ((hash X Y) X -> (hash X Y))

Constructs an immutable hash table with one less mapping than an existing immutable hash table.

hash-remove! : ((hash X Y) X -> void)

Removes an mapping from a mutable hash table.

hash-set : ((hash X Y) X Y -> (hash X Y))

Constructs an immutable hash table with one new mapping from an existing immutable hash table.

hash-set! : ((hash X Y) X Y -> void)

Updates a mutable hash table with a new mapping.

hash-update

(case->

((hash X Y) X (Y -> Y) -> (hash X Y))

((hash X Y) X (Y -> Y) Y -> (hash X Y))

((hash X Y) X (Y -> Y) (-> Y) -> (hash X Y)))

Composes hash-ref and hash-set to update an existing mapping; the third argument is used to compute the new mapping value; the fourth argument is used as the third argument to hash-ref.

hash-update!

(case->

((hash X Y) X (Y -> Y) -> void)

((hash X Y) X (Y -> Y) Y -> void)

((hash X Y) X (Y -> Y) (-> Y) -> void))

Composes hash-ref and hash-set! to update an existing mapping; the third argument is used to compute the new mapping value; the fourth argument is used as the third argument to hash-ref.

hash? : (any -> boolean)

Determines if a value is a hash table.

make-hash

(case->

(-> (hash X Y))