1 Beginning Student

How to Design Programs Languages

1	Beginning Student
2	Beginning Student with List Abbreviations
3	Intermediate Student
4	Intermediate Student with Lambda
5	Advanced Student
	Index

1

Beginning Student

On this page:

1.1 Pre-Defined Variables

1.2 Template Variables

check-member-of

1.4 Pre-defined Functions

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

current-seconds

make-rectangular

1.4.3 Symbols

1.4.4 Lists

1.4.5 Posns

1.4.6 Characters

char-alphabetic?

char-lower-case?

char-upper-case?

char-whitespace?

1.4.7 Strings

string-alphabetic?

string-lower-case?

string-numeric?

string-upper-case?

string-whitespace?

1.4.8 Images

1.4.9 Misc

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1 Beginning Student

  program = def-or-expr ...

  def-or-expr = definition
| expr
| test-case
| library-require

  definition = (define (name variable variable ...) expr)
| (define name expr)
| (define name (lambda (variable variable ...) expr))
| (define-struct name (name ...))

  expr = (name expr expr ...)
| (cond [expr expr] ... [expr expr])
| (cond [expr expr] ... [else expr])
| (if expr expr expr)
| (and expr expr expr ...)
| (or expr expr expr ...)
| name
| ’name
| number
| string
| character

  test-case = (check-expect expr expr)
| (check-within expr expr expr)
| (check-member-of expr expr ...)
| (check-range expr expr expr)
| (check-error expr expr)
| (check-error expr)

  library-require = (require string)
| (require (lib string string ...))
| (require (planet string package))

  package = (string string number number)

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.

1.1 Pre-Defined Variables

empty : empty?

The empty list.

true : boolean?

The true value.

false : boolean?

The false value.

1.2 Template Variables

..

A placeholder for indicating that a definition is a template.

...

A placeholder for indicating that a definition is a template.

....

A placeholder for indicating that a definition is a template.

.....

A placeholder for indicating that a definition is a template.

......

A placeholder for indicating that a definition is a template.

1.3 Syntax

(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 name (lambda (variable variable ...) expression))

An alternate way on defining functions. The name is the name of the function, which cannot be the same as that of another function or variable.

A lambda cannot be used outside of this alternate syntax.

’name
(quote name)

A quoted name is a symbol. A symbol is a value, just like 0 or empty.

(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.

(name expression expression ...)

Calls the function named name. The value of the call is the value of name’s body when every one of the function’s variables are replaced by the values of the corresponding expressions.

The function named name must defined before it can be called. The number of argument expressions must be the same as the number of arguments expected by the function.

(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.

(and expression expression expression ...)

Evaluates to true if all the expressions are true. If any expression is false, the and expression 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, and reports an error.

(or 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 or expression evaluates to false.

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

1.4 Pre-defined Functions

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

* : (number number number ... -> number)

Evaluates the product of all of the input numbers.

+ : (number number number ... -> number)

Evaluates the sum of the input numbers.

- : (number number ... -> number)

subtracts the second (and following) number(s) from the first; negate the number if there is only one argument.

/ : (number number number ... -> number)

Divides the first by the second (and all following) number(s); try (/ 3 4) and (/ 3 2 2) only the first number can be zero.

< : (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 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 : (integer -> integer)

Generates a random natural number less than some given integer (exact only!).

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.

1.4.2 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.

1.4.3 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.

1.4.4 Lists

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

Creates a single list from several, by juxtaposition of the items.

assq :
(X
(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))
->
W)

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))
->
Z)

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.

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.

1.4.5 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.

1.4.6 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.

1.4.7 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).

1.4.8 Images

image=? : (image image -> boolean)

Determines whether two images are equal.

image? : (any -> boolean)

Determines whether a value is an image.

1.4.9 Misc

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

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

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.

identity : (any -> any)

Returns the argument unchanged.

struct? : (any -> boolean)

Determines whether some value is a structure.

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