500 lines
23 KiB
Racket
500 lines
23 KiB
Racket
#lang scheme
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(require mzlib/etc mzlib/list mzlib/math syntax/docprovide)
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;; Implements the procedures:
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(require "teachprims.rkt"
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"../posn.rkt"
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"../imageeq.rkt")
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;; procedures with documentation:
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(provide-and-document
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procedures
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("Numbers: Integers, Rationals, Reals, Complex, Exacts, Inexacts"
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(number? (any -> boolean)
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"Determines whether some value is a number.")
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(= (number number number ... -> boolean)
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"Compares numbers for equality.")
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(< (real real real ... -> boolean)
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"Compares real numbers for less-than.")
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(> (real real real ... -> boolean)
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"Compares real numbers for greater-than.")
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(<= (real real real ... -> boolean)
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"Compares real numbers for less-than or equality.")
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(>= (real real real ... -> boolean)
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"Compares real numbers for greater-than or equality.")
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((beginner-+ +) (number number number ... -> number)
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"Evaluates the sum of the input numbers.")
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(- (number number ... -> number)
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"subtracts the second (and following) number(s) from the first; negate the number if there is only one argument.")
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((beginner-* *) (number number number ... -> number)
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"Evaluates the product of all of the input numbers.")
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((beginner-/ /) (number number number ... -> number)
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"Divides the first by the second (and all following) number(s); try (/ 3 4) and (/ 3 2 2)"
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" only the first number can be zero.")
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(max (real real ... -> real)
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"Determines the largest number.")
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(min (real real ... -> real)
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"Determines the smallest number.")
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(quotient (integer integer -> integer)
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"Divides the second integer---also called divisor---into the first---known as dividend---to obtain the quotient; try (quotient 3 4) and (quotient 4 3).")
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(remainder (integer integer -> integer)
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"Determines the remainder of dividing the first by the second integer (exact or inexact).")
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(modulo (integer integer -> integer)
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"Finds the remainder of the division of the first number by the second; try (modulo 4 3) (modulo 4 -3).")
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((beginner-sqr sqr) (number -> number)
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"Evaluates the square of a number.")
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(sqrt (number -> number)
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"Evaluates the square root of a number.")
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(integer-sqrt (number -> integer)
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"Evaluates the integer (exact or inexact) square root of a number.")
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(expt (number number -> number)
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"Evaluates the power of the first to the second number.")
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(abs (real -> real)
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"Evaluates the absolute value of a real number.")
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(sgn (real -> (union 1 #i1.0 0 #i0.0 -1 #i-1.0))
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"Evaluates the sign of a real number.")
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;; fancy numeric
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(exp (number -> number)
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"Evaluates e raised to a number.")
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(log (number -> number)
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"Evaluates the base-e logarithm of a number.")
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;; trigonometry
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(sin (number -> number)
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"Evaluates the sine of a number (radians).")
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(cos (number -> number)
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"Evaluates the cosine of a number (radians).")
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(tan (number -> number)
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"Evaluates the tangent of a number (radians).")
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(asin (number -> number)
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"Evaluates the arcsine (inverse of sin) of a number.")
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(acos (number -> number)
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"Evaluates the arccosine (inverse of cos) of a number.")
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(atan (number [number] -> number)
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"Evaluates the arctan of the given number or the ratio of the two given numbers.")
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(sinh (number -> number)
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"Evaluates the hyperbolic sine of a number.")
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(cosh (number -> number)
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"Evaluates the hyperbolic cosine of a number.")
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(exact? (number -> boolean)
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"Determines whether some number is exact.")
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(integer? (any -> boolean)
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"Determines whether some value is an integer (exact or inexact).")
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(zero? (number -> boolean)
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"Determines if some value is zero or not.")
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(positive? (number -> boolean)
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"Determines if some value is strictly larger than zero.")
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(negative? (number -> boolean)
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"Determines if some value is strictly smaller than zero.")
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(odd? (integer -> boolean)
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"Determines if some integer (exact or inexact) is odd or not.")
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(even? (integer -> boolean)
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"Determines if some integer (exact or inexact) is even or not.")
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(add1 (number -> number)
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"Evaluates a number one larger than a given number.")
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(sub1 (number -> number)
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"Evaluates a number one smaller than a given number.")
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(lcm (integer integer ... -> integer)
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"Evaluates the least common multiple of two integers (exact or inexact).")
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(gcd (integer integer ... -> integer)
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"Evaluates the greatest common divisior of two integers (exact or inexact).")
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(rational? (any -> boolean)
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"Determines whether some value is a rational number.")
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(numerator (rat -> integer)
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"Evaluates the numerator of a rational.")
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(denominator (rat -> integer)
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"Evaluates the denominator of a rational.")
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(inexact? (number -> boolean)
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"Determines whether some number is inexact.")
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(real? (any -> boolean)
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"Determines whether some value is a real number.")
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(floor (real -> integer)
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"Determines the closest integer (exact or inexact) below a real number.")
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(ceiling (real -> integer)
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"Determines the closest integer (exact or inexact) above a real number.")
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(round (real -> integer)
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"Rounds a real number to an integer (rounds to even to break ties).")
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(complex? (any -> boolean)
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"Determines whether some value is complex.")
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(make-polar (real real -> number)
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"Creates a complex from a magnitude and angle.")
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(make-rectangular (real real -> number)
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"Creates a complex from a real and an imaginary part.")
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(real-part (number -> real)
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"Extracts the real part from a complex number.")
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(imag-part (number -> real)
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"Extracts the imaginary part from a complex number.")
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(magnitude (number -> real)
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"Determines the magnitude of a complex number.")
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(angle (number -> real)
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"Extracts the angle from a complex number.")
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(conjugate (number -> number)
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"Evaluates the conjugate of a complex number.")
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(exact->inexact (number -> number)
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"Converts an exact number to an inexact one.")
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(inexact->exact (number -> number)
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"Approximates an inexact number by an exact one.")
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; "Odds and ends"
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(number->string (number -> string)
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"Converts a number to a string.")
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(integer->char (integer -> char)
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"Lookups the character that corresponds to the given integer (exact only!) in the ASCII table (if any).")
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((beginner-random random) (integer -> integer)
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"Generates a random natural number less than some given integer (exact only!).")
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(current-seconds (-> integer)
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"Evaluates the current time in seconds elapsed"
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" (since a platform-specific starting date).")
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(e real
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"Euler's number.")
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(pi real
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"The ratio of a circle's circumference to its diameter."))
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("Booleans"
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(boolean? (any -> boolean)
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"Determines whether some value is a boolean.")
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(boolean=? (boolean boolean -> boolean)
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"Determines whether two booleans are equal.")
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(false? (any -> boolean)
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"Determines whether a value is false.")
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((beginner-not not) (boolean -> boolean)
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"Evaluates the negation of a boolean value."))
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("Symbols"
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(symbol? (any -> boolean)
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"Determines whether some value is a symbol.")
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(symbol=? (symbol symbol -> boolean)
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"Determines whether two symbols are equal.")
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(symbol->string (symbol -> string)
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"Converts a symbol to a string.") )
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("Lists"
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(cons? (any -> boolean)
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"Determines whether some value is a constructed list.")
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#;
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(pair? (any -> boolean)
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"Determines whether some value is a constructed list.")
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(empty? (any -> boolean)
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"Determines whether some value is the empty list.")
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(null? (any -> boolean)
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"Determines whether some value is the empty list.")
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((beginner-cons cons) (X (listof X) -> (listof X))
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"Constructs a list.")
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(null empty
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"The empty list.")
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((beginner-first first) ( (cons Y (listof X)) -> Y )
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"Selects the first item of a non-empty list.")
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((beginner-car car) ( (cons Y (listof X)) -> Y )
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"Selects the first item of a non-empty list.")
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((beginner-rest rest) ((cons Y (listof X)) -> (listof X))
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"Selects the rest of a non-empty list.")
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((beginner-cdr cdr) ((cons Y (listof X)) -> (listof X))
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"Selects the rest of a non-empty list.")
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(second ( (cons Z (cons Y (listof X))) -> Y )
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"Selects the second item of a non-empty list.")
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(cadr ( (cons Z (cons Y (listof X))) -> Y )
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"Selects the second item of a non-empty list.")
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(cdar ( (cons (cons Z (listof Y)) (listof X)) -> (listof Y) )
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"Selects the rest of a non-empty list in a list.")
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(caar ( (cons (cons Z (listof Y)) (listof X)) -> Z )
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"Selects the first item of the first list in a list.")
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(cddr ( (cons Z (cons Y (listof X))) -> (listof X) )
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"Selects the rest of the rest of a list.")
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(third ( (cons W (cons Z (cons Y (listof X)))) -> Y )
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"Selects the third item of a non-empty list.")
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(caddr ( (cons W (cons Z (cons Y (listof X)))) -> Y )
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"Selects the third item of a non-empty list.")
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(caadr ( (cons (cons (cons W (listof Z)) (listof Y)) (listof X)) -> (listof Z) )
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"Selects the rest of the first list in the first list of a list.")
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(caaar ( (cons (cons (cons W (listof Z)) (listof Y)) (listof X)) -> W )
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"Selects the first item of the first list in the first list of a list.")
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(cdaar ( (cons (cons (cons W (listof Z)) (listof Y)) (listof X)) -> (listof Z) )
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"Selects the rest of the first list in the first list of a list.")
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(cdadr ( (cons W (cons (cons Z (listof Y)) (listof X))) -> (listof Y) )
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"Selects the rest of the first list in the rest of a list.")
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(cadar ( (cons (cons W (cons Z (listof Y))) (listof X)) -> Z )
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"Selects the second item of the first list of a list.")
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(cddar ( (cons (cons W (cons Z (listof Y))) (listof X)) -> (listof Y) )
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"Selects the rest of the rest of the first list of a list.")
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(cdddr ( (cons W (cons Z (cons Y (listof X)))) -> (listof X) )
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"Selects the rest of the rest of the rest of a list.")
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(fourth ( (listof Y) -> Y ) ; domain: (cons V (cons W (cons Z (cons Y (listof X)))))
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"Selects the fourth item of a non-empty list.")
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(cadddr ( (listof Y) -> Y ) ; domain: (cons V (cons W (cons Z (cons Y (listof X)))))
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"Selects the fourth item of a non-empty list.")
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(fifth ( (listof Y) -> Y ) ; domain: (cons U (cons V (cons W (cons Z (cons Y (listof X))))))
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"Selects the fifth item of a non-empty list.")
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(sixth ( (listof Y) -> Y ) ; domain: (cons T (cons U (cons V (cons W (cons Z (cons Y (listof X)))))))
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"Selects the sixth item of a non-empty list.")
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(seventh ( (listof Y) -> Y ) ; domain: (cons S (cons T (cons U (cons V (cons W (cons Z (cons Y (listof X))))))))
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"Selects the seventh item of a non-empty list.")
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(eighth ( (listof Y) -> Y ) ; domain: (cons R (cons S (cons T (cons U (cons V (cons W (cons Z (cons Y (listof X)))))))))
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"Selects the eighth item of a non-empty list.")
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(list-ref ((listof X) natural-number -> X )
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"Extracts the indexed item from the list.")
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(list (any ... -> (listof any)) "Constructs a list of its arguments.")
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(make-list (natural-number any -> (listof any))
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"Constructs a list of k (the first argument) copies of x (the second argument).")
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((beginner-list* list*) (any ... (listof any) -> (listof any))
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"Constructs a list by adding multiple items to a list.")
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((beginner-range range) (number number number -> (listof number))
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"(range start end step) constructs a list of numbers by _step_ping from _start_ to _end_ list.")
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((beginner-append append) ((listof any) (listof any) (listof any) ... -> (listof any))
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"Creates a single list from several, by juxtaposition of the items.")
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(length ((listof any) -> number)
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"Evaluates the number of items on a list.")
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(memq (any (listof any) -> (union false list))
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"Determines whether some value is on some list"
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" if so, it produces the suffix of the list that starts with x"
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" if not, it produces false."
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" (It compares values with the eq? predicate.)")
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(memv (any (listof any) -> (union false list))
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"Determines whether some value is on the list"
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" if so, it produces the suffix of the list that starts with x"
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" if not, it produces false."
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" (It compares values with the eqv? predicate.)")
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((beginner-member? member?) (any (listof any) -> boolean)
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"Determines whether some value is on the list"
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" (comparing values with equal?).")
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((beginner-member member) (any (listof any) -> boolean)
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"Determines whether some value is on the list"
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" (comparing values with equal?).")
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((beginner-remove remove) (any (listof any) -> (listof any))
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"Constructs a list like the given one with the first occurrence of the given item removed"
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" (comparing values with equal?).")
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(reverse ((listof any) -> list)
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"Creates a reversed version of a list.")
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(assq (X (listof (cons X Y)) -> (union false (cons X Y)))
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"Determines whether some item is the first item of a pair"
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" in a list of pairs."))
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("Posns"
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(posn signature "Signature for posns.")
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(make-posn (any any -> posn) "Constructs a posn from two arbitrary values.")
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(posn? (any -> boolean) "Determines if its input is a posn.")
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(posn-x (posn -> any) "Extracts the x component of a posn.")
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(posn-y (posn -> any) "Extracts the y component of a posn."))
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("Characters"
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(char? (any -> boolean)
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"Determines whether a value is a character.")
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(char=? (char char char ... -> boolean)
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"Determines whether two characters are equal.")
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(char<? (char char char ... -> boolean)
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"Determines whether a character precedes another.")
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(char>? (char char char ... -> boolean)
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"Determines whether a character succeeds another.")
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(char<=? (char char char ... -> boolean)
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"Determines whether a character precedes another"
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" (or is equal to it).")
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(char>=? (char char char ... -> boolean)
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"Determines whether a character succeeds another"
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" (or is equal to it).")
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(char-ci=? (char char char ... -> boolean)
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"Determines whether two characters are equal"
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" in a case-insensitive manner.")
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(char-ci<? (char char char ... -> boolean)
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"Determines whether a character precedes another"
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" in a case-insensitive manner.")
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(char-ci>? (char char char ... -> boolean)
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"Determines whether a character succeeds another"
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" in a case-insensitive manner.")
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(char-ci<=? (char char char ... -> boolean)
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"Determines whether a character precedes another"
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" (or is equal to it) in a case-insensitive manner.")
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(char-ci>=? (char char char ... -> boolean)
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"Determines whether a character succeeds another"
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" (or is equal to it) in a case-insensitive manner.")
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(char-numeric? (char -> boolean)
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"Determines whether a character represents a digit.")
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(char-alphabetic? (char -> boolean)
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"Determines whether a character represents"
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" an alphabetic character.")
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(char-whitespace? (char -> boolean)
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"Determines whether a character represents space.")
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(char-upper-case? (char -> boolean)
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"Determines whether a character is an"
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" upper-case character.")
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(char-lower-case? (char -> boolean)
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"Determines whether a character is a"
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" lower-case character.")
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(char-upcase (char -> char)
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"Determines the equivalent upper-case character.")
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(char-downcase (char -> char)
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"Determines the equivalent lower-case character.")
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(char->integer (char -> integer)
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"Lookups the number that corresponds to the"
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" given character in the ASCII table (if any)."))
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("Strings"
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(string? (any -> boolean)
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"Determines whether a value is a string.")
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(string-length (string -> nat)
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"Determines the length of a string.")
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((beginner-string-ith string-ith) (string nat -> string)
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"Extracts the ith 1-letter substring from the given one.")
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((beginner-replicate replicate) (nat string -> string)
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"Replicates the given string.")
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((beginner-int->string int->string) (integer -> string)
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"Converts an integer in [0,55295] or [57344 1114111] to a 1-letter string.")
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((beginner-string->int string->int) (string -> integer)
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"Converts a 1-letter string to an integer in [0,55295] or [57344, 1114111].")
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((beginner-explode explode) (string -> (listof string))
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"Translates a string into a list of 1-letter strings.")
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((beginner-implode implode) ((listof string) -> string)
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"Concatenates the list of 1-letter strings into one string.")
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((beginner-string-numeric? string-numeric?) (string -> boolean)
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"Determines whether all 'letters' in the string are numeric.")
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((beginner-string-alphabetic? string-alphabetic?) (string -> boolean)
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"Determines whether all 'letters' in the string are alphabetic.")
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((beginner-string-whitespace? string-whitespace?) (string -> boolean)
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"Determines whether all 'letters' in the string are white space.")
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((beginner-string-upper-case? string-upper-case?) (string -> boolean)
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"Determines whether all 'letters' in the string are upper case.")
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((beginner-string-lower-case? string-lower-case?) (string -> boolean)
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"Determines whether all 'letters' in the string are lower case.")
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(string (char ... -> string)
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"Builds a string of the given characters.")
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(make-string (nat char -> string)
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"Produces a string of given length"
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" from a single given character.")
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(string-ref (string nat -> char)
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"Extracts the i-the character from a string.")
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(substring (string nat nat -> string)
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"Extracts the substring starting at a 0-based index"
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" up to the second 0-based index (exclusive).")
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(string-copy (string -> string)
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"Copies a string.")
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(string-append (string ... -> string)
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"Juxtaposes the characters of several strings.")
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(string=? (string string string ... -> boolean)
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"Compares two strings character-wise.")
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(string<? (string string string ... -> boolean)
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"Determines whether one string alphabetically"
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" precedes another.")
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(string>? (string string string ... -> boolean)
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"Determines whether one string alphabetically"
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" succeeds another.")
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(string<=? (string string string ... -> boolean)
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"Determines whether one string alphabetically"
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" precedes another (or is equal to it).")
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(string>=? (string string string ... -> boolean)
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"Determines whether one string alphabetically"
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" succeeds another (or is equal to it).")
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(string-ci=? (string string string ... -> boolean)
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"Compares two strings character-wise"
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" in a case-insensitive manner.")
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(string-ci<? (string string string ... -> boolean)
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"Determines whether one string alphabetically"
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" precedes another in a case-insensitive manner.")
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(string-ci>? (string string string ... -> boolean)
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"Determines whether one string alphabetically"
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" succeeds another in a case-insensitive manner.")
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(string-ci<=? (string string string ... -> boolean)
|
|
"Determines whether one string alphabetically"
|
|
" precedes another (or is equal to it)"
|
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" 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.")
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|
|
|
(string->symbol (string -> symbol)
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"Converts a string into a symbol.")
|
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(string->number (string -> (union number false))
|
|
"Converts a string into a number,"
|
|
" produce false if impossible.")
|
|
(string->list (string -> (listof char))
|
|
"Converts a string into a list of characters.")
|
|
(list->string ((listof char) -> string)
|
|
"Converts a s list of characters into a string.")
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|
|
|
(format (string any ... -> string)
|
|
"Formats a string, possibly embedding values."))
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|
|
|
("Images"
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|
(image? (any -> boolean)
|
|
"Determines whether a value is an image.")
|
|
(image=? (image image -> boolean)
|
|
"Determines whether two images are equal."))
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|
|
|
("Misc"
|
|
(identity (any -> any)
|
|
"Returns the argument unchanged.")
|
|
((beginner-error error) (any ... -> void) "signals an error, combining the given values into an error message.\n\nIf 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 signaling the error).")
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|
((beginner-struct? struct?) (any -> boolean)
|
|
"Determines whether some value is a structure.")
|
|
((beginner-equal? equal?) (any any -> boolean)
|
|
"Determines whether two values are structurally equal"
|
|
" where basic values are compared with the eqv? predicate.")
|
|
(eq? (any any -> boolean)
|
|
"Determines whether two values are equivalent from the"
|
|
" computer's perspective (intensional).")
|
|
(eqv? (any any -> boolean)
|
|
"Determines whether two values are equivalent from the"
|
|
" perspective of all functions that can be applied to it (extensional).")
|
|
((beginner-=~ =~) (number number non-negative-real -> boolean)
|
|
"Checks whether two numbers are within some amount (the third argument) of either other.")
|
|
((beginner-equal~? equal~?) (any any non-negative-real -> boolean)
|
|
"Compares like equal? on the first two arguments, except using =~ in the case of numbers.")
|
|
(eof eof
|
|
"The end-of-file value.")
|
|
(eof-object? (any -> boolean)
|
|
"Determines whether some value is the end-of-file value.")
|
|
((beginner-exit exit) ( -> void)
|
|
"Exits the running program.")))
|