493 lines
21 KiB
Scheme
493 lines
21 KiB
Scheme
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(module beginner-funs 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.ss"
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"../posn.ss"
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"../imageeq.ss")
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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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"to determine whether some value is a number")
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(= (number number number ... -> boolean)
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"to compare numbers for equality")
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(< (real real real ... -> boolean)
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"to compare real numbers for less-than")
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(> (real real real ... -> boolean)
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"to compare real numbers for greater-than")
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(<= (real real real ... -> boolean)
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"to compare real numbers for less-than or equality")
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(>= (real real ... -> boolean)
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"to compare real numbers for greater-than or equality")
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((beginner-+ +) (number number number ... -> number)
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"to compute the sum of the input numbers")
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(- (number number ... -> number)
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"to subtract 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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"to compute the product of all of the input numbers")
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((beginner-/ /) (number number number ... -> number)
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"to divide 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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"to determine the largest number")
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(min (real real ... -> real)
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"to determine the smallest number")
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(quotient (integer integer -> integer)
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"to divide the first integer (exact or inexact) into the second; try (quotient 3 4) and (quotient 4 3)")
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(remainder (integer integer -> integer)
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"to determine 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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"to find 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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"to compute the square of a number")
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(sqrt (number -> number)
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"to compute the square root of a number")
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(integer-sqrt (number -> integer)
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"to compute the integer (exact or inexact) square root of a number")
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(expt (number number -> number)
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"to compute the power of the first to the second number")
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(abs (real -> real)
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"to compute 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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"to compute the sign of a real number")
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;; fancy numeric
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(exp (number -> number)
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"to compute e raised to a number")
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(log (number -> number)
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"to compute the base-e logarithm of a number")
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;; trigonometry
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(sin (number -> number)
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"to compute the sine of a number (radians)")
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(cos (number -> number)
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"to compute the cosine of a number (radians)")
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(tan (number -> number)
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"to compute the tangent of a number (radians)")
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(asin (number -> number)
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"to compute the arcsine (inverse of sin) of a number")
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(acos (number -> number)
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"to compute the arccosine (inverse of cos) of a number")
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(atan (number -> number)
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"to compute the arctan (inverse of tan) of a number")
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(sinh (number -> number)
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"to compute the hyperbolic sine of a number")
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(cosh (number -> number)
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"to compute the hyperbolic cosine of a number")
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(exact? (number -> boolean)
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"to determine whether some number is exact")
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(integer? (any -> boolean)
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"to determine whether some value is an integer (exact or inexact)")
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(zero? (number -> boolean)
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"to determine if some value is zero or not")
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(positive? (number -> boolean)
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"to determine if some value is strictly larger than zero")
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(negative? (number -> boolean)
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"to determine if some value is strictly smaller than zero")
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(odd? (integer -> boolean)
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"to determine if some integer (exact or inexact) is odd or not")
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(even? (integer -> boolean)
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"to determine if some integer (exact or inexact) is even or not")
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(add1 (number -> number)
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"to compute a number one larger than a given number")
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(sub1 (number -> number)
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"to compute a number one smaller than a given number")
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(lcm (integer integer ... -> integer)
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"to compute the least common multiple of two integers (exact or inexact)")
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(gcd (integer integer ... -> integer)
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"to compute the greatest common divisior of two integers (exact or inexact)")
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(rational? (any -> boolean)
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"to determine whether some value is a rational number")
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(numerator (rat -> integer)
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"to compute the numerator of a rational")
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(denominator (rat -> integer)
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"to compute the denominator of a rational")
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(inexact? (number -> boolean)
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"to determine whether some number is inexact")
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(real? (any -> boolean)
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"to determine whether some value is a real number")
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(floor (real -> integer)
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"to determine the closest integer (exact or inexact) below a real number")
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(ceiling (real -> integer)
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"to determine the closest integer (exact or inexact) above a real number")
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(round (real -> integer)
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"to round a real number to an integer (rounds to even to break ties)")
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(complex? (any -> boolean)
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"to determine whether some value is complex")
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(make-polar (real real -> number)
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"to create a complex from a magnitude and angle")
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(make-rectangular (real real -> number)
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"to create a complex from a real and an imaginary part")
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(real-part (number -> real)
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"to extract the real part from a complex number")
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(imag-part (number -> real)
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"to extract the imaginary part from a complex number")
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(magnitude (number -> real)
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"to determine the magnitude of a complex number")
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(angle (number -> real)
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"to extract the angle from a complex number")
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(conjugate (number -> number)
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"to compute the conjugate of a complex number")
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(exact->inexact (number -> number)
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"to convert an exact number to an inexact one")
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(inexact->exact (number -> number)
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"to approximate 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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"to convert a number to a string")
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(integer->char (integer -> char)
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"to lookup 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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"to generate a random natural number less than some given integer (exact only!)")
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(current-seconds (-> integer)
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"to compute 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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"to determine whether some value is a boolean")
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(boolean=? (boolean boolean -> boolean)
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"to determine whether two booleans are equal")
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(false? (any -> boolean)
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"to determine whether a value is false")
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((beginner-not not) (boolean -> boolean)
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"to compute the negation of a boolean value"))
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("Symbols"
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(symbol? (any -> boolean)
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"to determine whether some value is a symbol")
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(symbol=? (symbol symbol -> boolean)
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"to determine whether two symbols are equal")
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(symbol->string (symbol -> string)
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"to convert a symbol to a string") )
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("Lists"
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(cons? (any -> boolean)
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"to determine whether some value is a constructed list")
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(pair? (any -> boolean)
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"to determine whether some value is a constructed list")
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(empty? (any -> boolean)
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"to determine whether some value is the empty list")
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(null? (any -> boolean)
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"to determine whether some value is the empty list")
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((beginner-cons cons) (X (listof X) -> (listof X))
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"to construct a list")
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(null empty
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"the empty list")
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(first ( (cons Y (listof X)) -> Y )
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"to select the first item of a non-empty list")
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(car ( (cons Y (listof X)) -> Y )
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"to select the first item of a non-empty list")
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(rest ((cons Y (listof X)) -> (listof X))
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"to select the rest of a non-empty list")
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(cdr ((cons Y (listof X)) -> (listof X))
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"to select the rest of a non-empty list")
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(second ( (cons Z (cons Y (listof X))) -> Y )
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"to select the second item of a non-empty list")
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(cadr ( (cons Z (cons Y (listof X))) -> Y )
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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select 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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"to select the eighth item of a non-empty list")
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(list-ref ((listof X) natural-number -> X )
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"to extract the indexed item from the list")
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(list (any ... -> (listof any)) "to construct a list of its arguments")
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(make-list (natural-number any -> (listof any)) "(make-list k x) constructs a list of k copies of x")
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((beginner-list* list*) (any ... (listof any) -> (listof any))
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"to construct a list by adding multiple items to a list")
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((beginner-append append) ((listof any) (listof any) (listof any) ... -> (listof any))
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"to create a single list from several, by juxtaposition of the items")
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(length ((listof any) -> number)
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"to compute the number of items on a list")
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(memq (any (listof any) -> (union false list))
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"to determine 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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"to determine 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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"to determine 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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"to construct 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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"to create 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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"to determine 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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(make-posn (number number -> posn) "to construct a posn")
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(posn? (anything -> boolean) "to determine if its input is a posn")
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(posn-x (posn -> number) "to extract the x component of a posn")
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(posn-y (posn -> number) "to extract the y component of a posn"))
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("Characters"
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(char? (any -> boolean)
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"to determine whether a value is a character")
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(char=? (char char char ... -> boolean)
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"to determine whether two characters are equal")
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(char<? (char char char ... -> boolean)
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"to determine whether a character precedes another")
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(char>? (char char char ... -> boolean)
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"to determine whether a character succeeds another")
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(char<=? (char char char ... -> boolean)
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"to determine 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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"to determine 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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"to determine 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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"to determine 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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"to determine 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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"to determine 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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"to determine 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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"to determine whether a character represents a digit")
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(char-alphabetic? (char -> boolean)
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"to determine whether a character represents"
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" an alphabetic character")
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(char-whitespace? (char -> boolean)
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"to determine whether a character represents space")
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(char-upper-case? (char -> boolean)
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"to determine 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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"to determine whether a character is a"
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" lower-case character")
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(char-upcase (char -> char)
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"to determine the equivalent upper-case character")
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(char-downcase (char -> char)
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"to determine the equivalent lower-case character")
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(char->integer (char -> integer)
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"to lookup 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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"to determine whether a value is a string")
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(string-length (string -> nat)
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"to determine the length of a string")
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((beginner-string-ith string-ith) (string nat -> string)
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"to extract the ith 1-letter substring from the given one")
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((beginner-replicate replicate) (nat string -> string)
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"to replicate the given string")
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((beginner-int->string int->string) (integer -> string)
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"to convert 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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"to convert 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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"to translate a string into a list of 1-letter strings")
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((beginner-implode implode) ((listof string) -> string)
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"to concatenate the list of 1-letter strings into one string")
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((beginner-string-numeric? string-numeric?) (string -> boolean)
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"to determine whether all 'letters' in the string are numeric")
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((beginner-string-alphabetic? string-alphabetic?) (string -> boolean)
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"to determine whether all 'letters' in the string are alphabetic")
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((beginner-string-whitespace? string-whitespace?) (string -> boolean)
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"to determine 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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"to determine 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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"to determine whether all 'letters' in the string are lower case")
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(string (char ... -> string)
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"(string c1 c2 ...) builds a string")
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(make-string (nat char -> string)
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"to produce 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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"to extract the i-the character from a string")
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(substring (string nat nat -> string)
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"to extract 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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"to copy a string")
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(string-append (string ... -> string)
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"to juxtapose the characters of several strings")
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(string=? (string string string ... -> boolean)
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"to compare two strings character-wise")
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(string<? (string string string ... -> boolean)
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"to determine whether one string alphabetically"
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" precedes another")
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(string>? (string string string ... -> boolean)
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"to determine whether one string alphabetically"
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" succeeds another")
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(string<=? (string string string ... -> boolean)
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"to determine 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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"to determine 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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"to compare 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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"to determine 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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"to determine 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)
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"to determine whether one string alphabetically"
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" precedes another (or is equal to it)"
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" in a case-insensitive manner")
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(string-ci>=? (string string string ... -> boolean)
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"to determine whether one string alphabetically"
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" succeeds another (or is equal to it)"
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" in a case-insensitive manner")
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(string->symbol (string -> symbol)
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"to convert a string into a symbol")
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(string->number (string -> (union number false))
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"to convert a string into a number,"
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" produce false if impossible")
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(string->list (string -> (listof char))
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"to convert a string into a list of characters")
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(list->string ((listof char) -> string)
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"to convert a s list of characters into a string")
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(format (string any ... -> string)
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"to format a string, possibly embedding values"))
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("Images"
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(image? (any -> boolean)
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"to determine whether a value is an image")
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(image=? (image image -> boolean)
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"to determine whether two images are equal"))
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("Misc"
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(identity (any -> any)
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"to return the argument unchanged")
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((beginner-error error) (any ... -> void) "to signal an error, turning the given values into an error message ")
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((beginner-struct? struct?) (any -> boolean)
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"to determine whether some value is a structure")
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((beginner-equal? equal?) (any any -> boolean)
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"to determine whether two values are structurally equal"
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" where basic values are compared with the eqv? predicate")
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(eq? (any any -> boolean)
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"to determine whether two values are equivalent from the"
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" computer's perspective (intensional)")
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(eqv? (any any -> boolean)
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"to determine whether two values are equivalent from the"
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" perspective of all functions that can be applied to it (extensional)")
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((beginner-=~ =~) (real real non-negative-real -> boolean)
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"to check whether two real numbers are within some amount (the third argument) of either other")
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((beginner-equal~? equal~?) (any any non-negative-real -> boolean)
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"to compare like equal? on the first two arguments, except using =~ in the case of real numbers")
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(eof eof
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"the end-of-file value")
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(eof-object? (any -> boolean)
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"to determine whether some value is the end-of-file value")
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((beginner-exit exit) ( -> void)
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"to exit the running program"))))
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