913 lines
66 KiB
Racket
913 lines
66 KiB
Racket
#lang at-exp racket
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;; weed out: string-copy, eqv?, struct? -- no need for beginners, move to advanced
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;; eq? is questionable, but okay if someone uses BSL to teach not out of HtDP
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;;
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(require mzlib/etc mzlib/list mzlib/math syntax/docprovide
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(for-syntax "firstorder.rkt")
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(for-syntax syntax/parse)
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(for-syntax racket/syntax))
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;; Implements the procedures:
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(require "teachprims.rkt" "teach.rkt" lang/posn lang/imageeq "provide-and-scribble.rkt")
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(define-syntax (provide-and-wrap stx)
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(syntax-parse stx
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; (defproc (name args ...) range w ...)
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[(provide-and-wrap wrap doc-tag:id requires (title df ...) ...)
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(let* ((defs (map syntax->list (syntax->list #'((df ...) ...))))
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(names (map extract-names defs))
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(tmps (map generate-temporaries names))
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(internals (map (lambda (x)
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(map (lambda (n)
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(syntax-parse n
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[(internal-name:id external-name:id) #'internal-name]
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[n:id #'n]))
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x))
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names))
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(externals (map (lambda (x)
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(map (lambda (n)
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(syntax-parse n
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[(internal-name:id external-name:id) #'external-name]
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[n:id #'n]))
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x))
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names)))
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(with-syntax* ([((f ...) ...) tmps]
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[((internal-name ...) ...) internals]
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[((dg ...) ...)
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(map (lambda (d.. f.. ex..)
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(map (lambda (d f external-name)
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(syntax-case d ()
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[(defproc [name args ...] range w ...)
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#`(defproc [(#,f #,external-name) args ...] range w ...)]
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[(defthing name range w ...)
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#'(defthing name range w ...)]))
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d.. f.. ex..))
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defs tmps externals)])
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#'(begin ;; create two modules:
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;; one that makes definitions first-order
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(module+ with-wrapper
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(wrap f internal-name) ... ...
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(provide-and-scribble doc-tag requires (title dg ...) ...))
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;; and one that doesn't
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(module+ without-wrapper
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(provide-and-scribble doc-tag requires (title df ...) ...)))))]))
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;; MF: this is now an ugly kludge, left over from my original conversion of Matthew's docs for *SL
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(define-syntax (in-rator-position-only stx)
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(syntax-case stx ()
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[(_ new-name orig-name)
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(let ([new (syntax new-name)]
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[orig (syntax orig-name)])
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(cond
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;; Some things are not really functions:
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[(memq (syntax-e orig) '(pi e null eof))
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#'(define new-name orig-name)]
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[else
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#'(define-syntax new-name
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(make-first-order
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(lambda (stx)
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(syntax-case stx ()
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[(id . args) (syntax/loc stx (beginner-app orig-name . args))]
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[_else
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(raise-syntax-error
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#f
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"expected a function call, but there is no open parenthesis before this function"
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stx)]))
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#'orig-name))]))]))
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;; procedures with documentation:
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(provide-and-wrap
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in-rator-position-only
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procedures
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(begin
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(require scribble/manual scribble/eval "sl-eval.rkt")
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(define (bsl)
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(define *bsl
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(bsl+-eval
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(require 2htdp/image)
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(define c1 (circle 10 "solid" "green"))
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(define zero 0)
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(define one (list 1))
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(define q (make-posn "bye" 2))
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(define p (make-posn 2 -3))
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(define a (list (list 'a 22) (list 'b 8) (list 'c 70)))
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(define v (list 1 2 3 4 5 6 7 8 9 'A))
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(define w (list (list (list (list "bye") 3) true) 42))
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(define z (list (list (list (list 'a 'b) 2 3) ) (list false true) "world"))
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(define y (list (list (list 1 2 3) false "world")))
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(define x (list 2 "hello" true))))
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(set! bsl (lambda () *bsl))
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*bsl))
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("Numbers: Integers, Rationals, Reals, Complex, Exacts, Inexacts"
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@defproc[(number? [n any/c]) boolean?]{
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Determines whether some value is a number:
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@interaction[#:eval (bsl) (number? "hello world") (number? 42)]
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}
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@defproc[(= [x number][y number][z number] ...) boolean?]{
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Compares numbers for equality.
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@interaction[#:eval (bsl) (= 42 2/5)]
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}
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@defproc[(< [x real][y real][z real] ...) boolean?]{
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Compares (real) numbers for less-than.
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@interaction[#:eval (bsl) (< 42 2/5)]
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}
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@defproc[(> [x real][y real][z real] ...) boolean?]{
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Compares (real) numbers for greater-than.
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@interaction[#:eval (bsl) (> 42 2/5)]
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}
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@defproc[(<= [x real][y real][z real] ...) boolean?]{
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Compares (real) numbers for less-than or equality.
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@interaction[#:eval (bsl) (<= 42 2/5)]
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}
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@defproc[(>= [x real][y real][z real] ...) boolean?]{
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Compares (real) numbers for greater-than or equality.
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@interaction[#:eval (bsl) (>= 42 42)]
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}
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@defproc[((beginner-+ +) [x number][y number][z number] ...) number]{
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@index["plus"]{}@index["add"]{Adds} up all numbers.
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@interaction[#:eval (bsl) (+ 2/3 1/16) (+ 3 2 5 8)]
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}
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@defproc[(- [x number][y number] ...) number]{
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@index["subtract"]{Subtracts} the second (and following) number(s) from the first ;
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negates the number if there is only one argument.
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@interaction[#:eval (bsl) (- 5) (- 5 3) (- 5 3 1)]
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}
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@defproc[((beginner-* *) [x number][y number][z number] ...) number]{
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@index["times"]{}@index["product"]{}@index["multiply"]{Multiplies} all numbers.
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@interaction[#:eval (bsl) (* 5 3) (* 5 3 2)]
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}
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@defproc[((beginner-/ /) [x number][y number][z number] ...) number]{
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@index["divide"]{Divides} the first by the second (and all following) number(s).
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@interaction[#:eval (bsl) (/ 12 2) (/ 12 2 3)]
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}
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@defproc[(max [x real][y real] ...) real]{
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Determines the largest number---aka, the @index["maximum"]{maxiumum}.
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@interaction[#:eval (bsl) (max 3 2 8 7 2 9 0)]
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}
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@defproc[(min [x real][y real] ...) real]{
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Determines the smallest number---aka, the @index["minimum"]{miniumum}.
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@interaction[#:eval (bsl) (min 3 2 8 7 2 9 0)]
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}
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@defproc[(quotient [x integer][y integer]) integer]{
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Divides the second integer---also called divisor---into the first---known as
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dividend---to obtain the @index[(list "divide" "quotient")]{quotient}.
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@interaction[#:eval (bsl) (quotient 9 2) (quotient 3 4)]
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}
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@defproc[(remainder [x integer][y integer]) integer]{
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Determines the @index[(list "divide" "remainder")]{remainder} of dividing the first by the second integer
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(exact or inexact).
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@interaction[#:eval (bsl) (remainder 9 2) (remainder 3 4)]
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}
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@defproc[(modulo [x integer][y integer]) integer]{
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Finds the remainder of the division of the first number by the second:
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@interaction[#:eval (bsl) (modulo 9 2) (modulo 3 -4)]
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}
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@defproc[((beginner-sqr sqr) [x number]) number]{
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Computes the @index["square"]{square} of a number.
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@interaction[#:eval (bsl) (sqr 8)]
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}
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@defproc[(sqrt [x number]) number]{
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Computes the square root of a number.
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@interaction[#:eval (bsl) (sqrt 9) (sqrt 2)]
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}
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@defproc[(integer-sqrt [x number]) integer]{
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Computes the integer (exact or inexact) square root of a number.
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@interaction[#:eval (bsl) (sqrt 11)]
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}
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@defproc[(abs [x real]) real]{
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Determines the absolute value of a real number.
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@interaction[#:eval (bsl) (abs -12)]
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}
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@defproc[(sgn [x real]) (union 1 #i1.0 0 #i0.0 -1 #i-1.0)]{
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Determines the sign of a real number.
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@interaction[#:eval (bsl) (sgn -12)]
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}
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;; exponents and logarithms
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@defproc[(expt [x number][y number]) number]{
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Computes the power of the first to the second number.
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@interaction[#:eval (bsl) (expt 16 1/2) (expt 3 -4)]
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}
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@defproc[(exp [x number]) number]{
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Determines e raised to a number.
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@interaction[#:eval (bsl) (exp -2)]
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}
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@defproc[(log [x number]) number]{
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Determines the base-e logarithm of a number.
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@interaction[#:eval (bsl) (log 12)]
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}
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;; trigonometry
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@defproc[(sin [x number]) number]{
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Computes the @index["sine"]{sine} of a number (radians).
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@interaction[#:eval (bsl) (sin pi)]
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}
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@defproc[(cos [x number]) number]{
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Computes the @index["cosine"]{cosine} of a number (radians).
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@interaction[#:eval (bsl) (cos pi)]
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}
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@defproc[(tan [x number]) number]{
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Computes the @index["tangent"]{tangent} of a number (radians).
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@interaction[#:eval (bsl) (tan pi)]
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}
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@defproc[(asin [x number]) number]{
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Computes the arcsine (inverse of sin) of a number.
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@interaction[#:eval (bsl) (asin 0)]
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}
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@defproc[(acos [x number]) number]{
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Computes the arccosine (inverse of cos) of a number.
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@interaction[#:eval (bsl) (acos 0)]
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}
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@defproc[(atan [x number] [y number]) number]{
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Computes the arctan of the given number or the ratio of the two given numbers.
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@interaction[#:eval (bsl) (atan 0) (atan 3 4)]
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}
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@defproc[(sinh [x number]) number]{
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Computes the hyperbolic sine of a number.
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@interaction[#:eval (bsl) (sinh 10)]
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}
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@defproc[(cosh [x number]) number]{
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Computes the hyperbolic cosine of a number.
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@interaction[#:eval (bsl) (cosh 10)]
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}
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;; predicates
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@defproc[(exact? [x number]) boolean?]{
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Determines whether some number is exact.
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@interaction[#:eval (bsl) (exact? (sqrt 2))]
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}
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@defproc[(integer? [x any/c]) boolean?]{
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Determines whether some value is an integer (exact or inexact).
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@interaction[#:eval (bsl) (integer? (sqrt 2))]
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}
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@defproc[(zero? [x number]) boolean?]{
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Determines if some value is zero or not.
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@interaction[#:eval (bsl) (zero? 2)]
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}
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@defproc[(positive? [x number]) boolean?]{
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Determines if some value is strictly larger than zero.
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@interaction[#:eval (bsl) (positive? -2)]
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}
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@defproc[(negative? [x number]) boolean?]{
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Determines if some value is strictly smaller than zero.
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@interaction[#:eval (bsl) (negative? -2)]
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}
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@defproc[(odd? [x integer]) boolean?]{
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Determines if some integer (exact or inexact) is odd or not.
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@interaction[#:eval (bsl) (odd? 2)]
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}
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@defproc[(even? [x integer]) boolean?]{
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Determines if some integer (exact or inexact) is even or not.
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@interaction[#:eval (bsl) (even? 2)]
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}
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@defproc[(rational? [x any/c]) boolean?]{
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Determines whether some value is a rational number.
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@interaction[#:eval (bsl) (rational? 1-2i)]
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}
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@defproc[(inexact? [x number]) boolean?]{
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Determines whether some number is inexact.
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@interaction[#:eval (bsl) (inexact? 1-2i)]
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}
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@defproc[(real? [x any/c]) boolean?]{
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Determines whether some value is a real number.
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@interaction[#:eval (bsl) (real? 1-2i)]
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}
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@defproc[(complex? [x any/c]) boolean?]{
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Determines whether some value is complex.
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@interaction[#:eval (bsl) (real? 1-2i)]
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}
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;; common utilities
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@defproc[(add1 [x number]) number]{
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Incrementes the given number.
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@interaction[#:eval (bsl) (add1 2)]
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}
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@defproc[(sub1 [x number]) number]{
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Decrements the given number.
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@interaction[#:eval (bsl) (sub1 2)]
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}
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@defproc[(lcm [x integer][y integer] ...) integer]{
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Determines the least common multiple of two integers (exact or inexact).
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@interaction[#:eval (bsl) (lcm 6 12 8)]
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}
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@defproc[(gcd [x integer][y integer] ...) integer]{
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Determines the greatest common divisior of two integers (exact or inexact).
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@interaction[#:eval (bsl) (gcd 6 12 8)]
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}
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@defproc[(numerator [x rational?]) integer]{
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Computes the numerator of a rational.
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@interaction[#:eval (bsl) (numerator 2/3)]
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}
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@defproc[(denominator [x rational?]) integer]{
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Computees the denominator of a rational.
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@interaction[#:eval (bsl) (denominator 2/3)]
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}
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@defproc[(floor [x real]) integer]{
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Determines the closest integer (exact or inexact) below a real
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number. See @racket[round].
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@interaction[#:eval (bsl) (floor 12.3)]
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}
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@defproc[(ceiling [x real]) integer]{
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Determines the closest integer (exact or inexact) above a real
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number. See @racket[round].
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@interaction[#:eval (bsl) (ceiling 12.3)]
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}
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@defproc[(round [x real]) integer]{
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Rounds a real number to an integer (rounds to even to break ties). See
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@racket[floor] and @racket[ceiling].
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@interaction[#:eval (bsl) (round 12.3)]
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}
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@defproc[(make-polar [x real ][y real]) number]{
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Creates a complex from a magnitude and angle.
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@interaction[#:eval (bsl) (make-polar 3 4)]
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}
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@defproc[(make-rectangular [x real][y real]) number]{
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Creates a complex from a real and an imaginary part.
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@interaction[#:eval (bsl) (make-rectangular 3 4)]
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}
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@defproc[(real-part [x number]) real]{
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Extracts the real part from a complex number.
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@interaction[#:eval (bsl) (real-part 3+4i)]
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}
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@defproc[(imag-part [x number]) real]{
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Extracts the imaginary part from a complex number.
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@interaction[#:eval (bsl) (imag-part 3+4i)]
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}
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@defproc[(magnitude [x number]) real]{
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Determines the magnitude of a complex number.
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@interaction[#:eval (bsl) (magnitude (make-polar 3 4))]
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}
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@defproc[(angle [x number]) real]{
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Extracts the angle from a complex number.
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@interaction[#:eval (bsl) (angle (make-polar 3 4))]
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}
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@defproc[(conjugate [x number]) number]{
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Extracts the conjugate of a complex number.
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@interaction[#:eval (bsl) (conjugate (make-polar 3 4))]
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}
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@defproc[(exact->inexact [x number]) number]{
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Converts an exact number to an inexact one.
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@interaction[#:eval (bsl) (exact->inexact 12)]
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}
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@defproc[(inexact->exact [x number]) number]{
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Approximates an inexact number by an exact one.
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@interaction[#:eval (bsl) (inexact->exact #i12)]
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}
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@defproc[(number->string [x number]) string]{
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Converts a number to a string.
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@interaction[#:eval (bsl) (number->string 42)]
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}
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@defproc[(integer->char [x exact-integer?]) char]{
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Lookups the character that corresponds to the given exact integer in the ASCII table (if any).
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@interaction[#:eval (bsl) (integer->char 42)]
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}
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@defproc[((beginner-random random) [x integer]) integer]{
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Generates a random natural number less than some given exact integer.
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@interaction[#:eval (bsl) (random 42)]
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}
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@defproc[(current-seconds) integer]{
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Determines the current time in seconds elapsed (since a platform-specific starting date).
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@interaction[#:eval (bsl) (current-seconds)]
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}
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@defthing[e real]{Euler's number.
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@interaction[#:eval (bsl) e]
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}
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@defthing[pi real]{The ratio of a circle's circumference to its diameter.
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@interaction[#:eval (bsl) pi]
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})
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("Booleans"
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@defproc[(boolean? [x any/c]) boolean?]{
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Determines whether some value is a boolean.
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@interaction[#:eval (bsl) (boolean? 42) (boolean? false)]
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}
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@defproc[(boolean=? [x boolean?][y boolean?]) boolean?]{
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Determines whether two booleans are equal.
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@interaction[#:eval (bsl) (boolean=? true false)]
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}
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@defproc[(false? [x any/c]) boolean?]{
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Determines whether a value is false.
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@interaction[#:eval (bsl) (false? false)]
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}
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@defproc[((beginner-not not) [x boolean?]) boolean?]{
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Negates a boolean value.
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@interaction[#:eval (bsl) (not false)]
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})
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("Symbols"
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@defproc[(symbol? [x any/c]) boolean?]{
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Determines whether some value is a symbol.
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@interaction[#:eval (bsl) (symbol? 'a)]
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}
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@defproc[(symbol=? [x symbol][y symbol]) boolean?]{
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Determines whether two symbols are equal.
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@interaction[#:eval (bsl) (symbol=? 'a 'b)]
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}
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@defproc[(symbol->string [x symbol]) string]{
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Converts a symbol to a string.
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@interaction[#:eval (bsl) (symbol->string 'c)]
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})
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("Lists"
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@defproc[(cons? [x any/c]) boolean?]{
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Determines whether some value is a constructed list.
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@interaction[#:eval (bsl-eval) (cons? (cons 1 empty)) (cons? 42)]
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}
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@defproc[(empty? [x any/c]) boolean?]{
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Determines whether some value is the empty list.
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@interaction[#:eval (bsl) (empty? empty) (empty? 42)]
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}
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@defproc[((beginner-cons cons) [x any/x][y list?]) list?]{
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Constructs a list.
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@interaction[#:eval (bsl-eval) (cons 1 empty)]
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}
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@defproc[((beginner-first first) [x cons?]) any/c]{
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Selects the first item of a non-empty list.
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@interaction[#:eval (bsl) x (first x)]
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}
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@defproc[((beginner-rest rest) [x cons?]) any/c]{
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Selects the rest of a non-empty list.
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@interaction[#:eval (bsl) x (rest x)]
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}
|
|
@defproc[(second [x list?]) any/c]{
|
|
Selects the second item of a non-empty list.
|
|
@interaction[#:eval (bsl) x (second x)]
|
|
}
|
|
@defproc[(third [x list?]) any/c]{
|
|
Selects the third item of a non-empty list.
|
|
@interaction[#:eval (bsl) x (third x)]
|
|
}
|
|
|
|
@defproc[(fourth [x list?]) any/c]{
|
|
Selects the fourth item of a non-empty list.
|
|
@interaction[#:eval (bsl) v (fourth v)]
|
|
}
|
|
|
|
@defproc[(fifth [x list?]) any/c]{
|
|
Selects the fifth item of a non-empty list.
|
|
@interaction[#:eval (bsl) v (fifth v)]
|
|
}
|
|
@defproc[(sixth [x list?]) any/c]{
|
|
Selects the sixth item of a non-empty list.
|
|
@interaction[#:eval (bsl) v (sixth v)]
|
|
}
|
|
@defproc[(seventh [x list?]) any/c]{
|
|
Selects the seventh item of a non-empty list.
|
|
@interaction[#:eval (bsl) v (seventh v)]
|
|
}
|
|
@defproc[(eighth [x list?]) any/c]{
|
|
Selects the eighth item of a non-empty list.
|
|
@interaction[#:eval (bsl) v (eighth v)]
|
|
}
|
|
@defproc[(list-ref [x list?][i natural?]) any/c]{
|
|
Extracts the indexed item from the list.
|
|
@interaction[#:eval (bsl) v (list-ref v 9)]
|
|
}
|
|
@defproc[(list [x any/c] ... ) list?]{
|
|
Constructs a list of its arguments.
|
|
@interaction[#:eval (bsl-eval) (list 1 2 3 4 5 6 7 8 9 0)]
|
|
}
|
|
@defproc[(make-list [i natural-number] [x any/c]) list?]{
|
|
Constructs a list of @racket[i] copies of @racket[x].
|
|
@interaction[#:eval (bsl-eval) (make-list 3 "hello")]
|
|
}
|
|
@defproc[((beginner-list* list*) [x any/c] ... [l list?]) list?]{
|
|
Constructs a list by adding multiple items to a list.
|
|
@interaction[#:eval (bsl-eval (define x (list 2 "hello" true))) x (list* 4 3 x)]
|
|
}
|
|
@defproc[((beginner-range range) [start number][end number][step number]) list?]{
|
|
Constructs a list of numbers by @racket[step]ping from @racket[start]
|
|
to @racket[end].
|
|
@interaction[#:eval (bsl-eval) (range 0 10 2)]
|
|
}
|
|
@defproc[((beginner-append append) [x list?][y list?][z list?] ...) list?]{
|
|
Creates a single list from several, by juxtaposition of the items.
|
|
@interaction[#:eval (bsl) (append (cons 1 (cons 2 empty)) (cons "a" (cons "b" empty)))]
|
|
}
|
|
@defproc[(length (l list?)) natural-number?]{
|
|
Evaluates the number of items on a list.
|
|
@interaction[#:eval (bsl) x (length x)]
|
|
}
|
|
@defproc[((beginner-memq memq) [x any/c][l list?]) boolean?]{
|
|
Determines whether some value @racket[x] is on some list @racket[l],
|
|
using @racket[eq?] to compare @racket[x] with items on @racket[l].
|
|
@interaction[#:eval (bsl) x (memq (list (list 1 2 3)) x)]
|
|
}
|
|
@defproc[((beginner-memq? memq?) [x any/c][l list?]) boolean?]{
|
|
Determines whether some value @racket[x] is on some list @racket[l],
|
|
using @racket[eq?] to compare @racket[x] with items on @racket[l].
|
|
@interaction[#:eval (bsl) x (memq? (list (list 1 2 3)) x)]
|
|
}
|
|
@defproc[(memv [x any/c][l list?]) (or/c 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.)
|
|
@interaction[#:eval (bsl) x (memv (list (list 1 2 3)) x)]
|
|
}
|
|
@defproc[((beginner-member? member?) [x any/c][l list?]) boolean?]{
|
|
Determines whether some value is on the list (comparing values with equal?).
|
|
@interaction[#:eval (bsl) x (member? "hello" x)]
|
|
}
|
|
@defproc[((beginner-member member) [x any/c][l list?]) boolean?]{
|
|
Determines whether some value is on the list (comparing values with equal?).
|
|
@interaction[#:eval (bsl) x (member "hello" x)]
|
|
}
|
|
@defproc[((beginner-remove remove) [x any/c][l list?]) list?]{
|
|
Constructs a list like the given one with the first occurrence of the
|
|
given item removed (comparing values with equal?).
|
|
@interaction[#:eval (bsl) x (remove "hello" x)]
|
|
}
|
|
@defproc[(reverse [l list?]) list]{
|
|
Creates a reversed version of a list.
|
|
@interaction[#:eval (bsl) x (reverse x)]
|
|
}
|
|
@defproc[(assq [x any/c][l list?]) (union false cons?)]{
|
|
Determines whether some item is the first item of a pair in a list of
|
|
pairs. (It compares the items with @racket[eq?].)
|
|
@interaction[#:eval (bsl) a (assq 'b a)]
|
|
}
|
|
|
|
|
|
;; LISP-ish selectors:
|
|
@defproc[(null? [x any/c]) boolean?]{
|
|
Determines whether some value is the empty list.
|
|
@interaction[#:eval (bsl) (null? empty) (null? 42)]
|
|
}
|
|
@defthing[null list]{Another name for the empty list
|
|
@interaction[#:eval (bsl) null]
|
|
}
|
|
@defproc[((beginner-car car) [x cons?]) any/c]{
|
|
Selects the first item of a non-empty list.
|
|
@interaction[#:eval (bsl) x (car x)]
|
|
}
|
|
@defproc[((beginner-cdr cdr) [x cons?]) any/c]{
|
|
Selects the rest of a non-empty list.
|
|
@interaction[#:eval (bsl) x (cdr x)]
|
|
}
|
|
@defproc[(cadr [x list?]) any/c]{
|
|
LISP-style selector: @racket[(car (cdr x))].
|
|
@interaction[#:eval (bsl) x (cadr x)]
|
|
}
|
|
@defproc[(cdar [x list?]) list?]{
|
|
LISP-style selector: @racket[(cdr (car x))].
|
|
@interaction[#:eval (bsl) y (cdar y)]
|
|
}
|
|
@defproc[(caar [x list?]) any/c]{
|
|
LISP-style selector: @racket[(car (car x))].
|
|
@interaction[#:eval (bsl) y (caar y)]
|
|
}
|
|
@defproc[(cddr [x list?]) list? ]{
|
|
LISP-style selector: @racket[(cdr (cdr x))].
|
|
@interaction[#:eval (bsl) x (cddr x)]
|
|
}
|
|
@defproc[(caddr [x list?]) any/c]{
|
|
LISP-style selector: @racket[(caddr x)].
|
|
@interaction[#:eval (bsl) x (caddr x)]
|
|
}
|
|
@defproc[(caadr [x list?]) any/c]{
|
|
LISP-style selector: @racket[(car (car (cdr x)))].
|
|
@interaction[#:eval (bsl) z (caadr z)]
|
|
}
|
|
@defproc[(caaar [x list?]) any/c]{
|
|
LISP-style selector: @racket[(car (car (car (car x))))].
|
|
@interaction[#:eval (bsl) w (caaar w)]
|
|
}
|
|
@defproc[(cdaar [x list?]) any/c]{
|
|
LISP-style selector: @racket[(cdr (cadr (car x)))].
|
|
@interaction[#:eval (bsl) w (cdaar w)]
|
|
}
|
|
@defproc[(cdadr [x list?]) any/c]{
|
|
LISP-style selector: @racket[(cdr (car (cdr x)))].
|
|
@interaction[#:eval (bsl) z (cdadr z)]
|
|
}
|
|
@defproc[(cadar [x list?]) any/c]{
|
|
LISP-style selector: @racket[(car (cdr (car x)))].
|
|
@interaction[#:eval (bsl) w (cadar w)]
|
|
}
|
|
@defproc[(cddar [x list?]) any/c]{
|
|
LISP-style selector: @racket[(cdr (cdr (car x)))]
|
|
@interaction[#:eval (bsl) w (cddar w)]
|
|
}
|
|
@defproc[(cdddr [x list?]) any/c]{
|
|
LISP-style selector: @racket[(cdr (cdr (cdr x)))].
|
|
@interaction[#:eval (bsl) v (cdddr v)]
|
|
}
|
|
@defproc[(cadddr [x list?]) any/c]{
|
|
LISP-style selector: @racket[(car (cdr (cdr (cdr x))))].
|
|
@interaction[#:eval (bsl) v (cadddr v)]
|
|
})
|
|
|
|
("Posns"
|
|
@defproc[(posn) signature]{Signature for posns.}
|
|
@defproc[(make-posn [x any/c][y any/c]) posn]{
|
|
Constructs a posn from two arbitrary values.
|
|
@interaction[#:eval (bsl) (make-posn 3 3) (make-posn "hello" true)]
|
|
}
|
|
@defproc[(posn? [x any/c]) boolean?]{
|
|
Determines if its input is a posn.
|
|
@interaction[#:eval (bsl) q (posn? q) (posn? 42)]
|
|
}
|
|
@defproc[(posn-x [p posn]) any]{
|
|
Extracts the x component of a posn.
|
|
@interaction[#:eval (bsl) p (posn-x p)]
|
|
}
|
|
@defproc[(posn-y [p posn]) any]{
|
|
Extracts the y component of a posn.
|
|
@interaction[#:eval (bsl) p (posn-y p)]
|
|
})
|
|
|
|
("Characters"
|
|
@defproc[(char? [x any/c]) boolean?]{
|
|
Determines whether a value is a character.
|
|
@interaction[#:eval (bsl) (char? "a") (char? #\a)]
|
|
}
|
|
@defproc[(char=? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characters are equal.
|
|
@interaction[#:eval (bsl) (char=? #\b #\a)]
|
|
}
|
|
@defproc[(char<? [x char][d char][e char] ...) boolean?]{
|
|
Determines whether the characterc are ordered in a strictly increasing manner.
|
|
@interaction[#:eval (bsl) (char<? #\a #\b #\c)]
|
|
}
|
|
@defproc[(char>? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characters are sorted in a strictly decreasing manner.
|
|
@interaction[#:eval (bsl) (char>? #\A #\z #\a)]
|
|
}
|
|
@defproc[(char<=? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characterc are ordered in a strictly increasing manner.
|
|
@interaction[#:eval (bsl) (char<=? #\a #\a #\b)]
|
|
}
|
|
@defproc[(char>=? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characters are sorted in a decreasing manner.
|
|
@interaction[#:eval (bsl) (char>=? #\b #\b #\a)]
|
|
}
|
|
@defproc[(char-ci=? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether two characters are equal in a case-insensitive
|
|
manner.
|
|
@interaction[#:eval (bsl) (char-ci=? #\b #\B)]
|
|
}
|
|
@defproc[(char-ci<? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characterc are ordered in a strictly increasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (char-ci<? #\B #\c) (char<? #\b #\B)]
|
|
}
|
|
@defproc[(char-ci>? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characters are sorted in a strictly decreasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (char-ci>? #\b #\B) (char>? #\b #\B)]
|
|
}
|
|
@defproc[(char-ci<=? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characterc are ordered in an increasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (char-ci<=? #\b #\B) (char<=? #\b #\B)]
|
|
}
|
|
@defproc[(char-ci>=? [c char][d char][e char] ...) boolean?]{
|
|
Determines whether the characters are sorted in a decreasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (char-ci>=? #\b #\C) (char>=? #\b #\C)]
|
|
}
|
|
@defproc[(char-numeric? [c char]) boolean?]{
|
|
Determines whether a character represents a digit.
|
|
@interaction[#:eval (bsl) (char-numeric? #\9)]
|
|
}
|
|
@defproc[(char-alphabetic? [c char]) boolean?]{
|
|
Determines whether a character represents an alphabetic character.
|
|
@interaction[#:eval (bsl) (char-alphabetic? #\Q)]
|
|
}
|
|
@defproc[(char-whitespace? [c char]) boolean?]{
|
|
Determines whether a character represents space.
|
|
@interaction[#:eval (bsl) (char-whitespace? #\tab)]
|
|
}
|
|
@defproc[(char-upper-case? [c char]) boolean?]{
|
|
Determines whether a character is an upper-case character.
|
|
@interaction[#:eval (bsl) (char-upper-case? #\T)]
|
|
}
|
|
@defproc[(char-lower-case? [c char]) boolean?]{
|
|
Determines whether a character is a lower-case character.
|
|
@interaction[#:eval (bsl) (char-lower-case? #\T)]
|
|
}
|
|
@defproc[(char-upcase [c char]) char]{
|
|
Produces the equivalent upper-case character.
|
|
@interaction[#:eval (bsl) (char-upcase #\t)]
|
|
}
|
|
@defproc[(char-downcase [c char]) char]{
|
|
Produces the equivalent lower-case character.
|
|
@interaction[#:eval (bsl) (char-downcase #\T)]
|
|
}
|
|
@defproc[(char->integer [c char]) integer]{
|
|
Lookups the number that corresponds to the given character in the ASCII table (if any).
|
|
@interaction[#:eval (bsl) (char->integer #\a) (char->integer #\z)]
|
|
})
|
|
|
|
("Strings"
|
|
@defproc[(string? [x any/c]) boolean?]{
|
|
Determines whether a value is a string.
|
|
@interaction[#:eval (bsl) (string? "hello world") (string? 42)]
|
|
}
|
|
@defproc[(string-length [s string]) nat]{
|
|
Determines the length of a string.
|
|
@interaction[#:eval (bsl) (string-length "hello world")]
|
|
}
|
|
@defproc[((beginner-string-ith string-ith) [s string][i natural-number]) 1string?]{
|
|
Extracts the @racket[i]th 1-letter substring from @racket[s].
|
|
@interaction[#:eval (bsl) (string-ith "hello world" 1)]
|
|
}
|
|
@defproc[((beginner-replicate replicate) [i natural-number][s string]) string]{
|
|
Replicates @racket[s] @racket[i] times.
|
|
@interaction[#:eval (bsl) (replicate 3 "h")]
|
|
}
|
|
@defproc[((beginner-int->string int->string) [i integer]) string]{
|
|
Converts an integer in [0,55295] or [57344 1114111] to a 1-letter string.
|
|
@interaction[#:eval (bsl) (int->string 65)]
|
|
}
|
|
@defproc[((beginner-string->int string->int) [s string]) integer]{
|
|
Converts a 1-letter string to an integer in [0,55295] or [57344, 1114111].
|
|
@interaction[#:eval (bsl) (string->int "a")]
|
|
}
|
|
@defproc[((beginner-explode explode) [s string]) (listof string)]{
|
|
Translates a string into a list of 1-letter strings.
|
|
@interaction[#:eval (bsl) (explode "cat")]
|
|
}
|
|
@defproc[((beginner-implode implode) [l list?]) string]{
|
|
Concatenates the list of 1-letter strings into one string.
|
|
@interaction[#:eval (bsl) (implode (cons "c" (cons "a" (cons "t" empty))))]
|
|
}
|
|
@defproc[((beginner-string-numeric? string-numeric?) [s string]) boolean?]{
|
|
Determines whether all 'letters' in the string are numeric.
|
|
@interaction[#:eval (bsl) (string-numeric? "123") (string-numeric? "1-2i")]
|
|
}
|
|
@defproc[((beginner-string-alphabetic? string-alphabetic?) [s string]) boolean?]{
|
|
Determines whether all 'letters' in the string are alphabetic.
|
|
@interaction[#:eval (bsl) (string-alphabetic? "123") (string-alphabetic? "cat")]
|
|
}
|
|
@defproc[((beginner-string-whitespace? string-whitespace?) [s string]) boolean?]{
|
|
Determines whether all 'letters' in the string are white space.
|
|
@interaction[#:eval (bsl) (string-whitespace? (string-append " " (string #\tab #\newline #\return)))]
|
|
}
|
|
@defproc[((beginner-string-upper-case? string-upper-case?) [s string]) boolean?]{
|
|
Determines whether all 'letters' in the string are upper case.
|
|
@interaction[#:eval (bsl) (string-upper-case? "CAT")]
|
|
}
|
|
@defproc[((beginner-string-lower-case? string-lower-case?) [s string]) boolean?]{
|
|
Determines whether all 'letters' in the string are lower case.
|
|
@interaction[#:eval (bsl) (string-lower-case? "CAT")]
|
|
}
|
|
@defproc[((beginner-string-contains? string-contains?) [s string] [t string]) boolean?]{
|
|
Determines whether the first string appears literally in the second one.
|
|
@interaction[#:eval (bsl) (string-contains? "at" "cat")]
|
|
}
|
|
@defproc[(string [c char] ...) string?]{
|
|
Builds a string of the given characters.
|
|
@interaction[#:eval (bsl) (string #\d #\o #\g)]
|
|
}
|
|
@defproc[(make-string [i natural-number][c char]) string]{
|
|
Produces a string of length @racket[i] from @racket[c].
|
|
@interaction[#:eval (bsl) (make-string 3 #\d)]
|
|
}
|
|
@defproc[(string-ref [s string][i natural-number]) char]{
|
|
Extracts the @racket[i]th character from @racket[s].
|
|
@interaction[#:eval (bsl) (string-ref "cat" 2)]
|
|
}
|
|
@defproc[(substring [s string][i natural-number][j natural-number]) string]{
|
|
Extracts the substring starting at @racket[i] up to @racket[j] (or the
|
|
end if @racket[j] is not provided).
|
|
@interaction[#:eval (bsl) (substring "hello world" 1 5) (substring "hello world" 4)]
|
|
}
|
|
@defproc[(string-copy [s string]) string]{
|
|
Copies a string. @;why is it included?
|
|
@interaction[#:eval (bsl) (string-copy "hello")]
|
|
}
|
|
@defproc[(string-append [s string] ...) string]{
|
|
Juxtaposes the characters of several strings.
|
|
@interaction[#:eval (bsl) (string-append "hello" " " "world" " " "good bye")]
|
|
}
|
|
@defproc[(string=? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether all strings are equal, character for character.
|
|
@interaction[#:eval (bsl) (string=? "hello" "world") (string=? "bye" "bye")]
|
|
}
|
|
@defproc[(string<? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically strictly increasing manner.
|
|
@interaction[#:eval (bsl) (string<? "hello" "world" "zoo")]
|
|
}
|
|
@defproc[(string>? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically strictly decreasing manner.
|
|
@interaction[#:eval (bsl) (string>? "zoo" "world" "hello")]
|
|
}
|
|
@defproc[(string<=? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically increasing manner.
|
|
@interaction[#:eval (bsl) (string<=? "hello" "hello" "world" "zoo")]
|
|
}
|
|
@defproc[(string>=? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically decreasing manner.
|
|
@interaction[#:eval (bsl) (string>=? "zoo" "zoo" "world" "hello")]
|
|
}
|
|
@defproc[(string-ci=? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether all strings are equal, character for character, regardless of case.
|
|
@interaction[#:eval (bsl) (string-ci=? "hello" "HellO")]
|
|
}
|
|
@defproc[(string-ci<? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically strictly increasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (string-ci<? "hello" "WORLD" "zoo")]
|
|
}
|
|
@defproc[(string-ci>? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically strictly decreasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (string-ci>? "zoo" "WORLD" "hello")]
|
|
}
|
|
@defproc[(string-ci<=? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically increasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (string-ci<=? "hello" "WORLD" "zoo")]
|
|
}
|
|
@defproc[(string-ci>=? [s string][t string][x string] ...) boolean?]{
|
|
Determines whether the strings are ordered in a lexicographically decreasing and case-insensitive manner.
|
|
@interaction[#:eval (bsl) (string-ci>? "zoo" "WORLD" "hello")]
|
|
}
|
|
@defproc[(string->symbol [s string]) symbol]{
|
|
Converts a string into a symbol.
|
|
@interaction[#:eval (bsl) (string->symbol "hello")]
|
|
}
|
|
@defproc[(string->number [s string]) (union number false)]{
|
|
Converts a string into a number, produce false if impossible.
|
|
@interaction[#:eval (bsl) (string->number "-2.03") (string->number "1-2i")]
|
|
}
|
|
@defproc[(string->list [s string]) (listof char)]{
|
|
Converts a string into a list of characters.
|
|
@interaction[#:eval (bsl) (string->list "hello")]
|
|
}
|
|
@defproc[(list->string [l list?]) string]{
|
|
Converts a s list of characters into a string.
|
|
@interaction[#:eval (bsl) (list->string (cons #\c (cons #\a (cons #\t empty))))]
|
|
}
|
|
@defproc[(format [f string] [x any/c] ...) string]{
|
|
Formats a string, possibly embedding values.
|
|
@interaction[#:eval (bsl)
|
|
(format "Dear Dr. ~a:" "Flatt")
|
|
(format "Dear Dr. ~s:" "Flatt")
|
|
(format "the value of ~s is ~a" '(+ 1 1) (+ 1 1))
|
|
]
|
|
})
|
|
|
|
("Images"
|
|
@defproc[(image? [x any/c]) boolean?]{
|
|
Determines whether a value is an image.
|
|
@interaction[#:eval (bsl) c1 (image? c1)]
|
|
}
|
|
@defproc[(image=? [i image][j image]) boolean?]{
|
|
Determines whether two images are equal.
|
|
@interaction[#:eval (bsl) c1 (image=? (circle 5 "solid" "green") c1) (image=? (circle 10 "solid" "green") c1)]
|
|
})
|
|
|
|
("Misc"
|
|
@defproc[(identity [x any/c]) any]{
|
|
Returns @racket[x].
|
|
@interaction[#:eval (bsl) (identity 42) (identity c1) (identity "hello")]
|
|
}
|
|
@defproc[((beginner-error error) [x any/c] ...) 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 suffixed with a colon and the
|
|
result pre-pended on to the error message.
|
|
@interaction[#:eval (bsl) zero (if (= zero 0) (error "can't divide by 0") (/ 1 zero))]
|
|
}
|
|
@defproc[((beginner-struct? struct?) [x any/c]) boolean?]{
|
|
Determines whether some value is a structure.
|
|
@interaction[#:eval (bsl) (struct? (make-posn 1 2)) (struct? 43)]
|
|
}
|
|
@defproc[((beginner-equal? equal?) [x any/c][y any/c]) boolean?]{
|
|
Determines whether two values are structurally equal where basic values
|
|
are compared with the eqv? predicate.
|
|
@interaction[#:eval (bsl) (equal? (make-posn 1 2) (make-posn (- 2 1) (+ 1 1)))]
|
|
}
|
|
@defproc[(eq? [x any/c][y any/c]) boolean?]{
|
|
Determines whether two values are equivalent from the computer's perspective (intensional).
|
|
@interaction[#:eval (bsl) (eq? (cons 1 empty) (cons 1 empty)) one (eq? one one)]
|
|
}
|
|
@defproc[(eqv? [x any/c][y any/c]) boolean?]{
|
|
Determines whether two values are equivalent from the perspective of all functions that can be applied to it (extensional).
|
|
@interaction[#:eval (bsl) (eqv? (cons 1 empty) (cons 1 empty)) one (eqv? one one)]
|
|
}
|
|
@defproc[((beginner-=~ =~) [x number][y number][z non-negative-real]) boolean?]{
|
|
Checks whether @racket[x] and @racket[y] are within @racket[z] of either other.
|
|
@interaction[#:eval (bsl) (=~ 1.01 1.0 .1) (=~ 1.01 1.5 .1)]
|
|
}
|
|
@defproc[((beginner-equal~? equal~?) [x any/c][y any/c][z non-negative-real]) boolean?]{
|
|
Compares @racket[x] and @racket[y] like @racket[equal?] but uses =~ in the case of numbers.
|
|
@interaction[#:eval (bsl) (equal~? (make-posn 1.01 1.0) (make-posn 1.01 .99) .2)]
|
|
}
|
|
@defthing[eof eof-object?]{A value that represents the end of a file:
|
|
@interaction[#:eval (bsl) eof]
|
|
}
|
|
@defproc[(eof-object? [x any/c]) boolean?]{
|
|
Determines whether some value is the end-of-file value.
|
|
@interaction[#:eval (bsl) (eof-object? eof) (eof-object? 42)]
|
|
}
|
|
@defproc[((beginner-exit exit)) void]{
|
|
Evaluating @racket[(exit)] terminates the running program.
|
|
}))
|