mirror of https://github.com/2martens/uni.git
249 lines
6.3 KiB
Racket
249 lines
6.3 KiB
Racket
#lang lazy
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SE 3 Funktional Blatt 10
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Abgebende: Jim 2martens, Britta 2noack, Jan-Simon 0giesel
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|#
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; 1)
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; 1.1
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(define (every pred xs)
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(foldl (λ (x best) (and x best))
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#t
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(map pred xs))
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)
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(define (some pred xs)
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(foldl (λ (x best)
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(if [pred x]
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x
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best))
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#f
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xs)
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)
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; 1.2
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(define (symmetrisch? r)
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(every (λ (x)
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(some (λ (y)
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(and (eq? (cdr y)
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(car x))
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(eq? (car y)
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(cdr x))))
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r))
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r))
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(define (asymmetrisch? r)
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(every (λ (x)
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(let ((t1 (some (λ (y)
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(and (eq? (cdr y)
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(car x))
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(eq? (car y)
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(cdr x)))
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))))
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r))))
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(define (reflexiv? r)
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(every (λ (x)
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(and (some (λ (y)
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(and (eq? (car y)
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(car x))
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(eq? (cdr y)
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(car x))))
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r)
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(some (λ (y)
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(and (eq? (car y)
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(cdr x))
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(eq? (cdr y)
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(cdr x))))
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r)))
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r))
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(define (transitiv? r)
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(every (λ (x)
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(let ((t1 (some (λ (y)
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(and (eq? (cdr x)
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(car y))
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(not (eq? (cdr x)
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(cdr y)))))
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r)))
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(if t1
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(some (λ (z)
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(and (eq? (car x)
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(car z))
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(eq? (cdr t1)
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(cdr z))))
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r)
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#t)))
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r))
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(define (aequi? r)
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(and (reflexiv? r)
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(symmetrisch? r)
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(transitiv? r)))
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(define (ord? r)
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(and (reflexiv? r)
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(not (symmetrisch? r))
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(transitiv? r)))
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; 2)
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; 1.
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(define (Kreuzprodukt m1 m2)
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(letrec ((inner (λ (x ys acc)
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(if (empty? ys)
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acc
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(inner x
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(cdr ys)
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(cons (list x
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(car ys))
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acc)))))
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(outer (λ (xs ys acc)
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(if (empty? xs)
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acc
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(outer (cdr xs)
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ys
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(inner (car xs)
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ys
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acc))))))
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(outer (reverse m1) (reverse m2) '())))
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; 2.
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;(define (Produkt xs)
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; 3.
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; abhängig von k machen.
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(define (Kombination k M)
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(letrec ((inner (λ (x ys acc)
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(if (empty? ys)
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acc
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(inner x
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(cdr ys)
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(cons (list x (car ys))
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acc)))))
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(outer (λ (xs acc)
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(if (empty? xs)
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acc
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(outer (cdr xs)
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(inner (car xs)
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(cdr xs)
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acc))))))
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(reverse (outer M '()))))
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; 3)
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; 1.
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; (a) -> -1, weil 2-3 = -1 und -1 < 2 und -1 >= -1
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; (b) -> '(+ -2 2), weil quasi-quote und (- 2 4) dennoch ausgeführt wird (wg. ,)
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; (c) -> Alle, weil Alle erstes Element der Liste
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; (d) -> '(auf (dem See))
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; (e) -> '(Listen sind einfach)
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; (f) -> '(Paare . auch)
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; (g) -> #t, da beide Listen gleiche Werte haben
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; (h) -> #f, da die beiden Listen nicht identisch sind
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; (i) -> '(1 8 27)
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; (j) -> '(1 3 5)
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; (k) -> 2, da 2 < 6
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; (l) -> #t, da 2 = 2
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; 2.
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; *a* hat ein wohldefinierten Wert und evaluiert zu 10
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; (+ *a* *b*) hat keinen wohldefinierten Wert
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; (+ (eval *a*) (eval *b*)) hat keinen wohldefinierten Wert
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; (and (> *a* 10) (> *b* 3)) hat wohldefinierten Wert und evaluiert zu #f
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; (or (> *a* 10) (/ *a* 0)) hat keinen wohldefinierten Wert
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; (+ 2 (merke 3)) hat keinen wohldefinierten Wert
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; (+ 2 ((merke 3))) hat einen wohldefinierten Wert und evaluiert zu 5
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; (test 4) hat keinen wohldefinierten Wert
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; 3.
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; (a)
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(+ (* 3 4) (* 5 6))
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; (b)
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(define wurzel (λ (x) (sqrt (- 1 (sqr (sin x))))))
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; 4.
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(define (c a b)
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(sqrt (+ (sqr a) (sqr b))))
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(define (mythan a)
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(/ (sin a)
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(sqrt (- 1 (sqr (sin a))))))
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; 5.
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; (a)
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(- (+ 1 (/ 4 2)) 1)
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; (b)
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(/ (- 2 (/ (+ 1 3) (+ 3 (* 2 3)))) (sqrt 3))
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; 6.
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; (1 + 2 + 3) * (2 - 3 - (2 - 1))
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; 7.
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(define (laengen xss)
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(map length xss))
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(define (laengenRekEnd xss)
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(letrec ((rec (λ (xs acc)
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(if (empty? xs)
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acc
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(rec (cdr xs)
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(cons (length (car xs))
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acc))))))
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(reverse (rec xss '()))))
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(define (laengenRekNorm xss)
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(if (empty? xss)
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'()
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(cons (length (car xss))
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(laengenRekNorm (cdr xss)))))
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; 8.
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; (a)
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(define (make-length value unit)
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(list value unit))
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; (b)
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(define (value-of-length len)
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(car len))
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(define (unit-of-length len)
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(cadr len))
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; (c)
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(define (scale-length len fac)
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(list (* (car len) fac) (cadr len)))
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; (d)
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(define *conversiontable* ;
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'( ; (unit . factor)
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(m . 1)
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(cm . 0.01)
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(mm . 0.001)
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(km . 1000)
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(inch . 0.0254)
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(feet . 0.3048)
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(yard . 0.9144)))
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(define (factor unit)
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(cdr (assoc unit *conversiontable*)))
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(define (length->meter len)
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(list (car (scale-length len (factor (cadr len))))
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'm))
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(define (length< len1 len2)
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(< (car (length->meter len1)) (car (length->meter len2))))
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(define (length= len1 len2)
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(= (car (length->meter len1)) (car (length->meter len2))))
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(define (length+ len1 len2)
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(list (+ (car (length->meter len1)) (car (length->meter len2)))
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'm))
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(define (length- len1 len2)
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(list (- (car (length->meter len1)) (car (length->meter len2)))
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'm))
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; (e)
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(define xs '((6 km) (2 feet) (1 cm) (3 inch)))
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(map length->meter xs)
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(filter (λ (x) (< (car x) 1)) (map length->meter xs))
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(foldl (λ (x best) (+ (car x) best)) 0 (map length->meter xs))
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