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authorJulian T <julian@jtle.dk>2021-10-05 16:05:43 +0200
committerJulian T <julian@jtle.dk>2021-10-05 16:05:43 +0200
commita0b956c465d7297d185d362bc5f774daeecf3f39 (patch)
tree4f4bd929ba90dd506d942dfd5a1dd2bdf617bd93
parent4c9e4b9a65dc507fae927158ddc236f5e0632c01 (diff)
Add solution to pp lecture 4
-rw-r--r--sem7/pp/lec4.scm94
1 files changed, 94 insertions, 0 deletions
diff --git a/sem7/pp/lec4.scm b/sem7/pp/lec4.scm
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+;; Needed definitions
+(define-syntax cons-stream
+ (syntax-rules ()
+ ((cons-stream x y)
+ (cons x (delay y)))))
+
+(define head car)
+
+(define (tail stream) (force (cdr stream)))
+
+(define empty-stream? null?)
+
+(define the-empty-stream '())
+
+
+(define (stream-section n stream)
+ (cond ((= n 0) '())
+ (else (cons (head stream)
+ (stream-section
+ (- n 1)
+ (tail stream))))))
+
+(define (add-streams s1 s2)
+ (let ((h1 (head s1))
+ (h2 (head s2)))
+ (cons-stream
+ (+ h1 h2)
+ (add-streams (tail s1) (tail s2)))))
+
+(define ones (cons-stream 1 ones))
+
+(define nat-nums
+ (cons-stream 1
+ (add-streams ones nat-nums)))
+
+;;# Exercise 4.2
+;;? Make a stream of factorial numbers.
+;;? Use a helper function combine-streams that combines streams
+;;? with a binary function.
+
+(define (combine-streams op a b)
+ (cons-stream (op (head a) (head b))
+ (combine-streams op (tail a) (tail b))
+ ))
+
+(define fib-stream
+ (cons-stream 1
+ (combine-streams *
+ (tail nat-nums)
+ fib-stream)))
+
+;;# Exercise 4.4
+;;? Create a stream that converges on the square root of x.
+;;? The initial guess is 1.0 and the rest is done with newtons method.
+;;-- BEGIN FUNCTIONS GIVEN
+(define (improve-sqrt-guess guess x)
+ (/ (+ guess (/ x guess)) 2))
+(define (map-stream f stream)
+ (cond ((empty-stream? stream) the-empty-stream)
+ (else (cons-stream (f (head stream)) (map-stream f (tail stream))))))
+;;-- END
+
+(define (newton-approx-stream x)
+ (letrec
+ ([res (cons-stream 1.0 (map-stream (lambda (g) (improve-sqrt-guess g x)) res))]
+ ) res))
+
+;;# Exercise 4.3
+;;? Program af append-streams. How will it work for infinite lists.
+;; Hmm this seems kind of useless if the first is an infinite list.
+(define (append-streams a b)
+ (if (empty-stream? a)
+ b
+ (cons-stream (head a) (append-streams (tail a) b))))
+
+(define finite-test-stream
+ (cons-stream 'a (cons-stream 'b (cons-stream 'c the-empty-stream))))
+
+;;? Now program a merge-streams that alternates two streams
+;; This is more like it, here is makes sense even if both are infinite
+(define (merge-streams a b)
+ (cond [(empty-stream? a) b]
+ [(empty-stream? b) a]
+ [else (cons-stream (head a) (cons-stream (head b) (merge-streams
+ (tail a)
+ (tail b))))]
+ ))
+
+;;? Now use the merge to create a list of all natural numbers.
+(define (negate x) (* -1 x))
+(define all-integers
+ (cons-stream 0
+ (merge-streams nat-nums
+ (map-stream negate nat-nums))))