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;; "relate" accepts a positive integer x and relation R and returns { y | (x y) €R }. ;; Type signature: (relate positive-int relation) -> set-of-ints (define (relate x R) (define (relate-helper x R) (cond [(null? R) '0] [(= x (caar R)) (cons (cadar R) (relate-helper x (cdr R)))] [else (relate-helper x (cdr R))])) (make-set (relate-helper x R)))

;; "relate" accepts a positive integer x and relation R and returns { y | (x y) €R }. ;; Type signature: (relate positive-int relation) -> set-of-ints (define (relate x R) (define (relate-helper x R) (cond [(null? R) '0] [(= x (caar R)) (cons (cadar R) (relate-helper x (cdr R)))] [else (relate-helper x (cdr R))])) (make-set (relate-helper x R)))

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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The question is the first screenshot, and in the second I have attached the "relate" helper function. I keep trying and feel I am overcomplicating things majorly and was wondering if there's a simpler way to complete this.

#| Implement "compose" to accept two relations S and R, and return S R, or S composed with R. |S•R = { (x z) | 3y: (x y) ER A (y z) E S }. Advice for implementation: Consider each edge (a b) in R. For every edge (c d) in S, if b and c are equal then add (a d) to the output. See if you can leverage the "relate" helper function! | Examples: (compose '() '((3 2) (2 4)) ) -> (). (compose '((1 1) (2 1) (1 3)) '() ) -> () (compose '((2 4) (3 5) (4 6) (5 7)) '((1 2) (2 3) (3 4) (4 5)) ) -> ((1 4) (2 5) (3 6) (4 7)) (compose '((2 4) (5 8) (3 4)) '((2 4) (5 8) (3 4)) ) -> (). (compose '((1 1) (2 2) (3 2)) '((1 1) (2 2) (2 3)) ) -> ((1 1) (2 2)) (compose '((1 1) (2 1) (3 1) (4 1)) '((1 1) (1 2) (1 3)) ) -> ((1 1)) (compose '((1 1) (1 2) (1 3)) '((1 1) (2 1) (3 1) (4 1)) ) -> ((1 1) (1 2) (1 3) (2 1) (2 2) (2 3) (3 1) (3 2) (3 3) (4 1) (4 2) (4 3)) |# ;; Type Signature: (compose relation relation) -> relation (define (compose S R) "TODO: Implement")
Transcribed Image Text:#| Implement "compose" to accept two relations S and R, and return S R, or S composed with R. |S•R = { (x z) | 3y: (x y) ER A (y z) E S }. Advice for implementation: Consider each edge (a b) in R. For every edge (c d) in S, if b and c are equal then add (a d) to the output. See if you can leverage the "relate" helper function! | Examples: (compose '() '((3 2) (2 4)) ) -> (). (compose '((1 1) (2 1) (1 3)) '() ) -> () (compose '((2 4) (3 5) (4 6) (5 7)) '((1 2) (2 3) (3 4) (4 5)) ) -> ((1 4) (2 5) (3 6) (4 7)) (compose '((2 4) (5 8) (3 4)) '((2 4) (5 8) (3 4)) ) -> (). (compose '((1 1) (2 2) (3 2)) '((1 1) (2 2) (2 3)) ) -> ((1 1) (2 2)) (compose '((1 1) (2 1) (3 1) (4 1)) '((1 1) (1 2) (1 3)) ) -> ((1 1)) (compose '((1 1) (1 2) (1 3)) '((1 1) (2 1) (3 1) (4 1)) ) -> ((1 1) (1 2) (1 3) (2 1) (2 2) (2 3) (3 1) (3 2) (3 3) (4 1) (4 2) (4 3)) |# ;; Type Signature: (compose relation relation) -> relation (define (compose S R) "TODO: Implement")
;; "relate" accepts a positive integer x and relation R and returns { y | (x y) ER }. ;; Type signature: (relate positive-int relation) -> set-of-ints (define (relate x R) (define (relate-helper x R) (cond [(null? R) '01 [(= x (caar R)) (cons (cadar R) (relate-helper x (cdr R)))] [else (relate-helper x (cdr R))])) (make-set (relate-helper x R)))
Transcribed Image Text:;; "relate" accepts a positive integer x and relation R and returns { y | (x y) ER }. ;; Type signature: (relate positive-int relation) -> set-of-ints (define (relate x R) (define (relate-helper x R) (cond [(null? R) '01 [(= x (caar R)) (cons (cadar R) (relate-helper x (cdr R)))] [else (relate-helper x (cdr R))])) (make-set (relate-helper x R)))
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