5 Designing With Lists and Abstractions
Purpose: This lab focuses on designing programs on lists, as well as creating abstractions.
Textbook references:
Part II: Arbitrarily Large Data
Chapter 14: Similarities Everywhere
Chapter 15: Designing Abstractions
PARTNER CHANGE
Goals: Your new lab partner today will be your HW partner for the next several weeks.
Exercise 1 Sit next to your new partner.
Exercise 2 Exchange contact information with your partner: telephone number, latest-greatest social network scheme, whatever-app.
Exercise 3 Agree to a first meeting time and meeting place. At that meeting, agree to next meeting time and meeting place.
Finite Increasing Arithmetic Sequences
Goals: Use abstraction in an unfamiliar context.
Starter Code: Below is the data definition of a finite increasing arithmetic sequence.
(define Positive (signature (predicate (lambda (x) (and (number? x) (positive? x)))))) (define-struct fias [min max step]) (define AFIAS (signature [FiasOf Number Number Positive])) ; where (make-fias min max step) represents all numbers ; of the form min + (k * step), where k is a natural number, ; such that min + (k * step) < max. (define FIAS-EMPTY (make-fias 1 1 0.25)) ; empty sequence, as min >= max (define FIAS-1 (make-fias 0 1 0.25)) ; sequence with the elements (0, .25, .5, .75) ; fias-temp : AFIAS -> ? (define (fias-temp fias) (... (fias-min fias) ... (fias-max fias) ... (fias-step fias) ...))
Sample Problem Design a function that determines if AFIAS is empty.
(: empty-fias? (AFIAS -> Boolean)) ; determines if the given FIAS is empty (define (empty-fias? fias) (>= (fias-min fias) (fias-max fias)))
Sample Problem Design the function next-sequence, which takes AFIAS and returns a new AFIAS with the same max and step. The new min will be the original AFIAS’s min with its step added to it.
(: next-sequence (AFIAS -> AFIAS)) ; returns a new FIAS where the min is the original FIAS's min plus its step (define (next-sequence fias) (make-fias (+ (fias-min fias) (fias-step fias)) (fias-max fias) (fias-step fias)))
Sample Problem You may have noticed that next-sequence returns the rest of a AFIAS, empty-fias? determines if it is empty, and that if it is non-empty fias-min is the first element in it. Redefine your fias-temp to take advantage of this recursive structure.
; fias-temp : AFIAS -> ? (define (fias-temp fias) (cond [(empty-fias? fias) ...] [else (... (fias-min fias) ... (fias-temp (next-sequence fias)) ...)]))
Exercise 4 Design a function which sums the elements of a AFIAS.
Exercise 5 Design a function which multiplies the elements of a AFIAS. Hint: the product of an empty sequence is 1.
Exercise 6 Design a function which lists the elements of AFIAS.
Exercise 7 All of these functions look marvelously similar; abstract them, redefine them with your new function, and ensure all of your tests still pass.
Exercise 8 Design a function which determines if any element of AFIAS is a perfect square. Hint: integer?.
Exercise 9 Design a function which determines if any element of AFIAS is even.
Exercise 10 Both of these functions look marvelously similar; abstract them, redefine them with your new function, and ensure all of your tests still pass.
List Abstractions
(require 2htdp/image) (define Image (signature (predicate image?))) (define Color (signature (predicate image-color?))) (define Mode (signature (predicate mode?))) ; is one of ; - "solid" ; - "outline" (define-struct circl [radius mode c]) (define-struct squar [side-length mode c]) (define-struct rectangl [width height mode c]) (define Shape (signature (mixed [CirclOf Number Mode Color] [SquarOf Number Mode Color] [RectanglOf Number Number Mode Color]))) ; and represents either: ; - the radius in pixels, mode, and color of a circle ; - the side length in pixels, mode, and color of a square ; - the width and height in pixels, the mode, and color of a rectangle
Exercise 11 Provide examples and templates for the above data definitions.
Exercise 12 Use filter to design a function that takes a [ListOf Shape] and keeps only circles.
Exercise 13 Use foldr to design a function that takes a [ListOf Shape] and stacks all of its images vertically (hint: you may need to use map as well).
Signature Detective
Goals: Practice understanding what the data type restrictions on code must be when reading it.
Exercise 14 Determine the signature for the following functions.
(define (a supercut of us) (+ of (if (empty? supercut) (us #f) (us (first supercut))))) (define (the moments i play in the dark) (play (in (play the dark)) (play moments i))) (define (come home to my heart) (cond [(home my) (to heart)] [(my heart) " "] [else ""]))