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### 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

### Finite Increasing Arithmetic Sequences

Goals: Use abstraction in an unfamiliar context.

Starter Code: Below is the data definition of a finite increasing arithmetic sequence.

 ; A FIAS (Finite Increasing Arithmetic Sequence) is a: ; (make-fias Number Number Positive) (define-struct fias [min max step]) ; 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 : FIAS -> ? (define (fias-temp fias) (... (fias-min fias) (fias-max fias) (fias-step fias)))

Sample Problem Design a function that determines if a FIAS is empty.

 ; empty-fias? : FIAS -> 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 a FIAS and returns a new FIAS with the same max and step. The new min will be the original FIAS’s min with its step added to it.

 ; next-sequence : FIAS -> FIAS ; 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 FIAS, 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 : FIAS -> ? (define (fias-temp fias) (cond [(empty-fias? fias) ...] [else (... (fias-min fias) (fias-temp (next-sequence fias)))]))

Exercise 1 Design a function which sums the elements of a FIAS.

Exercise 2 Design a function which multiplies the elements of a FIAS. Hint: the product of an empty sequence is 1.

Exercise 3 Design a function which lists the elements of a FIAS.

Exercise 4 All of these functions look marvelously similar; abstract them, redefine them with your new function, and ensure all of your tests still pass.

Exercise 5 Design a function which determines if any element of a FIAS is a perfect square. Hint: integer?.

Exercise 6 Design a function which determines if any element of a FIAS is even.

Exercise 7 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

Goals: Practice understanding how to use the foldr list abstraction.
 (define-struct circl [radius mode c]) (define-struct squar [side-length mode c]) (define-struct rectangl [width height mode c]) ; A Shape is one of: ; - (make-circl Number Mode Color) ; - (make-squar Number Mode Color) ; - (make-rectangl 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 ; A Mode is one of: ; - "solid" ; - "outline"

Exercise 8 Provide examples and templates for the above data definitions.

Exercise 9 Use foldr to design a function that takes a [List-of Shape] and stacks all of its images vertically.

Exercise 10 Use filter to design a function that takes a [List-of Shape] and keeps only circles.

Exercise 11 Use map to design a function that takes a [List-of Shape] and outputs their colors.

Exercise 12 Use ormap to design a function that takes a [List-of Shape] and determines if any of then are "green".

### Signature Detective

Goals: Practice understanding what the data type restrictions on code must be when reading it.

Exercise 13 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 ""]))