TDDC74 Programming: Abstraction and Modelling
PRAM, Tutorial 3
The tutorial should cover the following topics:
• Scheme data types: pairs, lists, and symbols
• Visualization: box-and-pointer notation
• List operations
• Creating and using ADTs
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Data types: pairs, lists, & symbols
Problem 1 ------------------------------------------------------------------------------------------------------------------Diagram the following:
(define foo ’(1 2))
foo −→ ???
(list foo ’bar foo) −→ ???
Problem 2 ------------------------------------------------------------------------------------------------------------------Diagram the following:
(cons ’(a) ’(b)) −→ ???
(define ho ’(cons + ()))
(car ho) −→ ???
(define hoho (cons list *))
(car hoho) −→ ??
(define hohoho (list ’cons - ’()))
(car hohoho) −→ ???
Problem 3 ------------------------------------------------------------------------------------------------------------------Write a Scheme expression that will return the following structure:
-->XX-->2
|
V
XX-->3
|
V
XX-->4
|
V
XX-->5
|
V
6
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Problem 4 ------------------------------------------------------------------------------------------------------------------Write a Scheme expression that will return the following structure:
--->XX--->XX----->X/
|
|
|
V
V
V
darth saruman XX--->pookie
|
V
voldemort
Problem 5 ------------------------------------------------------------------------------------------------------------------The exponentiation algorithms in SICP section 1.2 are based on performing exponentiation means
of repeated multiplication.1 In a similar way, one can perform integer multiplication means of
repeated addition.
(define (my-mult num1 num2)
(if (= num2 0)
0
(+ num1 (my-mult num1 (- num2 1)))))
This algorithm takes a number of steps that is linear in num2. Now suppose we include, with
addition, operations double, which doubles an integer, and halve, which divides integer by 2.
Using these, design a multiplication procedure that uses logarithmic number of steps. You can
assume that num1 and num2 are positive integers.
(define (double num)
(* num 2))
(define (halve num)
(/ num 2))
Problem 6 ------------------------------------------------------------------------------------------------------------------Given the following ADT:
;; symbol -> coin
(define (make-coin upside)
upside)
;; coin -> boolean
(define (heads? coin)
(eq? coin ’heads))
;; coin -> boolean
(define (tails? coin)
(eq? coin ’tails))
;; coin coin -> boolean
(define coin-eq? eq?)
Implement the procedure make-random-coin which creates a random coin:
> (define *a-coin* (make-random-coin))
> (heads? *a-coin*)
#f
> (tails? *a-coin*)
#t
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This is a variation of SICP 1.17
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