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Lecture 8: Cons

car

cdr

sdr

wdr

David Evans

http://www.cs.virginia.edu/~evans

CS200: Computer Science

University of Virginia

Computer Science

Confusion Is Good!It means you are learning new ways of thinking.

CS 200 Spring 2003

History of Scheme

- Scheme [1975]
- Guy Steele and Gerry Sussman
- Originally “Schemer”
- “Conniver” [1973] and “Planner” [1967]
- Based on LISP
- John McCarthy (late 1950s)
- Based on Lambda Calculus
- Alonzo Church (1930s)
- Last few lectures in course

CS 200 Spring 2003

LISP

“Lots of Insipid Silly Parentheses”

“LISt Processing language”

Lists are pretty important – hard to write a useful Scheme program without them.

CS 200 Spring 2003

Making Lists

CS 200 Spring 2003

Splitting a Pair

cons

> (car (cons 1 2))

1

> (cdr (cons 1 2))

2

1

2

car

cdr

car extracts first part of a pair

cdr extracts second part of a pair

CS 200 Spring 2003

Why “car” and “cdr”?

- Original (1950s) LISP on IBM 704
- Stored cons pairs in memory registers
- car = “Contents of the Address part of the Register”
- cdr = “Contents of the Decrement part of the Register” (“could-er”)
- Doesn’t matters unless you have an IBM 704
- Think of them as first and rest

(define first car)

(define rest cdr)

CS 200 Spring 2003

Implementing cons, car and cdr

- Using PS2:

(define cons make-point)

(define car x-of-point)

(define cdr y-of-point)

- As we implemented make-point, etc.:

(define (cons a b) (lambda (w) (if (w) a b)))

(define (car pair) (pair #t)

(define (cdr pair) (pair #f)

CS 200 Spring 2003

Pairs are fine, but how do we make threesomes?

CS 200 Spring 2003

Threesome?

- (define (threesome a b c)
- (lambda (w)
- (if (= w 0) a (if (= w 1) b c))))
- (define (first t) (t 0))
- (define (second t) (t 1))
- (define (third t) (t 2))

Is there a better way of thinking about our triple?

CS 200 Spring 2003

Triple

- A triple is just a pair where one of the parts is a pair!

(define (triple a b c)

(cons a (cons b c)))

(define (t-first t) (car t))

(define (t-second t) (car (cdr t)))

(define (t-third t) (cdr (cdr t)))

CS 200 Spring 2003

Quadruple

- A quadruple is a pair where the second part is a triple

(define (quadruple a b c d)

(cons a (triple b c d)))

(define (q-first q) (car q))

(define (q-second q) (t-first (cdr t)))

(define (q-third t) (t-second (cdr t)))

(define (q-fourth t) (t-third (cdr t)))

CS 200 Spring 2003

Multuples

- A quintuple is a pair where the second part is a quadruple
- A sextuple is a pair where the second part is a quintuple
- A septuple is a pair where the second part is a sextuple
- An octuple is group of octupi
- A list (any length tuple) is a pair where the second part is a …?

CS 200 Spring 2003

Lists

List ::= (consElementList)

A list is a pair where the second part is a list.

One little problem: how do we stop?

This only allows infinitely long lists!

CS 200 Spring 2003

From Lecture 6Recursive Transition Networks

ORNATE NOUN

end

begin

NOUN

ARTICLE

ADJECTIVE

ORNATE NOUN ::= ARTICLE ADJECTIVE NOUN

ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE NOUN

ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE ADJECTIVE NOUN

ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE ADJECTIVE ADJECTIVE NOUN

ORNATE NOUN ::= ARTICLE ADJECTIVE ADJECTIVE ADJECTIVE ADJECTIVE ADJECTIVE NOUN

CS 200 Spring 2003

Recursive Transition Networks

ORNATE NOUN

end

begin

NOUN

ARTICLE

ADJECTIVE

ORNATE NOUN ::= ARTICLE ADJECTIVES NOUN

ADJECTIVES ::= ADJECTIVE ADJECTIVES

ADJECTIVES ::=

CS 200 Spring 2003

Lists

List ::= (consElementList)

List ::=

It’s hard to write this!

A list is either:

a pair where the second part is a list

or, empty

CS 200 Spring 2003

Null

List ::= (consElementList)

List ::=

null

A list is either:

a pair where the second part is a list

or, empty (null)

CS 200 Spring 2003

List Examples

> null

()

> (cons 1 null)

(1)

> (list? null)

#t

> (list? (cons 1 2))

#f

> (list? (cons 1 null))

#t

CS 200 Spring 2003

More List Examples

> (list? (cons 1 (cons 2 null)))

#t

> (car (cons 1 (cons 2 null)))

1

> (cdr (cons 1 (cons 2 null)))

(2)

CS 200 Spring 2003

List Recursion

CS 200 Spring 2003

Defining Recursive Procedures

- Be optimistic.
- Assume you can solve it.
- If you could, how would you solve a bigger problem.
- Think of the simplest version of the problem, something you can already solve. (This is the base case.)
- Combine them to solve the problem.

CS 200 Spring 2003

Defining Recursive Procedures

on Lists

Be very optimistic

- Be optimistic.
- Assume you can solve it.
- If you could, how would you solve a bigger problem.
- Think of the simplest version of the problem, something you can already solve.
- Combine them to solve the problem.

For lists, assume we can solve

it for the cdr

For lists, the simplest version is

usually null (the zero-length list)

Combine something on the car of the list with

the recursive evaluation on the cdr. Remember

to test null? before using car or cdr.

CS 200 Spring 2003

Defining Sumlist

> (sumlist (list 1 2 3 4))

10

> (sumlist null)

0

(define sumlist

(lambda (lst)

(if (null? lst)

( (car lst) (sumlist (cdr lst))

0

+

CS 200 Spring 2003

Defining Productlist

> (productlist (list 1 2 3 4))

24

> (productlist null)

1

(define productlist

(lambda (lst)

(if (null? lst)

( (car lst) (sumlist (cdr lst))

1

*

CS 200 Spring 2003

Defining Length

> (length (list 1 2 3 4))

4

> (length null)

0

(define length

(lambda (lst)

(if (null? lst)

( (car lst) (length (cdr lst))

0

+

1

CS 200 Spring 2003

Defining insertl

(define insertl

(lambda (lst f stopval)

(if (null? lst)

stopval

(f (car lst)

(insertl (cdr lst) f stopval)))))

CS 200 Spring 2003

(define insertl

(lambda (lst f stopval)

(if (null? lst)

stopval

(f (car lst)

(insertl (cdr lst) f stopval)))))

Definitions(define (sumlist lst)

(insertl lst + 0))

(define (productlist lst)

(insertl lst * 1))

(define (length lst)

(insertl lst

(lambda (head rest) (+ 1 rest))

0))

CS 200 Spring 2003

Charge

- Next Time: lots more things you can do with lists (including the peg board puzzle!)
- PS3 Out Today
- Use lists to make fractals
- You have seen everything you need for it after today
- Due next week Wednesday

CS 200 Spring 2003

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