Class 6:Programming with Data

cs1120 Fall 2011David Evans5 September 2011

Plan

Practice Procedures from Friday

Introducing Lists

Practice Procedure: identity

1. Define a procedure, identity, that takes one input, and outputs that value.

Practice Procedure: pick-oneDefine a procedure, pick-one, that takes three inputs. The first input is a Boolean value (either true or false). If the value of the first input is true, the output is the value of the second input; if the value of the first input is false, the output is the value of the third input.

Practice Procedure: middle

Define a procedure, middle, that takes three numbers as inputs, and outputs the number that is in the middle.

a b c

a < b

b < c

a < cb

c a

yes

yes no

yes no

b < c

a < c b

a c

yes no

yes no

Binary Decision Diagram

Cartoon by Geoff Draper

a < b

b < c

a < cb

c a

yes

yes no

yes no

b < c

a < c b

a c

yes no

yes no

(define middle (lambda (a b c)

Is there a better middle procedure?

A Better Middle?

(define middle (lambda (a b c) (min (max a b) (max b c) (max a c))))

Suggested by Peter Chapman

Code Golf

http://codegolf.com/

Size matters…but isn’t everything: speed, clarity, memory use, etc.

Practice Procedure: find-fixedpoint

Define a procedure, find-fixedpoint, that takes as input a function and an initial value, and outputs the fixed point of the function starting from that value. A fixed point of a function f is a value x such that (f x) evaluates to x.

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Ways to Design Programs

1. Think about what you want to do, and turn that into code.

2. Think about what you need to represent, and design your code around that.

Which is better?

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History of Scheme

Guy Steele

Guy Steele co-designed Scheme, with Gerry Sussman, and created the first Scheme interpreter for his 4th year project (1975)

More recently, Steele specified Java [1995]

Pre-History of Scheme

Scheme [1975]Conniver [1973] Planner [1967]

Based on LISP [John McCarthy, 1958]

Based on Lambda Calculus [Alonzo Church, 1930s]

John McCarthy

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LISP

“Lots of Insipid Silly Parentheses”

“LISt Processing language”

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

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Making Lists

Freedom Park, Tshwane/Pretoria, South Africa

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Making a Pair

> (cons 1 2)(1 . 2)

cons constructs a pair

1 2

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Splitting a Pair> (car (cons 1 2))1> (cdr (cons 1 2))2

car extracts first part of a paircdr extracts second part of a pair

1 2

car cdr

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Pair Examples> (cons (cons 1 2) 3))((1 . 2) 3)> (cdr (car (cons (cons 1 2) 3)))2> (car (car (cons 1 (cons 2 3))))car: expects argument of type <pair>; given 1

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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 matter unless you have an IBM 704

The names “car” and “cons” will come to have mnemonic significance only when we discuss the representation of the system in the computer.John McCarthy, Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I, 1960

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Implementing cons, car and cdr

Next class:how to define cons, car, and cdr ourselves!

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Charge• Quiz Wednesday– Course book through Chapter 4– Gleick’s The Information, Chapters 1-3– Classes 1-5 (including all questions in the class

notes)

• Class Wednesday and Friday: Lots of examples and practice programming with procedures and recursive definitions