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Announcements

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Title: Announcements

1
Announcements

Test No. 4 Monday (11/13)
Functional Programming
Closed Book Closed Notes
Multiple Choice
Challenging

2
Quiz

(define deepsum
(lambda (list)
(cond ((null? list) 0)
((number? (car list))
( (car list) (deepsum (cdr list))))
(else ( (deepsum (car list))
(deepsum (cdr list)))))))

(deepsum '(((2 (3) (((4)) (4 4) 54 3) 22) ((((4
5)))))))
105
3
Quiz

Function bound to variables

(define x (lambda (y) y))

Function passed as a parameter

(define f (lambda (x y) (x y))) (f car '(a b c))

Function returned as a value

(define f (lambda (a) (lambda (b) ( a
b)))) (f 5) ((f 5) 6)
4
OOP in Scheme

Simple example
Box object
Stores a value
State of the box is defined by the value
Use a box-maker function to create a box object

5
OOP in Scheme

Methods
update! Update the value in the box
show Show the value stored in the box
swap! Swap the value in the box with another
value
reset! Reset the value in the box to the initial
value
type Return the type of the object

6
OOP in Scheme

What are boxes?
Functions
Sending a message to the object would entail
applying the object to the arguments
Simulate message passing by using a send function
(send object method-name operands..)

7
Example

(define box-a (box-maker ( 3 4)))
(define box-b (box-maker 5))
(send box-a 'show) 7
(send box-b 'show) 5
(send box-a 'update! 3)
(send box-a 'show) 3
(send box-b 'update! (send box-a 'swap! (send
box-b 'show)))
(send box-a 'show) 5
(send box-b 'show) 3
(send box-a 'reset!)
(send box-a 'show) 7
(send box-a 'type) box
(send box-a 'update 27) Error Bad method name
update sent
to object of box type.

8
OOP in Scheme

Methods
update! Update the value in the box
show Show the value stored in the box
swap! Swap the value in the box with another
value
reset! Reset the value in the box to the initial
value
type Return the type of the object

9
Boxmaker

(define box-maker
(lambda(init-value)
(let ((contents init-value))
(lambda msg
(case (1st msg)
((type) "box")
((show) contents)
((update!) (for-effects-only (set!
contents (2nd msg))))
((swap!) (let ((ans contents)) (set!
contents (2nd msg)) ans))
((reset!) (for-effects-only (set! contents
init-value)))
(else (delegate base-object msg)))))))

10
Boxmaker

Takes an argument to initialize the value in the
box
Returns a function that takes arbitrary number of
arguments
Parameter list is specified by msg
Each invocation of box-maker returns an object
E.g. box-a, box-b

11
Auxiliary Functions

(define delegate
(lambda (obj msg)
(apply obj msg)))
(define base-object
(lambda msg
(case (1st msg)
((type) "base-object")
(else invalid-method-name-indicator))))

12
Sending Messages

(define send
(lambda args
(let ((object (car args)) (message (cdr
args)))
(let ((try (apply object message)))
(if (eq? invalid-method-name-indicator
try)
(error "Bad method name" (car
message)
"sent to object of"
(object 'type)
"type.")
try)))))

13
Error Functions

(define error
(lambda args
(display "Error")
(for-each (lambda (value)
(display " ")
(display value))
args)
(newline)))

14
Lambda Calculus

Square maps real numbers to real numbers

15
Lambda Calculus

Foundation of functional programming
Developed by Church (1940s)
Defines
Function parameters
Body
Does NOT define a name

16
Lambda Calculus

Given a lambda expression

Application of lambda expression

17
Lambda Calculus

Any identifier is a lambda expression
If M and N are lambda expressions, then the
application of M to N, (MN) is a lambda expression

18
Lambda Calculus
Examples
19
Lambda Calculus
Not bound implies free
20
Lambda CalculusSubstitution

A substitution of an expression N for a variable
x in M is written as MN/x
If free variables of N have no bound occurrence
in M,
MN/x is formed by replacing all free
occurrences of x in M by N
Else
Assume that variable y is free in N and bound in
M
Consistently replace the binding and
corresponding bound occurrences of y in M by a
new variable (say u)
Repeat this in M until there is no bound
occurrence
Replace all free occurrences in M by N

21
Lambda CalculusSubstitution
22
Lambda CalculusSemantics

This is called Beta-Reduction
Replace the lambda expression using the
substitution principle
Represents a single function application

23
Lambda CalculusSemantics

Evaluation of lambda expression is a sequence of
beta reductions
A lambda expression that does not contain a
function application is called a normal form

24
Lambda Calculus