Scope: Whats in a Name

1
ScopeWhats in a Name?

• CMSC 11500
• Introduction to Computer Programming
• October 16, 2002

2
Roadmap

• Recap Procedural Abstraction
• Procedures as Parameters scale
• Unnamed Procedures Lambda
• Scope
• Bound and free variables
• Local variables
• With formal parameters
• With let
• Procedures as return values

3
Procedural Abstraction

• Goal single point of control
• Avoid copying and modifying code
• Identify similarities in procedures
• E.g. differ only in some function
• Solution Abstract, and pass differing
  procedure(s) as parameter
• Example map
• Doublelist, squarelist, etc,...

4
Scalelist (before abstraction)
(define (scalelist scale alon) (define
(scale-fn x) ( x scale)) (cond ((null?
alon) ()) (else (cons (scale-fn (car
alon)) (scalelist (cdr alon)))))

• Observation1 Same pattern as squarelist, map
• Observation2 Defining scale-fn is silly
• Observation3 Where does scale get its value?

5
Scalelist (after abstraction)
(define (scalelist scale alon) (define
(scale-fn x) ( scale x))
(map scale-fn alon))
6
Unnamed Functions Lambda

• Issue Defining lots of trivial procedures
• E.g. add2, double, triple
• Solution unnamed function
• Cant be recursive
• (lambda (ltpar1gtltpar2gt..ltparngt) exp)
• E.g. Add2 (lambda (x) ( x 2))
• Apply like other procedures
• ((lambda (x) ( x 2)) 10) -gt 12

7
Redefining with Lambda
(define (doublelist alon) (map (lambda (x)
( x x)) alon)) (define (triplelist alon)
(map ???? alon)) (define (scalelist scale alon)
(map ???? alon))
8
Abstraction with Sum Product
(define (sum alist) (cond ((null? alist) 0)
(else ( (car alist) (sum (cdr alist))))

• Product?
• General Pattern?

9
Observation 3 Value of Scale
(define (scalelist scale alon) (define
(scale-fn x) ( scale x))
(map scale-fn alon))

• Lexical scope
• Variable binding Parameters
• Binding occurrence Formal parameter of procedure
  BINDS to value in procedure call
• Bound occurrence Appearances of variable inside
  procedure defn get value
• free variable Global scope top-level define

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Scope

• Region where binding gives value
• Nearest enclosing block with binding occurrence
• Renaming
• Consistently rename variable w/in scope
• Meaning is unchanged
• (define (square x) ( x x))
• (define (double x) ( x x))
• (define (double y) ( y y))
• No change in meaning no effect on square..

11
Scope Examples
(define (p1 x y) ( ( x y) ( ( 2
x) ( ( 2 y) 22)))) (define (p2 x) ( ( 55
x) ( x 11))) (define (p3 x) ( (p1 x 0)
( (p1 x 1) (p2 x))))
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Defining Local Variables with Let

• Local variables
• Store and name partial result
• Avoid repeated computation if result reused
• Make code more intelligible

(let ((x 3) (y 4)) ( x y))
12
13
Let example

• Reverse-and-double
• ((a b) (c d)) -gt((b a) (b a) (d c) (d c) )

(define (reverse-and-double alist) (cond
((null? alist) ()) (else (cons (reverse (car
alist)) (cons (reverse (car
alist)) (reverse-and-double (cdr alist)))))
Problems?????
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Let Example

• Avoid repeated work

(define (reverse-and-double alist) (cond
((null? alist) ()) (else (let
((reverse-first (reverse (car alist)) (reverse-
rest (reverse-and-double (cdr alist))))
(cons (reverse-first (cons (reverse-first
reverse-rest))))
15
Procedures as First-class Objects

• Can be
• Named by variables
• Can be passed as arguments to functions
• Can be included in data structures
• Can be returned as the results of functions

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Procedures as Results of Functions

• Class of procedures
• E.g. scale1, scale2, scale3 ---gt scale-n

(define (scale-n scaler) (lambda (x) ( x
scaler))) (define scale3 (scale-n 3)) (scalelist
scale3 (1 2 3 4)) ----gt (3 6 9 12)
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Summary

• Unnamed procedures
• Scope
• Variable binding
• Parameters as binding instances
• Naming local variables with let
• Returning procedures as results

18
Next Time

• Extended Example