Assignment: Changing Data CMSC Introduction to Computer Programming November 1, 2002

Roadmap Recap: Binary Search Trees State: Changing Data over Time –Assignment with set! –Multiple statements with begin –Objects with state Traffic light example Bank account example Summary

Sets: Binary Search Trees Bst is: 1) #f 2) (make-bt val left right) –, where val: number; left, right: bst (define-struct bt (val left right)) INVARIANT: For node n, all vals in (bt-left n) n Define operations on sets with bst’s –Element-of?, Adjoin, Intersection, Union,.. –More efficient – O(log n) – search, adjunction.. –Functions exploit & maintain invariant If true of inputs, must be kept true of output

State of the Data Computationally model objects in world Objects change over time –E.g. traffic light: red, yellow, green –Bank account: balance up/down –Age, temperature, etc,…

Changing State in Scheme So far, value in variable once –Bind values to variables with formal params To change state must change value assigned to variable Assignment: set! –(set! var exp) var: variable name; exp: any scheme expression –(set! x 1) –(set! x (factorial 10))

Evaluating set! Expressions evaluate to values –(+ 3 4) => 7 –(set! x 1) ??? Void - nothing Set! is produces an effect, not a value –Changes value of variable Problem: Need to set! AND return value Solution: Do both! –(begin exp1 …. expn) –Does evaluates all exps; returns value of last –(begin (set! x (+ 3 4)) x) -> 7

Example: Traffic Lights State of traffic light: color –TL-color is ‘green, ‘yellow, or ‘red –; contract: current-color: TL-color (define current-color ‘red) –? (set! current-color 5) –? (set! current-color ‘green)

Changing Traffic Lights First step: What would it change to? Function: –;;contract:next-color: TL-color -> TL-color –;; purpose: To identify next color in sequence (define (next-color color) (cond ((eq? color ‘red) ‘green) ((eq? color ‘yellow) ‘red) ((eq? color ‘green) ‘yellow)))

Really Changing Lights Key: change value of state variable with set! (define (turn-light) (begin (set! current-color (next-color current-color)) current-color))) (turn-light) Return value? Current-color?

Example: Bank Account State of bank account: balance –Varies over time: withdrawal, deposit, check.. (define balance 100) (set! balance (- balance 25)) Goal: encapsulation in function –Test if enough money If there is, reduce balance O.w., report error

Make-Withdraw Contract: –;;make-withdraw: number -> (number -> number) –Note: returns a procedure Purpose: –;; to create a procedure to process withdrawal

Make-withdraw (define (make-withdraw initial-balance) (let ((balance initial-balance)) (lambda (amount) (if (<= amount balance) (begin (set! balance (- balance amount)) balance) (error “Insufficient funds!!))))

Using Make-withdraw (define w1 (make-withdraw 100)) (w1 20) –> 80 (w1 100) –> “Insufficient funds!!” (w1 60) –> 20

Summary State variables –Represent objects: state changes over time Forms: –(set! var expression) –(begin exp1 … expn) Modeling traffic lights and bank accounts