Section 4.3: Conditions and Conditional Functions.

Section 4.3: Conditions and Section 4.3: Conditions and Conditional FunctionsConditional Functions

Conditions

Conditions are most useful in the context of a program.

• We call the programs that use them conditional programs.

• We formulate them using conditional expressions.

Question 1: Type into Definitions Window

(define age 10)(cond

[(< age 3) “toddler”][(and (>= age 3) (< age 13)) “pre-

teen”][(and (>= age 13) (< age 20)) “teen”][(>= age 20) “adult”])

; returns “pre-teen”Experiment by changing age & re-executing

Syntax Rule #4: ConditionalsSyntax Rule #4: Conditionals

((cond cond [question … answer][question … answer]……[question … answer]) [question … answer])

Often, the last part is what answer do you want Often, the last part is what answer do you want for everything else, in which case, the last for everything else, in which case, the last question is question is elseelse..

((cond cond [question … answer][question … answer]……[[elseelse answer]) answer])

Exercise 4.3.1Exercise 4.3.1

Decide which of these expressions is Decide which of these expressions is legal:legal:

((condcond ((condcond

[(< n 10) 20][(< n 10) 20] [(< n 10) 20] [(< n 10) 20]

[(> n 20) 0][(> n 20) 0] [(and (> n 20) (<= n [(and (> n 20) (<= n 30))]30))]

[[elseelse 1]) 1]) [ [elseelse 1]) 1])

Exercise 4.3.1 solution

• The expressions are identical except for the third line so look at those.

• The second expression does not have an answer on the third line:

[(and (> n 20) (<= n 30)]

so it is an illegal expression.

Why is the following illegal?

(cond

[(< n 10) 20]

[ * 10 n]

[else 555])

Because…

There is no question on the third line.

Question 2: interest-rate

A bank pays higher interest rates to

depositors with larger balances:

• over $10,000, 6%

• over $5000 and up to $10,000, 5.5%

• over $1000 and up to $5000, 4.5%

• up to $1000, 4%

How do we write this in Scheme?Use a conditional

(cond

[… …]

[… …]

[… …]

[… …])

How do we write this in Scheme?Filling in the questions

(cond

[(<= n 1000) …]

[(<= n 5000) …]

[(<= n 10000) …]

[( > n 10000) …])

How do we write this in Scheme?Filling in the answers

(cond

[(<= n 1000) .040]

[(<= n 5000) .045]

[(<= n 10000) .055]

[( > n 10000) .060])

Write the program

(define (interest-rate amount)

(cond

[(<= amount 1000) .040]

[(<= amount 5000) .045]

[(<= amount 10000) .055]

[( > amount 10000) .060]))

Section 4.4: Designing Conditional Section 4.4: Designing Conditional FunctionsFunctions

Strategy for conditionals

• Identify number of cases; write cond with

that many clauses

• If answers are simple, write all the answers

& then go back to fill in questions

• If questions are simple, write all the

questions & then fill in answers

Design Recipe – Version 2Design Recipe – Version 2

Figure out precisely what you need to do.Figure out precisely what you need to do.

1. Understand the problem1. Understand the problem2. Function contract2. Function contract3. NEW STEP – Data Analysis3. NEW STEP – Data Analysis4. Write examples (in Scheme notation)4. Write examples (in Scheme notation)

Tell the computer how to do it.Tell the computer how to do it.5. Write a skeleton5. Write a skeleton6. NEW STEP – Choose a template6. NEW STEP – Choose a template

7. Fill in the function body7. Fill in the function body Check that the computer does it right. Check that the computer does it right.

8. Testing and debugging8. Testing and debugging

“interest-rate” again

• Understand

This problem is about determining the interest rate given an amount of money in the bank.

• Contract;; interest-rate: number -> number

“interest-rate” again

• NEW STEP: Data Analysis--We take in a number and determine

which of four intervals it is in.

--We print out a different number for each of the intervals.

“interest-rate” again

• ExamplesBorderline Cases

;; (interest-rate 0) -> ??;; (interest-rate 1000) -> ??;; (interest-rate 5000) -> ??;; (interest-rate 10000) -> ??

Interval Cases;; (interest-rate 500) -> ??;; (interest-rate 3000) -> ??;; (interest-rate 7000) -> ??;; (interest-rate 12000) -> ??

“interest-rate” again

• ExamplesBorderline Cases

;; (interest-rate 0) -> .040;; (interest-rate 1000) -> .040;; (interest-rate 5000) -> .045;; (interest-rate 10000) -> .055

Interval Cases;; (interest-rate 500) -> .040;; (interest-rate 3000) -> .045;; (interest-rate 7000) -> .055;; (interest-rate 12000) -> .060

“interest-rate” again

• Skeleton

(define (interest-rate amount)

( … amount … ) )

“interest-rate” again

• NEW STEP: TemplateSo far we only have one template, for conditionals,so we will use that one.

(define (interest-rate amount) (cond

[ question answer ] … [ question answer ])

“interest-rate” again

• NEW STEP: TemplateSince we have four cases, we will have four lines ofquestions and answers, so the template is refined asfollows:

(define (interest-rate amount) (cond

[ question answer ] [ question answer ]

[ question answer ] [ question answer ]))

“interest-rate” again

• Fill in the Function Body --First fill in the questions.

(define (interest-rate amount) (cond

[(<= n 1000) answer] [(<= n 5000) answer] [(<= n 10000) answer]

[( > n 10000) answer]))

“interest-rate” again

• Fill in the Function Body --Now fill in the answers.

(define (interest-rate amount)(cond

[(<= n 1000) .040] [(<= n 5000) .045] [(<= n 10000) .055] [( > n 10000) .060]))

“interest-rate” again

• Testing and Debugging

--As always, type each of your examples into the interactions window.

--If you get an error message or unexpected answer, debug the program to find your mistake.

Next time…

• More on Conditional Functions

• Conditional Functions with other data types – string and images