Conditionals

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Conditionals
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Outline

• Prerequisites
• Basic functions
• Boolean Expressions
• Objectives
• (if )
• (cond )
• Designing conditional functions
• Reference
• HTDP Sections 4.3, 4.4

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Background

• We frequently need to make choices depending on
  the value of data
• e.g. if we were looking for only real roots of a
  quadratic, we might test the discriminant for
  being negative
• Choices will use boolean expressions to determine
  the appropriate result
• We will use the (if ) or(cond ) function to
  make these choices
• Warning There may be some deliberate errors in
  the code used in examples today

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The if function

• General form of (if )
• (if ()
• ()
• ())

The condition is a boolean expression
Each action is either a literal or a function to
be evaluated
Each action is either a literal or a function to
be evaluated
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Calculating pass - fail

• Consider the task of assigning a pass or fail
• pass-fail number - symbol
• to determine pass or fail for a given
• numerical grade
• examples
• 80 - pass
• under 80 - fail
• (define (pass-fail grade)
• (if ( grade 80)
• 'pass
• 'fail ) )

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The cond function

• General form of (cond )
• (cond
• else )

Each condition is a boolean expression
Each result is either a literal or a function to
be evaluated
A catch-all else condition is optional but
highly recommended
may be used instead of ( ) wherever
they improve readability
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Calculating a grade

• Consider the task of assigning a letter grade
• letter-grade number - symbol
• to determine the letter grade for a given
• numerical grade
• examples
• 90 - A
• under 60 - F
• (define (letter-grade grade)
• (cond ( grade 90) 'A
• ( grade 80) 'B
• ( grade 70) 'C
• ( grade 60) 'D
• else 'F))

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Designing Conditional Functions

• We will follow an outline similar to that for
  designing ordinary functions.
• We add a new step Data Analysis and Definition
• We elaborate the process of developing the
  function body to allow for the complexity of the
  (cond ) function.

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Still the Same Questions to Answer

• Problem statement
• What is relevant?
• What can I safely ignore?
• The Program
• What does it consume? its inputs
• What does it produce? its output
• How are the inputs and outputs related? its
  body
• Resources
• Does Scheme provide the functions I need?
• If not, must I develop those functions myself?
• Testing
• How will I know this thing is doing what I want?

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Programs Purpose (different problem)

• Begin every program with a CONTRACT which states
  its purpose, first logically
• interest-rate number - number
• Generate a program header
• (define (interest-rate amount) )
• Write a brief explanatory statement
• to determine the interest rate for a
• given amount of money
• see HTDP Page 39 for the problem statement

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New Step Data Analysis and Definition

• Draw a picture of the situation
• 4 4.5
  5

(
(

5,000
10,000
0
to determine the interest rate for a
given amount of money if amount 4 if amount
5,000, use 5
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Program Examples (unchanged)

• Do this before you write the body
• Predict the behavior of the program
• Think about the computations involved
• Illustrate the purpose statement with examples
• to determine the interest rate for a
• given amount of money
• if amount
• if amount
• if amount 5,000, use 5
• test with -1, 700, 1000, 2000, 5000,
• 7000, 9999, 10000, 12000

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Write the Body (expanded)

• Replace the ellipses () in the header with the
  code necessary to implement the computation
• Add the (cond ) function to the header
• (define (interest-rate amount)
• (cond
• else )

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Write the Body (expanded)

• Define each condition and insert it in the body
• (define (interest-rate amount)
• (cond (
• (and ( amount 1000) (
• ( amount 5000)
• else )
• Simplify the expressions
• (define (interest-rate amount)
• (cond (
• (
• ( amount 5000)
• else )

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Write the Body (expanded)

• Insert the proper results
• (define (interest-rate amount)
• (cond (
• (
• ( amount 5000) 5.0
• else 0.0))
• Pop Quiz what could be used instead of a
  literal as the result?
• Test the behavior
• Is this going to work properly?

• Constant
• Built-in or user-defined function
• Sequence of functions
• (returns the result of the last function)

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Design the Tests (expanded)

• As a minimum, ensure that the examples work
• Cannot show correct behavior for all inputs
• Look for difficult logical situations
• Mathematical (could I divide by 0?)
• Logical (test all paths)
• i.e. make sure each condition is tested
• Check normal operation, and both upper and lower
  extremes
• Large numbers
• Small numbers

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Demo
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Actual Code

• to determine the interest rate for a
• given amount of money
• if amount
• if amount
• if amount 5,000, use 5
• test with -1, 700, 1000, 2000, 5000,
• 7000, 9999, 10000, 12000
• (define (interest-rate amount)
• (cond (
• (
• (
• else 5.0))

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Questions?
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Summary

• You should now know
• How to use (if )
• How to use (cond )
• Designing conditional functions

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