Representing Information as Data�Part I: Scalar, Itemization, and Partition Data

CS 5010 Program Design Paradigms “Bootcamp”

Lesson 1.3

​

Learning Objectives for Lessons 1.3-1.4

• By the time you finish this lesson, you should be able to:
• name the 5 kinds of information.
• given a piece of information, determine which of the 5 kinds it is.
• for each of the 5 kinds of information, choose a data representation for it and write down your choice as a data definition, including the template.

Information Analysis and Data Design

• Information is what lives in the real world
• Need to decide what part of that information needs to be represented as data.
• Need to decide how that information will be represented as data
• Need to document how to interpret the data as information

Let’s recall what we learned about this step in the last lesson.

Information and Data

Information Analysis

• Of all the information in the world, which parts do we need to represent?
• Choice depends on the application
• Let’s take a look at some applications you might want to write to help you manage a classroom.

Some of the information about a classroom

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

Classroom Scheduling Application

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

If we were writing a classroom scheduling application, what information would we need to represent?

HVAC Application

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

(Heating, Ventilation, and Air-Conditioning)

If we were writing an application to control the heating, ventilation, and air-conditioning, what information would we need to represent?

Building Maintenance Application

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

• Location
• Capacity
• Schedule
• Arrangement of blackboards
• Who’s in it now?
• What color are their clothes?
• Current temperature
• Number of Windows
• Color of seats
• Status of projector
• Status of internet connection
• Number of pieces of chalk in the tray…

​

If we were writing a building maintenance application, what information would we need to represent?

Data Design

• For each kind of information we want to manipulate, we must choose a representation.
• The data definition documents our choice of representation. It has 3 components:
• It shows how to construct a value of the right kind.
• It always shows how to interpret the data as information
• For structured data, it includes a template that provides an outline for functions that manipulate that data
• This serves as a reference as we design the rest of our program.

​

Kinds of Information

• Before we can choose a representation for our information, we need to know what kind of information we are trying to represent.
• We will consider 5 kinds of information:
1. scalar information
2. itemization information
3. partition information
4. compound information
5. mixed information

We’ll do 1-3 in this lesson, and 4-5 in the next lesson

1. Scalar Information

• Simple data, eg numbers, strings, etc.
• These are already values in Racket.
• Racket has lots more kinds of values, but these will be enough for now.
• For scalar information, there’s no data definition or template.
• You’ll get to these when you use scalar data as part of more complicated data.

​

2. Itemization Information

• Itemization information is data that is one of a few values.
• The data definition lists the possible values and their interpretation, and the template shows how to write a function that looks at each of the possible values.

Sample Data Definition for Itemization Information

Itemization Data was called “Enumeration Data” in HtDP 1/e.

interpretation is obvious, so it’s not necessary here. We'll get to more complicated examples later.

Video: How to write a template for itemization data

Itemization Data: Example

;; A TLState is one of

;; -- "red" interp: the traffic light is red

;; -- "yellow" interp: the traffic light is yellow

;; -- "green" interp: the traffic light is green

​

;; tls-fn : TLState -> ??

;(define (tls-fn tls)

; (cond

; [(string=? tls "red") ...]

; [(string=? tls "yellow") ...]

; [(string=? tls "green") ...]))

​

Write it without comments, then comment it

Templates give us the shape of the program

• This template gives us the exact form for every function that manipulates values from the data definition.

3. Partition Information

• Sometimes you need to divide up an existing scalar data type into groups.
• Examples:
• partition the integers into NegInt, 0, and PosInt
• partition the integers into NegInt and NonNegInt
• partition NonNegInt into [0-10000), [10000,20000), and [20000,infinity)
• partition the strings into strings of length 1 and all others.

​

Partition Data

• The data definition must show
• What kind of data is being partitioned into cases
• Exactly which values are in each case
• The interpretation of each case
• The cases must be
• Mutually exclusive
• Exhaustive
• So each value of the data falls into one and only one case.
• The template will be similar to one for itemization data, but it will usually have an “else” clause for the “all others” case.

Data Definitions for Partition Data: Example 1

;; A TaxableIncome is a partition of NonNegInt into

;; the following categories:

;; [0-10000) interp: low income

;; [10000,20000) interp: medium income

;; all others interp: high income

​

;; taxable-income-fn : TaxableIncome -> ??

;; (define (taxable-income-fn income)

;; (cond

;; [(< income 10000) ...]

;; [(and

;; (<= 10000 income)

;; (< income 20000)) ...]

;; [else ...]))

Every positive number falls into exactly one of these categories

The predicates in the cond clause distinguish between them

Data Definition for Partition Data: Example 2

;; An FallingCatKeyEvent is a partition of

;; KeyEvent into the following categories:

;; -- " " (interp: pause/unpause)

;; -- any other KeyEvent (interp: ignore)

​

;; cat-kev-fn : FallingCatKeyEvent -> ??

(define (cat-kev-fn kev)

(cond

[(string=? kev " ") ...]

[else ...]))

​

Itemization Data vs. Partition Data: how to tell the difference

• Partition data will always have an “all others” clause.
• Itemization data never has an “all others” clause.

Summary

• Information lives in the world, data lives in the computer
• Choice of information to be represented depends on the application
• Represent information as data; interpret data as information
• Data definition includes representation, interpretation, and template.
• Kinds of data
• scalar, partition, enumeration, compound, mixed
• templates for each kind of data

To be covered in the next lesson

Next Steps

• Ask Questions on the Discussion Board
• Go on to Lesson 1.4. There we will learn about compound and mixed information.