Understanding Compound Data Structures in Scheme Programming

Scheme: Compound Data Chapter 6 of HTDP Ms. Knudtzon September 19

Checkpoint • Homework: check-color Exercise

Introduction • Rarely do we have such simple data that we can represent it with a single number, string, symbol, or boolean • Usually we have several pieces of data about one object that we are interested in • Example: A cd with artist name, title, price, etc • We compound several pieces of data into one • In Scheme, this is a structure

Representing Pixels • A pixel is like a Cartesian point, with x & y coordinates (but the y direction is downwards) • In Scheme, there is a posn structure that combines two numbers • To create a posn: (make-posn 3 4) • To get the individual numbers back: (posn-x myPosn) (posn-y myPosn)

Distance to 0 • Let’s write a function that computes how far a pixel is from the origin ;; distance-to-0: posn --> number ;; computes distance of a-posn to the origin ;; Example: (distance-to-0 (make-posn 8 6)) = 10 (define (distance-to-0 a-posn) • What is our next step? • Let’s start with what we know about the data

Distance Function (define (distance-to-0 a-posn) … (posn-x a-posn) … … (posn-y a-posn) … ) This is basically our template for any posn function - then we can just fill in the parts that are specific to this specific problem: (define (distance-to-0 a-posn) (sqrt (+ (sqr (posn-x a-posn)) (sqr (posn-y a-posn))))) ;; Test Cases should follow

Structure Definitions • You’ve seen how to use an already defined structure, but how do you create your own structures? • Let’s look at how posn is written as an example

Posn Definition (define-struct posn (x y)) • When DrScheme evaluates this definition, it automatically creates three operations for use to create data and to program: • make-posn, the constructor, which creates posn structures • posn-x, a selector, which extracts the x coordinate • posn-y, a selector, which extracts the y coordinate

Another Example (define-struct entry (name zip phone)) To use: (make-entry “Ms. K” 20016 ‘537-2932) (define x (make-entry “Ms. K” 20016 ‘537-2932)) Think of the structure as a box with a compartment for each field: And you can access each compartment separately: (entry-name x) or (entry-zip x) or (entry-phone x) Just gives the struct a name x

Formalizing Matters • What if we said: (define p (make-posn ‘Albert ‘Einstein)) and then tried to use the “posn” with: (distance-to-0 p) • We would get errors! • So we need to formalize how we intend to use out structures and how we construct the elements of those structures • We do this with a Data Definition

Data Definition • Combination of English and Scheme that is the contract for that structure • Scheme doesn’t check the contract, but you assume that users of your structure or functions will follow what you have specified • For example, we would say ; A posn is a structure ; (make-posn x y) ; Where x and y are numbers

Design Recipe • Let’s see how the Design Recipe scales to make it easy to think out the problems for programs with structures • Data Definition • Examples of Data • Template • Contract & Purpose • Examples (Test Cases) • Header and Body

Data Definition • Search the problem statement for descriptions of the objects needed and design data representations based on that (define-struct student (last first teacher)) ; A student is a structure: (make-student l f t) where l, f & t ; are symbols Or a shortcut I use: (define-struct student (last first teacher)) ; A student is a structure: (make-student symbol symbol symbol)

Examples of Data • Then show (or define) the kinds of data that are acceptable with your data definition (make-student ‘henry ‘mills ‘Ms.K) (define nickI (make-student ‘nick ‘ink ‘Ms.K)) (define nickM (make-student ‘nick ‘m ‘ms.k))

Template • A function that inputs a structure is likely to compute its results from the components of the structure, so it helps to start with those (using the selector expressions) ;; student-func: student --> ???? ;; purpose: (define (student-func aStudent) … (student-last aStudent) … … (student-first aStudent) … … (student-teacher aStudent) … )

Rest of Recipe • Contract & Purpose: do these for the specific functions you are writing • Examples: Write examples (test cases) for the function • Use the data examples you wrote earlier (that’s why I recommend using the defines) (my-s-func nickM) • Header & Body: Using the template, formulate an expression that computes the answer from the available data and other Scheme functions

Putting It All Together • Class Exercise: Create data for boas containing name, length, what they eat   • Write a function isShorter? that determines whether a boa is shorter than a given amount • Design Recipe • Data Definition • Examples Of Data • Template • Contract & Purpose • Examples (Test Cases) • Header & Body

Scheme Mini-Project • Draw Teachpack: Introduces simple graphics operations using posn structures • draw-solid-line: posn posn • draw-solid-rect: posn number number color • draw-solid-disk: posn number color • draw-circle: posn number color • Each operation produces boolean • Each has a matching clear- operation • Your Scheme mini-project (see project handout) will use this drawing package

Scheme: Mixed Data Chapter 7 of HTDP Ms. Knudtzon September 20

Checkpoint • 80-point Quiz #3

Graphical Test Cases • Special > Insert Test Case

Structures • Yesterday our structures were made up of symbols, numbers, booleans & strings • Today, let’s consider structures that can be made of other structures • We will also look at how to do some error checking in our functions to make sure we get the expected kind of data

Distinguishing Data • The other day, I introduced the symbol? and string? operators called predicates • They recognize particular kinds of data • Also available: number? boolean? struct? • For each structure that we make, Scheme also makes a predicate • posn? • student? • boa? • Etc • So any function we write can check the type of its inputs

Mixed Data • We can have one name refer to multiple types of data • Yesterday we defined a dillo and a boa • Let’s do a data definition for an animal ; An animal is either ; a boa structure: ; (make-boa symbol number), or ; a dillo stucture ; (make-dillo symbol number number boolean)

Animal-func • So given that we can use predicates to distinguish our data, let’s make a template for animal data ; animal-func: animal --> ???  (define (animal-func an-ani)  (cond [(boa? an-ami) … (boa-name an-ami) (boa-length an-ami) (boa-food an-ami) … ]  [(dillo? an-ami) … (dillo-name an-ami) (dillo-age an-ami) (dillo-timesRunOver an-ami) (dillo-dead? an-ami) … ]))

New template • Make a cond block to distinguish the different kind of available data • Pull out the available data for each case • Then you can put this all in a comment box   • When you need to write a new function, you can copy the template, fill in the blanks and erase the stuff you don’t need anymore

Animal Function • Let’s add a length field to the dillo definition so that we could compare animal lengths • Using our template, we could then create a new animal function, tooShort? which takes an animal and returns true if the boa is shorter than 6 or 2 for a dillo

Another Example • Lets define a shape class which can be circle or square structures (which also need to be defined), each of which require a posn and a number • The posn is the circle’s center and the upper left corner of the square • The number is the circle’s radius and the square’s length • Follow the design recipe to sketch out everything for a shape • Then write a perimeter function for a shape

Scheme: Mixed Data Cont’d and Lists Chapter 7 & 9 of HTDP Ms. Knudtzon September 21

Shapes Continued • Lets define a shape class which can be circle or square structures (which also need to be defined), each of which require a posn and a number • The posn is the circle’s center and the upper left corner of the square • The number is the circle’s radius and the square’s length • Follow the design recipe to sketch out everything for a shape • Then write a perimeter function for a shape

Error checking • Note: the predicates (type questions) that we have been using to check type for functions could also be used for simple input checking • If we expect a function to only receive numbers and we get something else, we could cause an error, which input a symbol (the function name) and a string (the error message you want displayed) (define (my-func foo) (cond [ (number? foo) …] [ else (error ‘my-func “number expected”)])) • This way you aren’t returning something that isn’t expected (like a string message when the function contract says it returns a number)

Lab Exercise (Homework) • Develop structure and data definitions for a collection of vehicles. The collection should include at least buses, limos, cars, and police-cars. All vehicles should have a licensePlate, milesDriven, and gasTankCapacity. Add a structure-specific attribute for each class of vehicle. Then develop a template for functions that inputs a vehicle. • Expanding on the template, write a function that checks the license plate of a vehicle against a “wantedVehicle” and returns true if it is a match (inputting two vehicles to the function) • Make another function that calculates the miles per gallon that a given vehicle has gotten, assuming it has used a whole tank.

Lists The wonderful world of arbitrary-length structures

Lists • We all understand what a list is - we make them all the time • So the question is how do we make these lists in Scheme? • When we form a list, we always start with the empty list and then we add elements to it

Lists in Scheme • In Scheme, the empty list is simply: empty • And then to construct a longer list, we use the cons operator: (cons “Buy milk” empty)

And again • To add more items, we keep using cons again: (cons “Water plants” (cons “Buy milk” empty)) First rest “Water plants” Etc

Lists of Numbers • We can makes lists of anything - here’s a list of 10 numbers: (cons 0 (cons 1 (cons 2 (cons 3 (cons 4 (cons 5 (cons 6 (cons 7 (cons 8 (cons 9 empty ))))))))))

Mixed Data Lists • Lists can also have values of multiple kinds: (cons ‘APCS (cons 3 (cons “testing testing” (cons true empty))))

Using Lists • Let’s says we are given a list a numbers and we want to add the numbers on the list. How do we do this? • For simplicity, let’s say that we only have a list of three numbers ;; A list-of-3-nums is ; (cons x (cons y (cons z empty))) ;; where x, y, and z are numbers

Writing add-up-3 ;; add-up-3: list-of-3-nums --> number ;; to add up 3 numbers in a list ;; example/test case: ;; (= (add-up-3 (cons 2 (cons 1 (cons 3 empty)))) 6) (define (add-up-3 mylist) …)

Selectors for lists • first and rest are the operators we need to pull out parts of a list • The data definitions for first and last are: • ;; first: non-empty-list --> value  • ;; rest: non-empty-list --> list (define li (cons 10 (cons 20 (cons 5 empty))) What is: • (rest li) • (first (rest li)) • (rest (rest li)) • (first (rest (rest li))) • (rest (rest (rest li)))

Add-up-3 So what do we need to do here? ;; add-up-3: list-of-3-nums --> number ;; to add up 3 numbers in a list ;; example/test case: ;; (= (add-up-3 (cons 2 (cons 1 (cons 3 empty)))) 6) (define (add-up-3 mylist) …)

List Data Definitions • We need a way to describe the lists we want to store and the kind of data they store. • The data definitions good references and they remind us how to build data • Example: ;; A list-of-symbols is either: ; the empty list, empty, or ; (cons s los) where s is a symbol and los is a list of symbols • Note here we have the data definition referring back to itself

LOS or LOST?? ;; A list-of-symbols is either: ; the empty list, empty, or ; (cons s los) where s is a symbol and los is a list of symbols • How does this work? Does it make sense? • We can construct elements from it (the data definition) • It works for any cases of our list that we can think of

Using the Design Recipe • Everything is as before, but the template needs to have cond-expressions for each clause in the data definition • In the case of a list, empty and cons ;; General Template for list-of-symbols ;; alos-func: list-of-symbols --> ???  (define (alos-func alos)  (cond [ (empty? alos) … ]   [ (cons? alos) … (first alos) … … (alos-func (rest alos)) …. ])) Same number of arrows as in data definition

LOS Function Example 1 ;; length : list-of-symbols --> number  ;; consumes a list of symbols and returns ;; the number of items in the list  (define (length alos)  … ) Try this together in Scheme

Homework • Lab Exercise from yesterday (Vehicle Structures) • Review lengthof function from class

(Thursday Lecture) • Review and practice on the whiteboard about lists and list functions • Individual students should have notes

Scheme: Lists Cont’d Chapter 9-10 of HTDP Ms. Knudtzon September 23

Checkpoint • 80 point quiz #4b (instead of yesterday’s) • List exercises • dollar-store? • delta • check-range1? • check-range? • average-price we will do together

Understanding Compound Data Structures in Scheme Programming