Building Abstractions with Data (Part 1)

1. Building Abstractions with Data (Part 1) CS 21a: Introduction to Computing I First Semester, 2013-2014

2. Last Time… • Procedural Abstraction • Creating layers of abstraction for algorithms

3. Today… • Data Abstraction • Creating layers of abstraction for data

4. Outline • The Notion of Types • Abstractions with Data Types • Same Type, Different Implementations

5. The Notion of Types • “G” is a letter, but not a number. • “800-9000” is a telephone number, but “name@example.com” is an e-mail address. • What you’re sitting on is a chair, not a table (hopefully). • You are a person, not a dog (don’t let your significant other change that).

6. The Notion of Types • Any value has a type. • Any piece of data has a data type. • Why is this important?

7. Type Safety • There are procedures that can only be meaningfully carried out if the input data is of a certain type. • Examples: • Sitting should be done on chairs, (maybe occasionally on tables if you have good reasons), but not on candles. • Squaring should be done on numbers, but not on words.

8. Type Safety • Helps catch programming errors early • No accidental squaring of words and using the result as a prescribed amount of medicine.

9. Which Assignments Are Allowed? inta = 16; double b = 18.5; a = b; double c = 18; a = c; c = a;

10. Type Safety in Variables inta = 16; double b = 18.5; a = b; // not allowed double c = 18; // allowed: integers are real numbers a = c; // still not allowed c = a; // allowed: integers are real numbers

11. Type Safety in Variables inta = 16; double b = 18.5; a = b; // not allowed double c = 18; // allowed: integers are real numbers a = c; // still not allowed c = a; // allowed: integers are real numbers Type specifiersput a restriction on what values a variable can hold.

12. Type Safety in Procedures staticintsquare(int x) { return x*x;} parameter type specifier return type specifier return value must be of correct type

13. Will This Work? int a = square("Hello");

14. Will This Work? int a = square("Hello"); square expects integer arguments. Design by contract, and propagate type safety down the barriers of abstraction: square needs to ensure that it’s given an integer, because it will use that argument in a * operation, which also requires its operands to be numbers. The user of square must therefore follow this restriction and only pass an integer argument.

15. How About This? inta = square(3);

16. How About This? inta = square(3.0);

17. How About This? double x = 3; inta = square(x);

18. How About This? double x = 3; inta = square(x); It’s kind of annoying that our square procedure can’t work for real numbers too. We’ll fix this later so that we can have a generic procedure definition that works for both integers and real numbers.

19. A Quick Fix? staticdouble square(doublex) { return x*x;} … double x = 3; double y = square(x); // this works now double a = square(3.5); // and so does this intb = square(5); // but now this won’t work

20. A Quick Fix? staticdouble square(doublex) { return x*x;} … double x = 3; double y = square(x); // this works now double a = square(3.5); // and so does this intb = square(5); // but now this won’t work The complete fix? Much later, or maybe in CS21B.

21. How About This? booleana = square(3);

22. How About This? booleana = square(3) > square(4);

23. How About This? booleana = square(3) + square(4);

24. How About This? staticintsquare(int x) { return"Hello";}

25. The voidReturn Type • Recall: imperative programming insists that some instructions are statements, and others are expressions. • Expressions always have values. • Statements do not always do.

26. The void Return Type • Some instructions can be statements without values. • The print statement doesn’t have an output value, because it already directly prints out to console. There’s no point keeping its “value” somewhere or using it in another expression. • Same goes with main.

27. The void Return Type • So, we invent a new “return type” called void. • Putting void as a return type for a procedure definition means that the procedure does something, but does not return a value to the procedure that called it.

28. Example staticvoidsayFavorite(String name, intnumber) { print(person); print("'s favorite number is "); print(number);} … sayFavorite("Grandma", 42); int x = sayFavorite("Grandma", 42);

29. Example staticvoidsayFavorite(String name, intnumber) { print(person); print("'s favorite number is "); print(number);} … sayFavorite("Grandma", 42); int x = sayFavorite("Grandma", 42); Ok. Procedure call is a statement. Prints “Grandma’s favorite number is 42”.

30. Example staticvoidsayFavorite(String name, intnumber) { print(person); print("'s favorite number is "); print(number);} … sayFavorite("Grandma", 42); int x = sayFavorite("Grandma", 42); Not ok. Procedure call does not produce a value. Alternatively, procedure does not have the correct return type.

31. Example staticvoidsayFavorite(String name, intnumber) { print(person); print("'s favorite number is "); print(number);} … sayFavorite("Grandma", 42); int x = sayFavorite("Grandma", 42); By the way, the String is another built-in type over the set of words or series of characters.

32. Example staticvoidsayFavorite(String name, intnumber) { print(person); print("'s favorite number is "); print(number);} … sayFavorite("Grandma", 42); int x = sayFavorite("Grandma", 42); Strings can take on series of characters enclosed in double quotes as values.

33. Question • Why is it possible to print(square(4)); • But not to print(print(4)); ?

34. Question • Why is it possible to print(square(4)); • But not to print(print(4)); ? All expressions have values, but not all procedure calls do. The print procedure has a void return type specifier.

35. Outline • The Notion of Types • Abstractions with Data Types • Same Type, Different Implementations

36. Three Basic Kinds of Answers to Computational Questions • Number • How far is the earth from the sun? • Yes/No • Is Venus farther from the earth from the sun? • Words • What are the planets closer to the sun than the earth is?

37. Review: “Problem” Versions for Those Questions • Number • How far is a given planet from the sun? • Yes/No • Is this given planet farther from that given planet from the sun? • Words • What are the planets closer to the sun than this given planet is?

38. Three Basic Kinds of Input to Computational Problems • Number • Given mass and acceleration, what’s the force? • Yes/No • Depending on whether the stock goes up or down, what’s the best next investment move? • Words • Given a search phrase, what are the most relevant web pages?

39. Three Kinds of Primitive Data Types • Numerical Data Types • Central assumption of information theory: everything can be represented as a number • Numbers encoded in binary (0s and 1s) • Usually in many variants for efficiency’s sake • The Boolean Data Type • True or False • Assign 0 to false, 1 to true

40. Three Kinds of Primitive Data Types • Symbolic Data Types • Characters • Can be represented as numbers, and later encoded to 0s and 1s • Strings (not really primitive, because Strings are sequences of characters) • Maybe more advanced A.I. can answer some “how” and “why” questions, but even for those, symbolic data will be enough.

41. Primitive Data Types in Java • Read about them here: http://docs.oracle.com/javase/tutorial/java/nutsandbolts/datatypes.html

42. Are These Enough? • Consider: • Given the x and y coordinates of a point, find the x and y coordinates of its reflection across the line with the given A, B, and C coefficients in its equation in general form. • Overly detailed! • And what if we want to expand to three dimensions later?

43. Are These Enough? • Limitation of Java: • Can’t have more than one output value • Only one return statement per procedure • Only one return value per return statement • Can’t output both x and y as two numbers from the same procedure, even if it makes sense to let one procedure simultaneously produce them

44. Are These Enough? • Other kinds of input: • Sound input • Keyboard/controller input • Biometric sensors

45. Are These Enough? • Information comes in many physical kinds. • Light, sound, matter, etc. • Information comes in many conceptual kinds. • Money, personal records, shapes, etc.

46. Are These Enough? • Every kind of data can be broken down into numbers (even symbolic and Boolean data). • For complex systems though, we don’t want to go to the level of primitives all the time.

47. Data Abstraction • It’s better to say: • Given a point, find its reflection across a given line. • Point and line are compound data types. • Procedure for doing this doesn’t have to worry about how points or lines are represented in terms of primitives, as long as the representation obeys certain properties. • Important point (no pun intended) we’ll get to later.

48. Adding Fractions: Without Data Abstraction staticintnumerator-add(inta, int b, intc, int d) { return a * d + b * c; } staticintdenominator-add(inta, int b, int c, int d) { return b * d; }

49. Adding Fractions: With Data Abstraction static Fraction add(Fraction a, Fraction b) { intnum = num(a) * denom(b) + num(b) * denom(a); intdenom = denom(a) * denom(b); returnmakeFraction(num, denom); }

50. Interfacing with Primitives • Input to outer procedure (world) might still be given as primitive data. • To chunk the primitive data, we need to use constructors. • Output from outer procedure (world) might still need to be primitive data. • To examine (and print out) the parts of a chunked piece of data, we need to use selectors.