Building Abstractions with Variables (Part 2)

Building Abstractions

with Variables (Part 2)

CS 21a: Introduction to Computing I

First Semester, 2013-2014

Last Time…►The three main “customers” good

programs must satisfy►Expressions and statements►Combinations through expressions

and statements►Recursive nature of expressions

Outline►Important Differences►Abstraction through Variables►Abstraction In-Depth►Values and Environments, Names and

Scope

A Combination of Expressions/Statements

►Gives an answer

►Instead of a solution

Program/Algorithm

Program/Algorithm

One answer

Infinitely manyanswers

Infinitely manyquestions

Difference between Computations and Algorithms

► A computation answers a question.► An algorithm solves a problem.► Each particular selection of the set of inputs

to a problem is called a problem instance or question.

► Every time a program runs or an algorithm “runs,” the instance is called a computation.“Instance” connotes “at this instant,” “at a certain

finite point in time.” The difference between instances and whatever it is they are instantiating is that the former is the finite realization of the latter, which is more “infinite” because of its generality.

Difference between Computations and Programs

Program/Algorithm

SolutionInfinitely many

answers

ProblemInfinitely many

questions

Computation/Program Instance AnswerProblem Instance

Choose one questionout of the infinitely many

Difference between Algorithms and Programs

►Algorithms are abstract ideas.►Programs are algorithms written down

in a specific programming language.►Programming is the act of turning

algorithms into programs.

Difference between Algorithms and Programs

►Programs can be run by a computer and each instance or run is a computation.

►Algorithms can’t be run, so there really is no algorithm instance. ►When you try to simulate an algorithm

(with specific inputs) in your mind, you have mentally turned the algorithm into a program, and are acting as a computer.


Scope


►Gives an answer

►Instead of a solution

Program/Algorithm

Program/Algorithm

One answer

Infinitely manyanswers

Infinitely manyquestions


print(3 * 12);

Abstraction through Variables

int number_of_coconuts = 3;

int cost_per_coconut = 12;

print(number_of_coconuts * cost_per_coconut);

Or



int total_cost = number_of_coconuts * cost_per_coconut;

print(total_cost);





Or




print(total_cost);

Variable declaration and assignment, like procedure call, is another kind of statement.





Or




print(total_cost);

Notice how expressions can contain variables. If an atomic expression is a variable, its value is based on a previous assignment.





Or




print(total_cost);

Notice how expressions can be assigned to variables. The expression is evaluated first and the resulting value becomes the value the variable takes on.

The Anatomy of a Variable

3number_of_coconutsname

value

variable


► Input and output values can now be referred to with names.► The variable can be thought of as a bridge that

allows this.► Inputs can be changed without touching the

central algorithm► For now, we can solve problems (answer many

questions) with the same algorithm but only the “same” program.►The program still needs to be recompiled. How to

avoid this? Next time…


►Variables allow each computation to be different, while still using the same algorithm.►+1 for the generality required for

science


►Variable names still have no meaning ► In itself – remember, these are all just

symbols►But the names can be very suggestive

of meanings we should give the symbols so to us the program now looks more meaningful►+1 for the modularity or readability

required for humans.

Practice Programming Problem:Adding Fractions

►Given two fractions, and , print out the numerator and the denominator, one on each line, of the sum . No need to express in lowest terms.

►Assume the following declarations:int a = 5, b = 3, c = 2, d = 6;

►Change the values to test if your program works. Prepare test cases (input/expected output pairs) in advance.


Scope

By Using Variables, You…►Are like using pronoun clauses►Do a multiplication on that which was

given to me as input

By Using Variables, You…►Allow the algorithm to be an algorithm,

instead of just a specific instance►Do something to whatever it is that was

given to me►Whatever it is that was given to me can be

given a short but descriptive name for convenience and meaningfulness.►Programmers choose the name, but they must

choose responsibly.►Don’t care about the specific selection of input

By Using Variables, You…►Give abstract symbols for concrete

things, and describe a general process in terms of the abstract symbols only, separate from the concrete things.►When it’s time to carry out the solution

for a specific instance, the abstract symbols are given concrete values and become concrete things again.

This Is Not A New Idea►Think about money.►Money (variables) is an abstraction

over the relative worth (values) of things against each other.

►The numbers (symbols) we use to talk about money are different from the money.

This Is Not A New Idea►We can have principles of finance, about

money alone.►Without respect to actual things that the

money can buy►Each time we are faced with a new concrete

situation, we can apply the same principles.►Example: Computing change. Actual prices

may vary but we apply the same process each time.

So In Reality, Algorithms Do Not Manipulate Data

►A particular execution instance of a program, a computation, manipulates data.

►Algorithms only manipulate variables which later refer to data.

►The written program is a representation of that manipulation, and the identifiers are representations of variables.

Remember►Thoughts are to algorithms are to variables►Abstract process, abstract language

as►Words are to programs are to identifiers►Abstract process, concrete language

as►Actions are to computations are to values►Concrete process, no language

Why We Have Laws►To prevent crime?►Not the computer scientist’s answer!

►To solve a problem►Problem: a party has inflicted harm on

another, and has caused a dispute, an imbalance in their relationship.

►Desire behind the problem: to give justice, to balance out the imbalance created

Why We Have Laws►A law (code or program) represents a

means (algorithm) of delivering justice (solving the problem) for a particular kind of dispute.

Why We Have Laws►To settle a dispute between two

parties, a judicial arbiter/court (computer) must execute a law (computation).►The code can include phrases like “5 to

10 years sentence” (symbols to represent variables).►The actual penalties (values) can be

different for different circumstances.

Discuss With Your Seatmates►Why we insist on discovering

mathematical formulae►If you ask a professional pianist to

play every other note of a piece, he can easily do it. On the other hand, a very good amateur fails at doing this. Give a possible explanation.

Outline►Important Differences►Abstraction through Variables►Abstraction In-Depth►Values and Environments, Names

and Scope

The Name is Not the Variable!►The name or identifier is a symbol.►The variable is the abstract entity

which the name refers to.►The variable is what the name means

(if it’s a name for a variable) at a given instant.►Other things with names: procedures,

keywords, classes

The Value is Not the Variable!

►The value is what a variable “means” at a given instant.

►What “at a given instant” means will be clearer later. The phrase doesn’t mean the same thing in the two sentences.

The Name is Not the Variable!

►Declaration is mapping a name to a variable.►To make it possible for the program to

refer to it►If it’s impossible to refer to a variable, it

might as well not exist.►Another definition: declaration is making a

variable exist.

The Value is Not the Variable!

►Assignment is mapping a variable to a value.►To make it possible for the computation

to use it.Declaration and assignment can be separate:

int x;x = 42;

The Name is Not the Variable!The Value is Not the Variable!

►You have a name, and you have values, but you are neither your name or your values!

►You are an abstract entity with a name and values!

Variables Need Memory►Need memory for the name-value

pairs they hold►Variables only have values with

respect to an environment, a context, or a space in short-term memory.

The Environment►Pronouns make no sense if they don’t

refer to anything.►You can declare variables without

assigning them anything, but you probably shouldn’t.

►Pronouns change what they mean depending on context.►Each new computation yields a new

environment.

The Environment is Like a Table

Identifier Valuenumber_of_coconuts 3cost_per_coconut 12

environment

variable

Identifiers Need Scope►Need a namespace or scope for the

names that refer to them.►Each new program yields a new scope.

►Two different variables can’t have the same name in the same scope!

int number_of_coconuts = 3;int number_of_coconuts = 5;

Identifiers Need Scope►Need a namespace or scope for the

names that refer to them.►Each new program yields a new scope.

►Two different variables can’t have the same name in the same scope!

int number_of_coconuts = 3;int number_of_coconuts = 5;

Also…►You can’t use a name that means

nothing (does not exist in the scope).

total_cost = number_of_coconuts * cost_per_banana;makes no sense, not just because the units are wrong

Does This Work? Why Or Why Not?

int x = 3;print(x);

How About This?int x;print(x);

How About This?int x = 1;print(y);

How About This?int car = 3;print(automobile);

How About This?int car = 3;int automobile = 4;

How About This?int car = 3;automobile = car;print(automobile);

How About This?int car = 3;int automobile = car;print(automobile);

How About This?int x = 3;print(x);int x = 5;print(x);

How About This?int x = 3;print(x);x = 5;print(x);

Summary►Algorithms, programs, and computations are

different.►Variables, identifiers, and values are different.►Problems and questions are different.►Solutions and answers are different.►We turn an answer into a solution with

abstraction.►Variables are the most basic tools for

abstraction.

Summary►Identifiers must be unique in every

scope.►Variable names can’t be used if they

haven’t been declared first (don’t exist in the scope).

►Computations have environment.►Programs have scope.

Practice Programming Problem:Big Balls?

►Read about data types in Java, particularly boolean data types.

►Read about operators in Java, particularly comparison operators.


►Given the dimensions of two spheres and a cube, figure out if the combined volume of the spheres is larger than the volume of the cube. Print true if they are, false otherwise.

►What declarations do you need? Include them on your own in your program.

►Test your program as done in the first practice.


►HintVolume of a

sphere:Volume of a cube:

Next Time…►More complicated programs will have

plenty of combinations of expressions and statements.►How to manage complexity, next time

Documents

Building Abstractions with Variables (Part 2)