Lec 15 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008

Lec 15 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008

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OpenCourseWare at ocw.mit.edu. PROFESSOR: Last time, Professor
Guttag introduced the idea of objects and classes
and this wonderful phrase called object-oriented
programming. And it’s a topic I want to pick
up on today, we’re going to do for the next few lectures,
and it’s a topic I want to spend some time on
because this idea of capturing data and methods, the term we’re
going to use for it, but data and functions that belong
to that data, things that can be used to manipulate them,
is a really powerful one. What we’re really getting at is
the idea of saying I want to have a way of grouping
together information into units that make sense. So I can go back to one of those
topics we had at the beginning, which is the idea
of abstraction, that I can create one of those units as a
simple entity, bury away the details and write really
modular code. And so we’re going to
talk about that a lot as we go along. What we’re really doing, or
I shouldn’t say what we’re really doing, a basic piece of
what we’re doing, when we talk about classes or objects, is
we’re doing something that Professor Guttag mentioned,
we’re defining an abstract data type. Now what in the world
does that mean? Well basically what we’re
doing is we’re giving ourselves the ability to create
data types the same way that we have some built-ins,
so we have things like int, float, string, these are
built-in data types. And if you think about it,
associated with each one of those data types is a set
of functions it’s intended to apply to. Sometimes the functions —
sometimes a function can be used on multiple data types,
plus, for example, we saw could add strings, or could
add ints, but each one of those data types has associated
with it a set of functions that are geared
to handling them. We want to do the same thing,
but with our data types. We want to create data types and
functions, or we’re going to call them methods, that
are specifically aimed at manipulating those
kinds of objects. And our goal is then to
basically see how we can build systems that take advantage
of that modularity. Right, so the fundamental idea
then, is, I want to glue together information, I want
to take pieces of data that naturally belong together, glue
them together, and attach some methods to it. And that’s, you know, saying
a lot of words, let’s do an example because it’s probably
easiest to see this by looking at a specific example. So here’s the example I’m
going to start with. Suppose I want to do little
piece of code that’s going to do planar geometry, points
in the plane. All right, so I want to have
some way of gluing those things together. Well you know what a point is,
it’s got an x- and a y- coordinate, it’s natural to
think about those two things as belonging as a
single entity. So an easy way to do this would
be to say, let’s just represent them as a list.
Just as a 2-list, or a list of 2 elements. It’s easy to think of a point as
just a list of an x- and a y- coordinate. OK, for example, I might say
point p1 is that list, x is 1, y is 2. in fact, if I draw
a little simple — it’s basically pointing to that point
in the plane, right, x is 1, y is 2. OK, fine, there’s another way
to represent points on the plane now, and that’s in
polar form, so this, if you like, is Cartesian. Another way to represent a point
in a plane is I’ve got a radius and I’ve got an angle
from the x-axis, right, and that’s a standard thing
you might do. So I might define, for example,
in polar form p 2, and let me see, which example
did I do here, we’ll make this the point of radius 2 and at
angle pi by 2, I’m going to make it easy because pi by 2
is up along this axis, and that’s basically that point. Ok, just fine, it’s
no big deal. But here now becomes
the problem. I’ve glued things together but
just using a list. Suppose I hand you one of these lists. How do you know which
kind it is? How do you know whether
it’s in Cartesian form or in polar form? You have nothing that identifies
that there, you have no way of saying what this
grouping actually means. Right, and just to get a sense
of this, let’s look at a simple little example, so on
your hand-out, you’ll see I’ve got a little piece of code that
says assuming I’ve got one of these points, I want to
do things with it, for example I might want to add
them together. So this first little piece of
code right here says, ok you give me 2 points, I’ll create
another 1 of these lists and I’ll simply take the x, sorry
I shouldn’t say x, I’m going to assume it’s the x, the
x-values are the two points, add them together, just right
there, the y-values, add them together and return that list.
And if I actually run this, which I’m going to do — excuse
me, do it again — OK, you can see that I’ve
added together and I’ve printed out the value of r, and
I’ll just show you that in fact that’s what I’ve got. This looks fine, right, I’m
doing the right thing. Another way of saying it is,
I’ve actually said, what did I use there, (1,2) and (3,1), It’s
basically saying there is the first point, there’s the
second point, add them together and I get that point. OK, that sounds fine. Now, suppose in fact these
weren’t x and y glued together, these were radius
and angle glued together. In that case point p 1 doesn’t
correspond to this point, it actually corresponds to the
point of radius 2 and angle 1, which is about here. I think I wrote this down
carefully so I would make sure I did it right. Sorry, said that wrong, radius
1 and angle 2, 2 radians is a little bit more than pi half. And the second point is of
radius 3 and angle 1, which is up about there. So what point, sorry, bad
pun, what point am I trying to make here? Different understandings of what
that piece means gives you different values, and that’s
a bit of a problem. The second problem is, suppose
actually I had p 1 and p 2 were in polar form, and I
ran add points on them. This little piece of code
here that I did. Does that even make any sense? Course not, right? You know when you add 2 polar
forms, you add the radii together, you don’t add the
angles together, you need to do it in Cartesian form. So what I’m leading up to here
is that we’ve got a problem. And the problem is, that we want
to build this abstract data type, but we’d like to
basically know what kind of object is it, and what functions
actually belong to it, how do we use them? And so I’m going to go back to
this idea of a class, and let’s build the first of these,
and that is shown right here on this piece
of your handout. I’m going to define a class,
and in particular, what I’m going to do, is walk through
what that says. So I’m going to now build
an object, it’s going to represent a point. So what does that thing
say up there? It’s got this funky looking
form, right, it says, I’ve got something that I’m going to
call a class, got that key word class right here. And I’m going to give it a name,
and right now I’m just building a simple piece of it —
but first of all, what does a class do? Think of this as, this is
a template for creating instances of an object. At the moment, it’s a really
dumb template. I’m going to add to it in
a second, but I want to build up to this. Right now it’s got that second
key word there called pass, which is just Python’s way
of saying there’s an empty body in here. Right,, we’re going to add to
it in a second, but the idea is class is going
to be a template for creating instances. How do I use it? Well, I call class just like
a function, and you can see that below. Having created this thing called
Cartesian point, I’m going to create two instances
of it. c p 1 and c p 2. Notice the form of it, it’s
just the name of the class followed by open paren,
close paren, treating it like a function. What that does, is that it
creates, c p 1 and c p 2 are both instances of this
type, specific versions of this type. For now the way to think about
this is, when I call that class definition, it goes off
and allocates a specific spot in memory that corresponds
to that instance. Right now it’s empty, actually
it’s not quite empty, it has a pointer back to the class. And I can give a name to that,
so c p 1 and c p 2 are both going to point to that. Once I’ve got that, I can now
start giving some variable names, sorry not, rephrase
that, I can give some attributes, I can give some characteristics to these classes. So each instance has some
internal, or will have some internal attributes. Notice how I did
that up there. Having created c p 1 and
c p 2, I had this weird looking form here. Not so weird, you’ve actually
seen it before. In which I said c p 1
dot x equals 1.0. What’s this doing? c p 1 points
to an instance, it points to a particular version
of this class. And I have now given an internal
variable name x and a value associated with that. So I’ve just given
it an x variable. All right, c p 1 dot y, I’ve
said assign that to the value 2, 2,0. So now c p 1 has inside of
it an x and y value. Did the same thing with
c p 2, give it a different x and y value. Again, remind you, c p 2
is a different instance of this data type. All right, when I call the class
definition it goes off and finds another spot in
memory, says that the spot I’m going to give you a pointer back
to that, give it the name c p 2, and then by running these
2 little assignments statements here, I’ve given it
an x and a y value for c p 2. So you see why I say it’s
a template, right? Right now it’s a simple
template, but it’s a template for creating what a class looks
like, and I now have an x- and y- value associated with
each instance of this. OK, and if I wanted to look at
it, we can come back over here, and we can see what does
c p 1 look like, interesting. It says some funky stuff,
and says it’s a kind of Cartesian point. And that’s going to be valuable
to me when I want to get back to using these
things, right? You see that little thing says
dot Cartesian point in there. If I want to get out right now
the versions of these things, I can ask what’s the value
of c p 1 x, and it returns it back out. I could say c p 2 dot x, that
was a bad one to use because they use the same valuable
in both places, didn’t I? So let’s do c p 1 dot
y, c p 2 dot y. OK, so I’ve just created local
versions of variables with each one of these objects. I can get at them just like I
would before, I can assign them in as I might
have done before. OK, now that I’ve got that, we
could think about what would I want to do with these points? Well one thing I might want to
do is say, is this the same point or not? So the next little piece of code
I’ve written here, just move down to it slightly. I’ve got a little piece of
code called same point. And you can look at it. What does it say to do? It says, if you give me two of
these data objects, I’m going to call them p 1 and p 2. I’m going to say, gee, is the
x value the same in both of them, and if it is, and the y
value’s the same, then this is the same point, I’m going
to return true. Notice the form. This is saying, that’s a class,
or sorry, an instance of a class, and I’m going
to get the x value associated with it. I going to come back in a second
to how it actually does that, but it basically says, get
me x value for p 1, get me the x value for p 2,
compare them, just as you would normally. I’ve got another little thing
here that I’m going to use a little later on that just prints
out values of things. OK, let’s see what happens
if I do this. Let me show you simple
little example. I’m going to go over here, and
let me define a couple of these things. I’m going to say p 1, try it
again, p 1 is a Cartesian, it would help if I could type,
Cartesian point, and I’m going to say p 1 of x is 3, p 1 of y
is 4, and I’m going to make p 2 another Cartesian point. And I’ll give it an x value
of 3 and a y value of 4. OK, now I want to say,
are these the same? Thing I’ve got a little
procedure that could do that, but you know the simplest thing
I could do is to say well, gee, wait a minute, why
don’t I just check to see if these are the same thing? So I can say is p 1 the same
as p 2, using Scheme’s built-in is comparator. Say — sorry? PROFESSOR 2: Part of Python? PROFESSOR: Part of Scheme, whoa,
there’s a Freudian slip, thank you, John. I’m showing my age, and my
history here, is p 1 and p 2 the same thing? Hey, there’s a bad English
sentence even worse, now I’m really thrown off. I’m using Python’s is comparator
to say is it the same thing? It says no. But if I say, are p 1 and p 2
the same point, it says yes. And this is a point I
want to stress here. So what’s going on in this case
is, I want to distinguish between shallow equality
and deep equality. The first thing is testing
shallow equality. What it is doing, that’s another
bad English sentence, but what it is doing? Is is essentially saying, given
2 things, do they point to exactly the same referent? Or another way of thinking about
it, is remember I said when I call that class
definition it creates an instance, that’s a pointer to
some spot in memory that’s got some local information
around it. Is is saying, do these things
point to exactly the same spot in memory, the same instance. Deep equality, we get to define,
that’s what I did by writing same point. OK, as I said, I want equality
in the case of points to be, are the x- and y- coordinates
the same? And I’m actually going to change
it. just to show you this point. If I do the following, and
I say, I’m going to assign p 1 to be p 2. What’s that doing? It’s taking the name p 1 and
it’s changing its value to point to exactly what
p 2 points to. And then I say, are they
the same thing? Answer’s yes, because now they
are pointing to exactly the same spot in memory. The same instance. OK, the reason I’m saying this
is, we have one class definition, is a cookie cutter,
it’s a template that’s going to let us build versions
of these things. Every time I use it, I’m
creating a new instance, that’s a different thing
inside of memory. And I want to have that because
I want to have lots of versions of points. OK, now, let’s go back
to where I was. I said one of the things I want
to do is, I want to have different versions of points. So I’ve got now things that
are Cartesian points. I could do the same thing, I
could build polar point. I wanted to show
it to you here. I’ve got a class called polar
point, which is right there, and same kind of thing, I can
create instances of it, and then assign to them things like
a radius and an angle, make instances of those. OK, John? PROFESSOR 2: I just want to
maybe mention that in some of the reading, you’ll see terms
like object equality and value equality, instead of shallow
equality and deep equality. PROFESSOR: Right, so, this
object, this is, right, value quality. Right. And you will see both
terms used. Some people like to use shallow
and deep, object and value, but they’re talking about
the same thing, which is it the same object or is it the
same, in this case, set of values, depending on what you
want to define as you use it. OK, so as I said, now I can go
off and I could create a different class. I’ve got Cartesian points, I
could create a polar points. And I’m going to run it in a
sec, but you can see, the same kind of idea. I define a class call polar
point, I create a couple of them, and I give them a
radius and an angle. And then I could do things like
again, say, okay having done, that let me just run it
here, run that, so I’ve now got polar point 1, and
polar point 2. I can say is polar point 1 the
same as polar point 2, and the answer should be no. And then I could say well, gee,
are they the same point? Oops. What happened? Well it bombed out. Because, what was I
expecting to do? I was expecting to compare
x- and y- values, not radius and angle. And so this doesn’t know how
to do it, it doesn’t have a method to deal with it,
so it complains. So what’s my problem here, and
this is what I want to now lead up to. I could imagine writing another
function for same point, and I have to give it a
name like same point polar, and same point Cartesian. A different function to compare
polar versions of these points. But that’s starting to
get to be a nuisance. What I’d really like to do is to
have 1 representation for a point that supports different
ways of getting information out, but has gathered within it,
a method or a function for dealing with things like how
do I know if it’s the same point or not. So I want to take this idea
classes now, and I want to generalize it. Right, and that is going to
lead us then to this funky looking thing. Right there, and I’d
like you to look at that in your handout. OK, I’m going to go back
and rebuild the class. Ok, and again, I’m going
to remind you, the class is this template. But now I’m going to change
it, so what is that new version of class say. I’m going to call it
c point just to make it a little shorter. You can see inside of it, it’s
got a set of definitions for things like functions. And that first one is this kind
of interesting thing, it’s two underbars, init,
and two underbars. Underscores, I guess
is the right way to say it, not underbars. Right that’s a specific name,
and what it basically says is, when I call the class
instance. That’s a bad mistake. When I call the class
definition, that is I call c point, I’m going to
call it with a specific set of arguments. And what is it going to
happen is that init is going to then apply. It’s going to apply to
those arguments. So let me in fact show
you an example. I’ve got a definition of
Cartesian point, I’ve got a definition of polar point. Let me just run these to
get them in there. Now let’s do the following. Let’s let p be Cartesian point,
and we’ll give it a couple of values. OK? So what happened? Notice in the class definition
here, is there, this is the first thing that’s got called,
and I just called with the value for x and the value for
y, and it went off and did something for me. Does that look right? This is where you all hate it, I
get no eye contact anywhere. Anything look odd about that? I said. When I call this class
definition, it calls init, and I give it an x and a y value. How many arguments
does init take? Three. How many arguments
did I give it? Two. What in the world’s going on? Well, this is a piece of
object-oriented coding that we get to talk about
a little bit. There’s this weird extra
variable in there called self. So what is self? And I have to admit, I did the
standard thing you do every time you run across something
you don’t know about, you go to Wikipedia. So I went and looked up self
in Wikipedia, and I have to read it out. Wikipedia informs us that the
self is the idea of a unified being, which is the source
of an idiosyncratic consciousness. Moreover, this self is the
agent responsible for the thoughts and actions
of an individual to which they are ascribed. It is a substance which
therefore endures through time, thus thoughts and actions
at different moments of time may pertain
to the same self. OK, how do we code that up? Sounds like an AI problem,
I guess right? But there’s actually hidden in
there an important element, and that is, when I create an
instance, I have to be able to get access to the things that
characterize that instance. I won’t say that they’re
thoughts and emotions or things, but what characterizes
an instance here, it’s the internal parameters that specify
what is going on. So in fact what happens inside
of an object-oriented system, and particularly in Python’s
object-oriented system, is the following. When we call init, it’s going
to create the instance, all right, just as we said before. But in particular, it’s
going to use self to refer to that instance. Right, so let me say this
a little differently. I have a class definition. It’s actually an object
somewhere. It has inside of it all those
internal definitions. When I call that class
definition, it calls init. Init creates a pointer
to the instance. And then it needs to have access
to that, so it calls it, passing in self as the
pointer to the instance. That is, it says it has access
to that piece in memory, and now inside of that piece of
memory, I can do things like, as you see here, define self
dot x to be the value passed in for x. What’s that doing? It’s saying where’s
self pointing to? Inside of that structure, create
a variable name x, and a value associated with it. Notice what I also do here, I
create self dot y, give it a value, and then, oh cool, I
can also set up what’s the radius and angle for this point,
by just doing a little bit of work. OK, in fact if you look at what
it does there, just put the pointer over here, it says,
get the value of x that I just stored away, square it,
add it to the value of y squared that I just stored away,
and then take square root, pass it back out. So I just computed the radius
of that particular thing. Right? Compute the angle the same
way, just using the appropriate things. So the idea is that self
will always point to the particular instance. Now you might say, why? Why do it this way? Well, basically because it was
a design choice when the creators of Python decided to
create the language, they basically said, we’re always
going to have an explicit pointer to the instance. Some other object-oriented
programming languages do not provide that pointer. This is kind of nice in my view,
I don’t know if John, you’d agree, but this
is explicit. It actually lets you see how to
get access to that pointer so you know what you’re
referring to. But it’s simply design choice. So another way saying it again
is, when I call the class definition, by default I’m going
to look to see is there an init method there, and if
there is, I’m going to use it. First argument by convention is
always self, because it has to point to the instance, and
then I pass, in this case, another couple of
arguments in. OK, now, if I actually do this,
and I’m going to show you the example, I just, what
did I type over there, I got p was a c point. If I want to get values back
out, I could in fact simply send to that instance a message,
in this case I could say p dot x. In fact let’s do it. If I do that over here — aha —
it gets me back the value. Now let me spend just a second
to say, what was this actually doing? p is an instance. It knows, or has stored away,
and in fact let’s look at it, if we look at what p does,
p says — it says reading through a little bit of this
stuff here, it says — it’s a kind of Cartesian point, it’s an
instance, there’s actually the memory location that it’s
at, that’s why I say this idea of it’s an instant at
a specific spot. It knows that it came from
this class, c point. So when I type, I’m sorry, I
shouldn’t say type, when I write, although I would have
typed it, p dot x, here’s what basically happens. p is an
instance, it’s being sent a message, in this case the
message x, it says I want the x-value back out. p knows that
it is a kind of Cartesian point, it actually goes and
gets, if you like, the class definition up here. And is able to then say,
inside of that class definition, find
the value of x. All right, now, that’s one of
the ways we could get things out, but in fact it’s really
not a good way. A better way to do this would
be the following. If I could type. What did I just do there? One of the things that I
defined inside my class definition here was an
internal method. That method has a name,
obviously, and what does it do? It’s going to go off and get the
values of x and y attached to this thing and return
them to me. And that’s one of the
things I want. I would like my classes
to have methods. So you can access the values
of the specific instance. Now, this is still a nuance, why
would I like to do this? Well this is leading up to why
I want to gather things together in classes
to start with. It’s perfectly legal in Python
to type that in and get the value back out. As I said, I would prefer to
do something that uses an accessor that I just wrote. So p dot Cartesian is a kind
of accessor, it’s getting access to the data. And here’s why I’d
like to have it. Right now, I still have the
problem that those classes, those instances of classes,
are exposed. What do I mean by that? Here’s something I could do. Let’s do it in fact. OK. What point in the plane
does p now point to? X-axis is foobar y-axis
ought to be foobass something else, right? I know it looks like a simple
and silly little example, but at the moment, I still have
the ability to go in and change the values of the
parameters by that little definition. And this makes no sense. And this is because I don’t have
something I would really like to have, which
is data hiding. So you’ll see lots of
definitions of this. I think of data hiding as
basically saying, one can only access instance values, or,
we’ll call them that, instance values through defined
methods. And that’s a wonderful thing to
have because it gives you that modularity, that
encapsulation that basically says, when I create a point, the
only way I can get at the values, is by using one of the
defined methods, in this case it could be Cartesian, and get
all the pieces of that. Unfortunately, Python
doesn’t do this. Which is really a shame. Or another way of saying it
is, please don’t do that. Don’t go in and change the
values of things by using the direct access. Have the computational hygiene,
if you like, to only go through accessors, only go
through methods that are actually provided to
you as you do this. I actually don’t remember,
John, C++ does have data hiding, I think, right? PROFESSOR 2: And not only
shouldn’t you change it, you shouldn’t even read it. PROFESSOR: Exactly. What you’re going to see in a
second I violated in some of my code, which Professor Guttag
is going to yell at me shortly because I should have
done it through accessors, but, he’s exactly right. A good, hygienic way of doing
this is, not only do I not go in and change things except
through a pre-defined method, I shouldn’t read it other than
through a pre-defined method. I should use Cartesian
or polar to pull out those pieces of it. Once I’ve got that, you notice
I can now define a polar point, same way. Notice I’ve now solved one of my
problems, which is, in each one of these cases here, I’m
creating both x y and radius angle values inside of there. If it’s in polar form I passed
in a radius and angle and I’ll compute what the x-
and y- value is. If its in Cartesian form I’ll
pass in an x and y and compute what a radius and angle is. But it now says that in any, in
no matter what kind of form I made it from, I can get out
that kind of information. So for example I defined p,
remember back over here, as a Cartesian point, but
I can actually ask for its polar form. It’s there accessible to me. OK, this is great. Just to drive home one more
reason why I don’t want to have changes to the
values other than through pre-defined things. Notice what happens if
I do the following. I could say I want to
change the radius of this particular thing. OK, perfectly reasonable
thing to do. And if I go look at the polar
form of this, OK, good, looks right, right? It’s now got a different radius,
same angle, so I just changed the radius of it. Oh, but what happened to
the Cartesian form. I should have done this
earlier by typing the Cartesian form earlier, so let
me go back to where I was, sorry for that, let me go
make this a 1 again. If I look at the Cartesian, oh,
I did have the Cartesian form, don’t mind me while I
mutter to myself here quietly. Yeah, that’s right, I did
screw that up badly. All right, we try one more time,
here we go, let’s try one more time. We’ll make p a new point, ok? There’s the Cartesian
representation of it, which is right, (1,2). Here’s the polar representation
of it, some random set of numbers
which makes sense. If I now say, I’m going to go
ahead and change the radius of this, something, my polar form
did it right, but what happened to the Cartesian
form? Ah yes, didn’t change. Which makes sense if you
think of my code. I didn’t have anything in there
that says, if you change one of these values, other
values depend on it, and I want to make that
change to it. So this is one more example of
stressing why I only want to come access to the instances
through defined methods. Because I could’ve built that
in, it says if you change the value of this thing, by the
way you need to change recompute those other values in
order to make this hold up. OK, so what else do I have
then in my little class definitions here? So, I’ve got an init
in both cases. I don’t have to put an init in,
but it’s again, usually a good idea to put that
in originally. I’ve got and init that says,
when you create an instance, here’s what you do. Notice that that typically also
defines for me what the internal variables are, what the
internal characteristics of the class are going to be. Again, I could have some other
functions to compute things, but this is typically
the place where I’m going to put them in. So this is giving me now that
template, better way of saying it, all right, a template
now, for a point is x, y, radius, angle. And I can see that in
those pieces there. And then I’ve got some things
that get me back out information about them. But I got a couple of other of
these strange looking things in there with underbars
to them. So let’s look at what some of
the traditional methods for classes are in Python. I have init. This is what’s actually going
to create the instance, instantiate it, create what
the set of variable values are for it. OK, I have another
one in there, underbar, underbar, str. Anybody have a sense of
what that’s doing? What’s s — sorry, I heard
something, sorry go ahead. STUDENT: Display what I have. PROFESSOR: Displaying what
I have. Thank you. Yeah, I was going to say, think
about what does str do, in general? It converts things into
a string type. How do we typically
print things, we convert them to strings. So str is basically telling
us how we want to have it printed out. OK, in fact if we look at this,
if I say, print of p, it prints it out in that form. Now this is actually a poor
way to do it, because you might say, well, it’s just the
list. But remember, it wasn’t a list. What does it do? It says, if I want to print
out something I built in Cartesian form up here, says,
again, I’m going to pass it in a pointer to the instance, that
self thing, and then I’m going to return a string that
I combine together with an open and close paren, a comma in
the middle, and getting the x-value and the y-value and
converting them into strings before I put the whole
thing together. So it gives me basically my
printed representation. OK. What else do I have in here? Well, I have cmp. My handout’s wrong, which I
discovered this morning after I printed them all out. So the version I’d like you to
have uses, that, greater than rather than equals that
I had in my handout. What’s cmp doing as a method? Yeah? STUDENT: Comparing values? PROFESSOR: Yeah, comparing
values, right? And again, it’s similar
to what cmp would do generically in Python. It’s a way of doing
comparisons. So this is doing comparisons. Now, I put a version up there,
I have no idea if this is the right way to do comparisons
or not. I said both the x- and y-
coordinates are bigger, then I’m going to return
something to it. And I think in the polar one I
said, if, what did I do there, I said, yeah, again if the x
and y are greater than the other one, I’m going to
return them to it. The version in the handout, what
was that actually doing? You could look at the handout. Well I think it was comparing,
are they the same? So that would actually be
another method I could put in. Underbar underbar eq,
underbar underbar. Would be a default or generic
way of doing, are these things the same? OK, in each case, what these
things are doing, is they’re doing, what sometimes gets
referred to as operator overloading. I know you don’t remember that
far back, but in about the second lecture I made a joke of
Professor Guttag which, you know, you didn’t laugh at, he
didn’t laugh at, that’s okay. In which I said, you know, I
didn’t like the fact that things like plus are overloaded,
because you can use plus to add strings, you can
use plus to add numbers, you can use plus
to add floats. And he quite correctly, because
he’s more senior than I am, more experienced
than I am, said it’s actually a good thing. And he’s right. Most of the time. The reason I say that is, by
having operator overloading I can use 1 generic interface
to all of the objects that I want to use. So it makes sense to be able to
say, look for many methods I do want to have a way of doing
comparison, and I don’t have to remember, at top level,
what the name of the comparison method was. I can simply use the built-in
Sc — about to say Scheme again — the built-in Python
comparison operation. Say, are these 2 things
the same? Same thing with cmp, that’s just
saying greater than, and greater than now can apply to
strings, it can apply to floats, it could apply to
points, it could add other pieces into it. So there are some downsides, in
my view, to doing operator overloading, but there’s
some real pluses. And the main one is, I get to
just decide, how do I want to use this, and call it. Yes, ma’am? STUDENT: [INAUDIBLE] PROFESSOR: Right, cmp other,
so how would I call this? A good question. Here’s the way I
would call it. Let me give you, I’m going to
create, a polar point, I’m going to call it q, and we’ll
give it some random values. OK, and now I want to know,
is p greater than q? Now happens to return true here,
but the question is, where’s the other come from? P is a particular object type. When I try and evaluate that
expression of greater than, is going to go into the class
to say greater than is a comp method. So let me say it very
carefully here. When I evaluate, yeah, when
I evaluate this, p is an instance of a point, in this
case it was actually a Cartesian point, it sends a
message to the instance, which sends a message to the
class, to get the cmp method from the class. And that then gets applied to
itself, just p, and one other argument, which is the second
piece there, so other points to the second argument
that was present. OK. John? PROFESSOR 2: — other,
it could have said who or zort or — PROFESSOR: Yeah, sorry, that
was part of the question, I could have a picked foobar could
put anything in here. It’s simply, notice the form of
it here is, it’s going to take two arguments, and
you’re right, self is the original instance. This says, I need a second
argument to it, and that second argument better be
a point so I can do the comparison. Yes ma’am? STUDENT: [INAUDIBLE] PROFESSOR: What do you
think happens? Sorry, the question was, what
happens if I said p is less than q? Got it, yes? Seems pretty obvious, right? Next time I bring the
right glasses. It’s still calling cmp, but it’s
knowing that cmp is just reversing the order
of the arguments. Ok, which makes sense. If greater than takes, expects,
arguments in order x y, less than simply takes
greater than, but with the arguments reversed. OK, so I don’t have to, it’s a
great question, I don’t have to create a second
one for cmp. Cmp is just saying, is this
bigger than, and if I want to reverse it, it goes
the other way. Question? STUDENT: [INAUDIBLE] PROFESSOR: Or equal equal? Let’s try equal equal because
I didn’t define it here. It says they’re not the same,
and boy, I need help on this one, John, it’s not, there’s
no pre-defined eq in there. PROFESSOR 2: So, what cmp does,
and maybe this isn’t exactly the right way to write
is, is cmp actually returns 1 of 3 values. A 0, minus a positive value,
zero or a negative value, depending upon whether
it’s less than, equal, or greater than. PROFESSOR: Right. PROFESSOR2: So it’s not really
a Boolean-valued function. It has 3 possible values
it could return. PROFESSOR: And so in this case,
it’s using the same piece, but it’s returning that
middle value that says they’re actually the same. Right, one the things you can
see now is, we start building up classes, we get
these methods. So you can actually say, how
do I know which methods are associated with the class? For that, we can call dir. And what it does, is it gives
me back a listing of all the things, all the methods, that
are associated with it. Some of which I built:
cmp, init, str. And there, notice, are the
internal definitions and there are the internal variables. And in fact I should’ve
said, we often call those things fields. So inside of an instance,
associated with an instance, we have both methods
and fields. These are both altogether
called attributes of the instance. And then there were a couple of
other ones in there that I hadn’t actually dealt with. The reason I want to point this
out to you is, if we go back up to the kinds of data
objects we started with, floats, ints, strings, they
actually behave the same way. They are instances of a class,
and associated with that class is a set of methods. So for example, I can say,
what are all the methods associated with the number,
or the integer 1? And you probably recognize some
of them in there, right, absolute value, add, comp, cors,
well we didn’t do cors, we did a bunch of
other things. It could also say, what are the
methods associated with the string, 1. I’m sure you can quickly
graph it, but notice they aren’t the same. That makes sense. We have some set of things we
want to do with strings, and different set of things we
want to do with numbers. But underlying Python
is the same idea. These are instances of a class,
and associated with that class are a set
of methods, things that I can deal with. So this is a handy way of being
able to see, what are in fact the methods that are
available if I don’t happen to remember them, and want
to go back to them. OK, I want to spend the last few
minutes just showing you a couple of other things that
we can do in here. Let me see where I want
to go with this. So let’s add one more
piece to this. OK, now that I’ve got points,
I might want to do something with points. So an easy thing to do in planar
geometry is I want to make a line segment. It’s got a start point,
it’s got an end point. Right, if you want to think
of it back over here. There’s a line segment, it’s
got a starting point and ending point. Well, I can do the same thing. And the reason I want to use
this as an example is, here’s my little definition
of segment. Again, it’s got an initializer,
or an instance creator, right there. Takes a start and an end point,
just going to bind local variable names start
and end to those pieces. But notice now, those aren’t
just simple things like numbers, those are
actually points. And that’s where the modularity
comes in. Now I have the ability to say,
I’ve got a new class, I can create instances of a line
segment, and it’s elements are themselves instances of points. OK? And then what might I want
to do with the segment? I might want to get the
length of the segment. And I know it’s kind of, you can
see it on your handout, it has the rest of the
pieces over here. Ok, what’s the geometry say? The length of a line segment? Well, it’s Pythagoras, right? I take the difference in the
x-values, squared, the difference in the y-values,
squared, add them up, take the square root of that. Notice what this says to do. It says if I want to get the
length of a segment, going to pass in that instance, it says
from that instance, get the start point, that’s the
thing I just found. And then from that start
point, get the x-value. Same thing, from that instance,
get the endpoint, from that end point get
the x-value, square. Add the same thing to the
y-values, squared, take the square root. Yes, ma’am? STUDENT: So are you entering a
tuple in for start and end? PROFESSOR: No. I’m entering — well,
let’s look at the example right down here. In fact, let me uncomment
it so we can look at it. All right. I’m going to uncomment that. So notice what I’m
going to do. I’m going to build, this case,
a Cartesian point, I’m going to build a second Cartesian
point, and my segment passes in those class instances. All right, they’re not tuples,
they’re simply an instance with some structuring. And in fact if I go off and
run this, OK, what I was printing here was s 1 dot
length, and that’s — What is it doing? S 1 is a segment. It has inside of it
pointers to 2 points which are instances. And when I call length on this,
it takes that starting point, sends it the message
saying give me your x-coordinate, takes the
endpoint, says give me your x-coordinate, and add
them together. Now, I prefaced this a few
minutes ago about saying Professor Guttag wasn’t
going to like me. He doesn’t like me generally,
but that’s between he and I. He beats me regularly at
tennis, which is why I don’t like him. Sorry, John. This is being taped, which
is really good, isn’t it? So why am I saying that? I said that if I was really
hygienic, and you can now wonder about how often
do I shower? If I was really hygienic. I would only ever access the
values through a method. And I’m cheating here, right,
because what am I doing? I’m taking advantage of the fact
that start is going to be a point, and I’m just directly
saying, give me your x-value. So I don’t know don’t, John, I
would argue if I’d written this better, I would have had a
method that returned the x- and the y- value, and it
would be cleaner to go after it that way. This is nice shorthand, all
right, but it’s something that in fact I probably would
want to do differently. Why would I want to
do it differently? Imagine that I’ve written
code like this, written a bunch of code. And I originally decided I was
going to have as points, it’s going to have internal values
of an x and a y. And then somewhere along the
line, I decide to store things in a different representation. If I had had a clean interface,
that I had a specific method to get those
values out, I wouldn’t have to change anything. Other than that interface. But here, if I decide I’m going
to store things not in x and y, but with some other set
of names, for example, I’ve gotta go back into these pieces
of code that use the points, and change them. So I’ve lost modularity. I’d really like to have that
modularity that says, I’m only going to get access to the
values, not by calling their names, but by calling some
specific method to get access to their names. You could argue, well, x is
in some sense inherently a method, but it’s not nearly as
clean as what I would like. And the last piece I want you to
see here, and then I’ll let you go is, notice now how that
encapsulation, that binding things together has
really helped me. Given the abstraction, the
notion of a point as an instance with some
values, I can now start building segments. And I could now extend that. I could have, you know,
polygonal figures, that are a sequence of segments. And I would be able to simply
bury away the details of how those other instances are
created from how I want to use them by simply calling methods
on the classes. We’ll come back to
this next time.

22 thoughts to “Lec 15 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008”

  1. The use of properties @property is preferred for accessing private fields. Also, __slots__ should be used to help reduce the overall memory usage of instances.

  2. ty MIT for these courses they are great , one question though you can come in even when the class has started already ?
    check the slacker at 00:41 walking in.

  3. Again He goes about  his glassesssssssssssssss….  good lectures, but it's getting hard to follow. And honestly I'm suprised with the students not paying attention..

  4. This is dead hard for beginners. If you are having a hard time in understanding this, check out Kunal's Lecture on udacity. Once you get comfortable you can return back to this.

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