[BLANK_AUDIO]. 
The problem in countdown to display 
starter is to design a function that 
consumes the countdown type we defined 
earlier and produces a little image of 
the current state of the countdown. 
It might be something that would display 
on your phone if you were watching the 
New Year's Eve countdown. 
So again, the first step of the recipe is 
signature, purpose, stub. 
We can do that quickly, we're going to 
consume a countdown and we're going to 
produce an image. 
And it's going to produce nice image of 
current state of countdown. 
The stub is, what we want to call the 
function countdown to image. 
Of a countdown and the stub for functions 
that produce an image, I think it's kind 
of nice to make the stub just produce a 
blank image, and the way I make a blank 
image is I make a square of size zero, 
and it can be any color you want, since 
it's of size zero, but I make it like 
that. 
Well that's our stub. 
Let's run it. 
Where this function is not defined, this 
square right here. 
Oh, this is the bug about not saying 
required 2HDP image. 
If we go to the top of the file, sure 
enough, there's no require there. 
So we'll say, require 2HTDP slash image, 
we'll run that. 
Okay, now we're okay. 
So this is a good example of why we check 
the wellformance of stubs, and in general 
why we want to run our code as often as 
we can. 
The sooner you find a little mistake, the 
easier it is to fix. 
It's easier to find one now and another 
mistake in a minute, and another mistake 
in a minute, than it is to find all three 
of them in three minutes. 
So run your code as often you can is the 
general rule that you're going to want to 
use. 
Okay, so now we need to do examples. 
The question is, how many examples do we 
need and what should they be? 
So again, you can get some guidance for 
this by going to the How to Design data 
page. 
Going down to the section on 
itemization's, because this is an 
itemization. 
And the guidance here that says, that 
there should be at least as many tests as 
there are cases in the itemization. 
And if there are intervals in the 
itemization, then there should be tests 
at all points of variance in the 
interval. 
Let's go back to the code, and I'll show 
you what that means. 
Well, we know there's at least three 
tests okay, so let's quickly do that. 
Check expect countdown to image of some 
value, some value, I'll just make three 
of these, we know there's at least three. 
Let's see the first one corresponds to 
this first case of the type comment 
false, so that's false. 
So now let's see. 
What should countdown to image produce 
when the countdown isn't running? 
Because remember, the interpretation 
tells me that this means the countdown 
has not yet started. 
So if the countdown hasn't yet started, I 
don't know, there's lots of things we 
could produce. 
Let's just produce that blank image 
again. 
You could produce something fancier than 
this. 
The goal here is not to make the best 
possible version of this function, but to 
understand what the design of this 
function's about. 
That'll be the first case. 
Now, we need a case for this interval. 
Now, we're suppose to test every point of 
variance in the interval. 
Conceivably, we can test with one 
somewhere in the middle, like five and 
ten. 
But in this particular function, the 
behavior doesn't meaningfully vary across 
the interval. 
Sure we're going to display one at one, 
and ten at ten, and three at three, but 
we're always going to display the number. 
So it's going to really be enough to have 
a single test for this interval. 
Maybe at five. 
Now the question is, what do we want to 
display? 
Well let's see, we need an image. 
And there's a function called text, which 
can turn a string into an image. 
And there's a function called number to 
string, that can turn a number into a 
string. 
So, if we made a text of some size, and 
right now, I'm just going to put the size 
of the text here. 
We'll see next week that the right thing 
to do is define a constant for this, but 
I'm just going to put the size right 
there. 
So what this is saying, is it's saying if 
we countdown to image of five. 
We should produce the text of the number 
five in font size 24 that's black. 
And what are we going to do if the 
countdown is complete? 
Complete is the third case. 
Well I say for that, we'll just say, text 
of Happy New Year. 
And that'll also be 24, but maybe it'll 
be some brighter color, like red. 
Now a very important thing has happened 
here, which is I've really worked out the 
behavior of this function using the 
concrete examples. 
So before I'm writing the actual code of 
the function, we get a lot of the 
designing of the behavior of this 
function. 
So that's the examples, let's run them. 
Right, they all run, but some are 
failing. 
That means they're well-formed. 
So now this was the stub, let's comment 
it out. 
Let's put a note that says, use template 
from countdown. 
Let's get that template. 
We'll copy it down here. 
And let's see. 
We rename it. 
We rename it countdown image, so in the 
false case well, this corresponds to this 
example. 
So that's just that blank image again. 
And this case is, let's see. 
We're going to convert, see whatever it 
is. 
This'll just be text of. 
Here's number to string, of see size 24 
and black. 
And when cons get complicated like this, 
we tend to put the question and answer on 
separate lines. 
That makes the con easier to read. 
And then in this final case, that 
corresponds to this example, which is 
just text Happy New Year, 24 red. 
Let's see what's happening here. 
Let's try it. 
Number-to-string, this function is not 
yet defined, not defined. 
I didn't get the error here, though. 
Oh right, the Doctor Racket version of 
this function is named with an arrow. 
Like this. 
Okay, one of the tests didn't pass. 
Happy New Year differs from happy, oh I 
didn't put the exclamation marks in. 
Now let's try. 
I'll save it and run it, and all three 
tests pass. 
Notice I had to fix two bugs there. 
In each case, what I did was I read the 
warning message, or I read the failing 
test. 
I looked at the highlighted code. 
And I used that to give me an idea of 
what the problem was and how to fix it. 
The key thing about having bugs in the 
code, is just to expect that that's part 
of it. 
Don't get upset about it, don't worry 
about it. 
It happens all the time. 
It's just part of it. 
The very best programmers in the world 
have bugs in their code. 
Fixing it is part of designing good 
programs. 
And we're going to talk more as we go 
through the course. 
About techniques for finding the bug as 
our programs get more and more 
sophisticated. 
Now again, notice that the data 
definition told us there were three 
cases. 
It's an itemization that includes an 
interval. 
That gave us the template. 
It also gave us the examples, and it 
helped us fill in the template for the 
function. 
A lot starts with the data definition. 
Let me show you one little side point 
here. 
We saw that Doctor Racket names its 
number-to-string function number arrow 
string. 
And we named our countdown to image 
function, countdown to image. 
That's because this naming convention 
here is something you're not going to get 
away with in other programming languages. 
So I wanted you to see this naming 
convention, too. 
But if you wanted to rename this 
function, let me show you a neat trick. 
What you're going to do is you click, 
going to click on check syntax here. 
And now, when I hover countdown to image 
here, it shows me all the calls to it. 
But when I hover over one of these it 
shows in the definition that defines it. 
Now what I'm going to do is on the Mac, 
I'm going to Ctrl-click. 
On Windows, I right-click and I go to 
Rename countdown-to-image. 
And I'll rename it up here using the 
other name in convention, and notice how 
I fixed all of them. 
But notice how I didn't fix the one that 
was in this comment. 
It only fixes the ones that aren't 
commented out. 
So now if you want to, you've got the 
function named the other way. 
This renaming command that I used is a 
thing called a refactoring, and it's very 
useful when programs start to get big, to 
have tools like that for doing things 
like renamings. 
We'll talk more about that as we go on in 
the course.