So I really hope that the quiz is going to work. My group is standing by to kill everything

else on the machine. It shouldn't have an effect on a 24 core machine that has currently an overall

load of 200, so that shouldn't be an issue, but we don't really know yet what it is. So I'm keeping

my fingers crossed. Otherwise, we have a plan namely 505, not 404. And the quiz is going to be

short because we only had one day of lectures last week.

Okay, my clock says 1615.

So, okay.

So, grammars. If we look at the time was pretty decent. Most of you attempted all. I think it's

probably a good idea to go to the tutorial and think about grammars. It's not totally unexpected.

You want to do something here. We're going to need grammars.

Okay, what are grammars? Grammars are just rules that allow you to replace symbols by other

symbols. You start out with a special symbol S and replace it with all kinds of things. For instance,

F to the K, left bracket T1 to TK, where the TKs are again the same things. And the quiz questions,

and even more so the homework questions or problems, are going to not only test whether you

remember what a grammar is or understand what the grammar is, but you can also apply what a grammar

is. And that was what was in the quizzes right now. And of course, we're using grammars as tools,

not because they're so beautiful and enhance your well-being. We need them as tools, which means if

you start learning them when we've used them, then you'll be too slow and distracted from the

stuff that you really want to understand at that point. Okay, any more questions?

We're still in the recap of the preliminaries of the stuff that I assume you know. And if I assume

wrong, which our nice colorful chart suggested, it's on you to actually change that. The last

thing that's caused trouble for people in the past is what we call abstract mathematical language,

especially mathematical language with structures. In math, we often see things like a foo is a

quadruple STVT where blah-de-blah-de-blah-de-blah. And indeed, that's in a way the most efficient way

of writing down what we need. And it's also the most precise way to write down what we need. It is

not necessarily the easiest way or the way that you have known since elementary school. So I would

like to basically briefly talk you through this, what's happening here. Very often, both in programming

as well as in math, we have these structures that have multiple components. For instance, in a phrase

structure grammar, we have four components. So a phrase structure grammar is made up of four things.

And that's all this thing here says. We have four things. We're giving each of them a name. The first

one we explain then is a finite set of something we call non-terminal symbols. We have another set,

capital Sigma, which is also a finite set of terminal symbols. And together, non-terminals and

terminals we call symbols. So you can see there is not a lot of black left over. It's almost all

content words. So it's very efficient and allows me to put the whole thing on one slide. We have a

third set P. We have an individual S for the start symbol. And those are the four parts. And I assume

that you will be able to decode that. So whenever I tell you about a grammar, knowing this definition

is you have to look out for four things. Terminal symbols, non-terminal symbols, rules and the start

symbol. If you understand all of those, then you understand the grammar. Typically, we give what you

as a computer scientist could think of a type. Right? Here, N is a finite set, Sigma is a finite

set, P is a finite set, and S is an N. So we have types for everything. And then to add insult to

injury, some of these components of the structure are again structures. Right? We have the production

rules. Those are actually structures again. They're made up of H and B. Only we're writing them

differently. We're writing them with an arrow so that they become easier to understand for you, I hope.

Okay? Again, something that has two parts. The head, again, we have a type where the head comes from and the B comes from.

And we use all of the parts typically have weird and wonderful names and they're going to matter.

Okay? So this is typically not something you can actually digest in a minute. It takes longer.

A good way of digesting is to come up with your own examples. Right? Make a grammar for English.

Or try to think what a grammar for prologue might look like. Or something like this. And try to solve

the stuff we're also giving you in the quizzes. They're the things we believe that you need. They're

not to frustrate you, but they're the stuff that we believe you need. Okay. So who of you knows what that is?