These grammars that we've been introducing describe something new context free languages.

It relates grammars to parsing, which is one of the concepts in this class.

These days I think your time, the human's time, is more important than the computers.

Finite State Machines, adding a lexer that follows them automatically,

Here I've written down four claims.

So in lecture, we spent a lot of time learning about context free grammars and languages.

But that's an example of an application that also uses this sort of linguistic analysis perhaps a little less related to context free grammars but still in the same vein.

The set of languages that can be described by re write rules or grammers like this are called context free languages.

like HTML or SQL, the language of database queries.

That line above it is the context.

That's much more important than knowing the particular syntax for any language.

Here's a new quiz. The Great Grammar Fix Up.

It handles LL. It handles LR. It handles LALR.

That's an excellent question.

They're the actual input that we're trying to match.

Sometimes this statement is true, and sometimes it's not.

A context free grammar can capture the language a N and b N, where N is the same.

This is called being lazy, and it's a phenomenal virtue when you're writing programs.

Units 3 and 4 were relatively abstract to some degree, intentionally so.

That's a good point, Peter, and the answer is yes.

Actually, they're both just concise notations for specifying possibly infinite sets of strings.

All right. So, it's another one of these puzzle like questions.

You might think, Boy, is there a context expensive grammar out there? What's the opposite of free?

It depends on the context.

They may get a little bit bigger, but it will totally work.

All of that is going to matter for figuring out the true interpretations of programs.

In theory, you could compose it over here as well.

For all three of these cases and regular expressions there is something corresponding we can do in the world of context free grammars.

This is always true because we have our Pac Man diagram here, and also because you can take any regular language and represent it with a context free grammar.

All right. Now that you've gone to the hard work of defining all of those procedures,

Well, because, sentences are more interesting.

This might seem a little counterintuitive but remember the glory of parsing, or the glory of context free grammars, is that a very concise grammar notation stands for an infinite number of strings.

In this problem we've been asked to define a function, cfgempty, which takes in a representation of a context free grammar, a starting state, and a list of visited states and determines whether or not that context free grammar is empty.

This branch of the family is all about representation.

They specify sets of strings, and they can be implemented under the hood with finite state machines.

We often want to check and see if a string is in the language of a context free grammar or matches that context free grammar, can be derived or generated by that context free grammar these are all the same question and one way to do that was memoization, which for many years I always wanted to call memorization, but it's just not.

Context free grammars are more powerful than regular expressions, and context free grammars can tell if a program declares a variable before using it.

But is there anything beyond that?

So we're going to need something more than just parsing, more than context free grammars, to reason about programs that include substrings like X 2.

Y has the value of 2.

I am just gonna pause for a moment to let you think about that.

In most interpreters, this is a problem.

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We need to know where we came from in order to know where we're going.