1. September 13th
Grammars

2. Grammars
They are a way of describing the syntax of programming languages
We will be using
BNF grammar (as in Mini-Language Core)
Syntax diagrams (in Pascal)
BNF grammar
Was invented in 1958 as a way of describing Algol 58 by John Backus

3. BNF grammars BNF grammar is context-free grammar
Noam Chomsky – classified grammars
Context-free grammar
Regular grammar
Context-sensitiver grammar …

4. Characteristics of grammar
A grammar consists of
A four-tuple
A set of terminals
A set of non-terminals
A set of rules (or productions)
A start (or goal) symbol

5. Uses of grammars
It can be used to generate legal sentences in a programming language
It can be used to determine whether a given sentence in a programming language is correct
parsing

6. What did we learn from Mini-Language Core’s BNF
It described the language well enough for most of us to write a program in an unfamiliar language
We could determine whether a given statement we wrote in Mini-Language Core was correct
It really only told us about syntax, not about semantics
There were a number of things that we could not determine from the grammar

7. Terminology Lexemes – lowest level syntactic units
Token – is a category of lexemes
index = 2 * count + 17;
Index, count are identifiers
=, *, + are operators
2, 17 are integer literals
; is a separator or terminator
Metalanguage – is a language used to describe other languages
Aside: identifiers can reference variables, constants, methods, programs, etc.

8. Potential Problems A grammar may be ambiguous
Two different parse trees may be generated for the same expression.

9. Sections 3.4 and later
Less important in this class – read to be able to answer homework questions but don’t agonize over the material in axiomatic and denotational semantics.