1. LANGUAGE DESCRIPTION: SYNTACTIC STRUCTURE
CHAPTER 2
LANGUAGE DESCRIPTION:
SYNTACTIC STRUCTURE

2. Description
The state of art can be summarized by saying that a language is described by a combination of formal syntax and informal semantics.
Syntax: How programs in the language are built up, grammar.
Semantics: what programs mean, meaning.

3. EXAMPLE
Suppose that dates are built up from digits represented by D and the symbol /, as follows:
D D / D D / D D D D
01/02/2001 is a date, not identified by syntax
January 2, 2001 or 1st February, 2001

4. Organization of Language Descriptions
Several Style of language description
Tutorials : It provides impressions of what the main constructs of the language are and how they are meant to be used
Reference Manuals : describing the syntax and semantics of a language is traditionally organized around the syntax of the language
Formal Definitions : a precise description of the syntax and semantics of a language; it is aimed at specialists.

5. Over View EXPRESSION NOTATIONS ABSTRACT SYNTAX TREES LEXICAL SYNTAX
CONTEXT-FREE GRAMMARS
GRAMMARS FOR EXPRESSIONS
VARIANTS OF GRAMMARS

6. Expression Notations It serves 2 purposes Expressions
Introducing notations for expressions
Providing examples for the syntax description methods
Expressions
Notation:how to combine operators and operands
Prefix, Postfix, Infix, Mixfix
write as expression:
(-b+sqrt(b*b-4.0*a*c)/(2.0*a)

7. Operator Expression1 Expression2
Prefix Notation
Operator Expression1 Expression2
is meaning summation of 3 and 5
Example 2.1
* = * = 3000
* = * = 1800
Try to do this
* = ?

8. Expression1 Expression2 Operator
Postfix Notation
Expression1 Expression2 Operator
is meaning summation of 3 and 5
Example 2.2
* = * = 3000
* = * = 1800
Try to do this
* = ?

9. Infix Notation Precedence and Associativity
Expression1 Operator Expression2
is meaning summation of 3 and 5
Example
4 – 2 – 1 = ( 4 – 2 ) – 1 = 2 – 1 = 1
Or = 4 – ( 2 – 1 ) = 4 – 1 = 3
Try to do this
b*b – 4*a*c = ?

10. Mixfix Notation
Combination of symbols do not fit neatly into the prefix, infix, postfix classification.
Example the keywords if, then and else
if a>b then a else b

11. ABSTRACT SYNTAX TREES
Identify the meaningful components of each construct in the language.
Prefix : + a b
Postfix : a b +
Infix : a + b
Corresponding tree representation is + a b

12. Tree Representation of Expression
A tree consists of nodes, k>0
A node with no children is called a leaf
A node with no parent is called root
A diagram for the tree is
Op denoted operator
Ek denoted operand Op E1 E2

13. Example A tree of expression b*b – 4*a*c (b*b)-(4*a*c)  E1 – E2
1. b*b  E1 * E2
2. (4*a)*c  E1 * E2 * b 4 a c -
Prefix : - * b b * * 4 a c
Infix: b * b – 4 * a * c
Postfix: b b * 4 a * c * -

14. LEXICAL SYNTAX
A lexical syntax for a language specified the correspondence between the written representation of the language and the tokens or terminals in a grammar for the language
Alphabetic sequences as units in a language, called keywords
Occurrences of a token; using token name for names and token number for integers
White space: blank not effect meaning

15. CONTEXT-FREE GRAMMARS
The concrete syntax of a language describes its written representation.
Context-free grammars are a notation for specifying concrete syntax.
BNF from: Backus-Naur Form
A way of writing grammars.

16. Grammars Parse tree 3 . 1 4 Real-number Integer-part fraction digit

17. Context-free grammar Terminals are the atomic symbols
Non-terminals are the variables
Production: A set of rules for identifying the components of a construct
A starting non-terminal represent in Main construct

18. BNF:Backus-Naur Form Terminals
Non-terminals enclosed between < and >
Production in form
non-terminal ::= terminal | <non-terminal>
::= “can be”
| “or”
A starting non-terminal

19. Example of BNF A BNF grammar for real numbers
Terminals : 0,1,2,3,4,5,6,7
Non-terminals : <real-number>,<integer-part>,<fraction>, and <digit>
Productions
<real-number> ::=<integer-part>.<fraction>
<integer-part> ::=<digit>|<integer-part><digit>
<fraction> ::=<digit>|<digit><fraction>
<digit> ::=0|1|2|3|4|5|6|7|8|9

20. Parse Trees Depict Concrete Syntax
Each leaf is labeled with a terminal or <empty>
Each non-leaf node is labeled with a non-terminal
The root is labeled with the starting non-terminal
Children of node, from left to right of right side

21. Example Real-number Integer-part fraction . Integer-part digit1 2 3 7 8 9

22. Ambiguity
Syntactic Ambiguity
Dangling-Else Ambiguity