1. Syntax (1)

2. Syntax
The syntax of a programming language is a precise description of all its grammatically correct programs.
Levels of syntax
Lexical syntax
Concrete syntax
Abstract syntax

3. Levels of Syntax Lexical syntax Concrete syntax Abstract syntax
all the basic symbols of the language (names, values, operators, etc.)
Concrete syntax
rules for writing expressions, statements and programs.
Abstract syntax
internal representation of the program, favouring content over form.

4. Grammars A metalanguage is a language used to define other languages.
A grammar is a metalanguage used to define the syntax of a language.
Backus-Naur Form (BNF)
version of a context-free grammar

5. BNF Grammar Set of terminal symbols: T Set of nonterminal symbols: N
Set of productions: P
Start symbol: S N

6. Example: Binary Digits
Consider the grammar:
binaryDigit  0
binaryDigit  1
or equivalently:
binaryDigit  0 | 1
Here, | is a metacharacter that separates alternatives.

7. Derivations A grammar for integers:
Integer  Digit | Integer Digit
Digit  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
How we can derive any unsigned integer, like 352, from this grammar?

8. Driving the Integer “352” using Integers Grammar
Integer  Integer Digit
 Integer 2
 Integer Digit 2
 Integer 5 2
 Digit 5 2
 3 5 2
Integer  Integer Digit
 Integer Digit Digit
 Digit Digit Digit
 3 Digit Digit
 3 5 Digit
 3 5 2
rightmost derivation
leftmost derivation

9. Parse Trees
A parse tree is a graphical representation of a derivation.
Each internal node of the tree corresponds to a step in the derivation.
Each child of a node represents a right-hand side of a production.
Each leaf node represents a symbol of the derived string, reading from left to right.

10. Example: The step Integer  Integer Digit
appears in the parse tree as:
Integer
Digit

11. Example: Parse Tree for “352” as an Integer
Integer  Digit | Integer Digit
Digit  0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

12. Arithmetic Expression Grammar
The following grammar defines the language of arithmetic expressions with 1-digit integers, addition, and subtraction.
Example : Parse of the String 5-4+3
Expr  Expr + Term | Expr – Term | Term
Term  0 | ... | 9 | ( Expr )

13. Example: Parse of the String 5-4+3
Expr  Expr + Term
| Expr – Term
| Term
Term  0 | ... | 9
| ( Expr )

14. Precedence
A grammar can be used to define and precedence among the operators in an expression.
* and / have higher precedence than + and -.
Example:
expr → expr + term | expr – term | term
term → term * factor | term \ factor | term % factor |factor
factor → digit | (expr)
digit → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

15. Associativity
A grammar can be used to define associativity among the operators in an expression.
+ and - are left-associative operators
Example: Parse of 4**2**3+5*6+7
Expr → Expr + Term | Expr – Term | Term
Term → Term * Factor | Term / Factor |Term % Factor | Factor
Factor → Primary ** Factor | Primary
Primary → 0 | ... | 9 | ( Expr )

16. Example Parse of 4**2**3+5*6+7
Expr → Expr + Term
| Expr – Term
| Term
Term → Term * Factor
| Term / Factor
| Term % Factor
| Factor
Factor → Primary ** Factor
| Primary
Primary → 0 | ... | 9 | ( Expr )

17. Ambiguous Grammars A grammar can have more than one parse tree.
Consider next grammar
Example:
Draw all a parse tree of (9-5+2) using previous grammar
string → string + string | string – string |0|1|2|3|4|5|6|7|8|9

18. ( 9 – 5 ) + 2
9 - ( )
string 9 5 2 - +
string 2 5 9 + -

19. Another Example: The Dangling Else
With which ‘if’ does the following ‘else’ associate
if (x < 0)
if (y < 0) y = y - 1;
else y = 0;

20. If statement Grammar IfStatement → if ( Expression ) Statement
| if ( Expression ) Statement else Statement
Statement → Assignment | IfStatement | Block
Block → { Statements }
Statements → Statements Statement | Statement

21. The Dangling Else Ambiguity

22. C and C++ Solution to dangling else ambiguity
Associate each else with closest if
Use { } to override

23. Extended BNF (EBNF) Additional metacharacters Braces { }
zero or more occurrences of the symbols that are enclosed within braces.
Parentheses ( )
Enclose a series of alternatives from which one must be chosen
Brackets [ ]
for an optional list; pick none or one

24. EBNF Example BNE EBNE A → x { y } z A → x A' z A' → | y A'
Expr → Expr + Term | Expr – Term| Term
EBNE
Expr → Term {(+ | -) Term}
A → x { y } z
A → x A' z
A' → | y A'

25. Syntax Diagram
A version of EBNE
Example:
Expr → Term {(+ | -) Term}