By Neng-Fa Zhou Programming language syntax 4 Three aspects of languages –Syntax How are sentences formed? –Semantics What does a sentence mean? –Pragmatics.

by Neng-Fa Zhou

Programming language syntax

Three aspects of languages – Syntax

• How are sentences formed?

– Semantics• What does a sentence mean?

– Pragmatics• How to use the language?

Only syntax can be described formally– Regular expressions and context-free grammars

by Neng-Fa Zhou

Regular expressions (RE)

The empty stringis a RE Every symbol in (alphabet) is a RE Let r and s be REs.

– r | s : or– rs : concatenation– (r)* : zero or more instances– (r)+ : one or more instances – (r)? : zero or one instance

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Precedence of operators

high

low

r* r+ r?

rs

r|s

all left associative Examples

= {a,b}1. a|b2. (a|b)(a|b)3. a*4. (a|b)*5. a| a*b

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Algebraic Properties of RE

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d1 r1

d2 r2

dn rn

....di is a RE over {d1,d2,...,di-1}

Regular Definitions

not recursive

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Examples

Identifiers

Decimal integers in Java

Hexadecimal integers

letter A | B | ... | Z | a | b | ... | zdigit 0 | 1 | ... | 9id letter ( letter | digit )*

DecimalNumeral 0 | nonZeroDigit digit*

HexaNumeral (0x | 0X) hexadigit+

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Lex

A tool for automatically generating lexical analyzers

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Lex Specifications

declarations%%

translation rules

%%auxiliary procedures

p1 {action1}p2 {action2}...pn {actionn}

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Lex Regular Expressions

Example-1

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%{ int num_lines = 0, num_chars = 0;%} %% \n ++num_lines; ++num_chars; . ++num_chars;

%%main(){ yylex(); printf( "# of lines = %d, # of chars = %d\n", num_lines, num_chars );}

yywrap(){return 0;}

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Example-2D [0-9]INT {D}{D}*

%%{INT}("."{INT}((e|E)("+"|-)?{INT})?)? {printf("valid %s\n",yytext);}. {printf("unrecognized %s\n",yytext);}%%int main(int argc, char *argv[]){

++argv, --argc;if (argc>0) yyin = fopen(argv[0],"r"); else yyin = stdin;yylex();

}

yywrap(){return 0;}

java.util.regex

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import java.util.regex.*;

class Number { public static void main(String[] args){

String regExNum = "\\d+(\\.\\d+((e|E)(\\+|-)?\\d+)?)?";if (Pattern.matches(regExNum,args[0])) System.out.println("valid");else System.out.println("invalid");

}}

String Pattern Matching in Perl

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print "Input a string :";$_ = <STDIN>;chomp($_);if (/^[0-9]+(\.[0-9]+((e|E)(\+|-)?[0-9]+)?)?$/){ print "valid\n";} else { print "invalid\n"; }

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Context-free Grammars

– is a finite set of terminals– N is a finite set of non-terminals– P is a finite subset of production rules– S is the start symbol

G=( ,N,P,S)

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E T | E + T | E - TT F | T * F |T / FF id | (E)

CFG: Examples

Arithmetic expressions

Statements

IfStatement if E then Statement else Statement

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CFG vs. Regular Expressions

CFG is more expressive than RE– Every language that can be described by regular

expressions can also be described by a CFG

Example languages that are CFG but not RE– if-then-else statement, {anbn | n>=1}

Non-CFG– L1={wcw | w is in (a|b)*}– L2={anbmcndm | n>=1 and m>=1}

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Derivations

if

and then

*

* *

S*

is a sentential form

is a sentence if it contains only terminal symbols

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Derivations

leftmost derivation

Rightmost derivation

if is a string of terminals

if is a string of terminals

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Parse Trees

A parse tree is any tree in which– The root is labeled with S– Each leaf is labeled with a token a or – Each interior node is labeled by a nonterminal– If an interior node is labeled A and has children

labeled X1,.. Xn, then A X1...Xn is a production.

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Parse Trees and Derivations

E E + E | E * E | E - E | - E | ( E ) | id

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YACC%token DIGIT %%lines : lines expr '\n' {printf("%d\n",$2);}

| lines '\n'|;

expr : expr '+' term {$$ = $1 + $3;} | expr '-' term {$$ = $1 - $3;}

| term;

term : term '*' factor {$$ = $1 * $3;}| term '/' factor {$$ = $1 / $3;}| factor;

factor : '(' expr ')'{$$ = $2;}| DIGIT;

 %%

DCG in Prolog Strings with an equal number of 0’s and 1’s

DCG Prolog clauses

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:-table e/2.e --> [].e --> [0],e,[1].e --> [1],e,[0].e --> e,e.

:-table e/2.e(A, A).e(A, B) :- 'C'(A, 0, C), e(C, D), 'C'(D, 1, B).e(A, B) :- 'C'(A, 1, C), e(C, D), 'C'(D, 0, B).e(A, B) :- e(A, C), e(C, B).