Application

1
Application

• Note that is synonymous with U in regular
  expressions.

2

• Why have different representation formalisms for
  the same class of languages?
• Convenience of expression
• For certain languages, a regular grammar may be
  substantially easier to write than a regular
  expression (or vice versa).
• Regular expression can be mapped to a recognizer
  in a language containing sequencing, conditional,
  and while-loop.
• Regular grammars can be mapped to finite
  automaton.

3

• Example
• RE difficult

4

• Example
• RE difficult
• Requires simulation of complement using
  union, concatenation, and Kleene-star operation,
  which is not straightforward. (Refer to Finite
  State Automata results.)

complement
5

• Closure properties
• Regular languages are closed under union,
  concatenation, and Kleene-star, by definition.
  However, closure under complementation and
  intersection is not obvious.
• Robustness of Regular Languages
• Various formalisms (such as regular expressions,
  regular grammars, and finite automata) converge
  to defining the same collection of languages.
• Intrinsic stability of regular languages.

6
Specifying and Automatically Generating Compiler
Front-end
(Refer to LEX,FLEX,YACC,BISON)
Lexical Analyzer
Syntax Analyzer
Back-end
Regular Expressions
Context-free Grammar
Attribute Grammars
7

• Pattern Matching in Scripts and PLs
• E.g., Regular expressions in awk, bash, UNIX
  grep, PERL, Python, Ruby, Java, .NET, etc
• Document type definition (DTD) in XML (eXtensible
  Markup Language)
• Specifies context-free syntax of a web-document
  using domain-specific vocabulary.
• Document cs480.html
• Language HTML
• Meta-language SGML, XML

8

• Formal specification of Input and Output formats
  for programs during Software Development and
  Documentation.
• Helpful to the users for clarification in user
  manuals.
• Helpful to the designers in order to make I/O
  details explicit in a standard way.
• Helpful to the developers, the integrators, and
  the testers for communication and clarification.

9
Some URLs

• LEX/YACC/FLEX/Bison
• http//dinosaur.compilertools.net/
• BNF for Java
• http//cui.unige.ch/db-research/Enseignement/analy
  seinfo/JAVA/BNFindex.html
• XML
• http//cm.bell-labs.com/cm/cs/who/wadler/xml/

10
Some URLs (Again!)

• URL for opening a web-page in a Browser
• Users concern What is the syntax of the URL for
  Googles homepage?
• http//www.google.com/
• soundness
• Programmers concern What are all syntactically
  legal URLs?
• (The following URLs work in several
  browsers!)
• http//yahoo.com, yahoo.com
• N\tkprasad\cs466\HW.txt
• file///N/tkprasad/cs466/HW.txt
• ftp//www.cs.wright.edu
• ftp//tkprasad_at_www.cs.wright.edu/
• completeness

11
Ambiguity in Grammars
12
Parse/derivation trees for x - x - x
Ambiguity Two parse trees for x-x-x Two
Interpretations x, -x
13

• Using associativity information, it is possible
  to rewrite the grammar.
• So, the language of expressions with x and is
  not inherently ambiguous.

Left associative
Right associative
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Operator Associativity and Precedences Examples

• Right associative
• a b 5
• a (b 5)
• Left associative
• cout ltlt 5 ltlt abc
• (cout ltlt 5)ltlt abc

• has precedence over
• 1 2 3 1 (2 3)
• 1 2 3 / (1 2)3
• Associativity and precedence information is
  typically used to disambiguate non-fully
  parenthesized expressions containing unary
  prefix/postfix operators or binary infix
  operators.

15
Dangling Else Problem
Grammar
if B1 then if B2 then S1 else S2 vs if B1 then
if B2 then S1 else S2
Ambiguity
16
Inherently ambiguous CFL

• A context-free language that does not have an
  unambiguous context-free grammar is called an
  inherently ambiguous context-free language.

17
Ambiguous Context-Free Grammar