PLT: Lecture 9

1
PLT Lecture 9

• Classifying Grammars and Parsing

2
Classifying Grammars

• Unrestricted Grammars
• a -gt b
• Otherwise no restrictions
• Context Sensitive Grammars
• a -gt b
• a !gt b
• Context Free Grammars
• A-gt b
• Regular Grammars
• A-gtaB
• A-gta

3
The Drunkards Lament

• Instances
• Some dirty swine stole my drink
• A pig stole my drink
• A lousy rat took my drink
• A rotten lousy dirty rat swiped my drink
• The lousy dirty rotten swine took my drink
• Try to make a Context Free Grammar out of it
• Try to make a Regular Grammar out of it.

4
Drunkards Lament CF Grammar

• ltLamentgt-gt ltArticlegtltAdjstuffgtltNoungtltVerbgt my
  drink
• ltArticlegt-gtSome A The
• ltAdjstuffgt-gtltAdjgtltAdjstuffgt
• ltAdjstuffgt-gtltAdjgt
• ltAdjstuffgt-gt l
• ltAdjgt-gt rotton lousy dirty
• ltNoungt-gt swine pig rat
• ltVerbgt-gt took swiped stole

5
Drunkards Lament Regular Grammar

• ltLamentgt-gt Some ltRestOfStuffgt
• ltLamentgt-gt A ltRestOfStuffgt
• ltLamentgt-gt The ltRestOfStuffgt
• ltRestOfStuffgt-gtrotton ltRestOfStuffgt
• ltRestOfStuffgt-gtlousy ltRestOfStuffgt
• ltRestOfStuffgt-gtdirty ltRestOfStuffgt
• ltRestOfStuffgt-gtswine ltVerbObjectgt
• ltRestOfStuffgt-gtpig ltVerbObjectgt
• ltRestOfStuffgt-gtrat ltVerbObjectgt
• ltVerbObjectgt-gttook ltObjectgt
• ltVerbObjectgt-gtswiped ltObjectgt
• ltVerbObjectgt-gtstole ltObjectgt
• ltObjectgt-gt my ltDrinkWordgt
• ltDrinkwordgt-gt drink

6
From Generating To Parsing

• So far, generative
• Now parsing
• Can we move, using the production rules, from the
  start symbol to the language instance
• Can we apply the production rules in reverse to
  work back up to the start symbol from the
  language instance
• If we establish at least 1 sequence of
  application of production rules
• If we prove we cant establish a sequence of
  application of production rules

7
A Simple Started E.G.

• Start Symbol
• E
• Production Rules
• E-gtET
• E-gtT
• T-gtTF
• T-gtF
• F-gt(E)
• F-gta
• Possible Parses 3
• Summation by Parse Tree

8
Top-Down parsing

• Start at the start symbol
• Leftmost derivation
• Rightmost derivation
• If unambiguous parse tree, then a successful
  top-down parse can be fully specified by
• The parse tree
• Specifying the strategy
• Specifying the production rules
• The need for an automaton
• Top-Down parsing
• Bottom-up parsing

9
CFGs and Mathematical Characteristics

• Can we impose some semantic knowledge in the
  grammar?
• Priority
• Check our example
• Associate a VN with each priority
• N VN with ops of priority P
• N VN with ops of priority P
• P is 1 priority greater than P
• N-gtNo1N
• N-gtNo2N
• .
• N-gtN