BNF and expressive power

1
BNF and expressive power

• Richard Connor

2
Language complexity

• As mentioned before
• Various classes of language exist
• Important classes
• Regular expressions
• Context-free grammars
• Context-sensitive grammars

3
Context sensitivity by example

• var x 3 return( x )
• var x 3 return( y )
• Or
• var x 3 mod 2
• var y 3 mod hello

4
CF and CS grammars

• The wrong programs are correct according to a
  context free grammar
• But this isnt ideal
• To exclude them, we need a context sensitive
  language definition
• Ie the correctness of the expression depends on
  its context
• can we define this in BNF?

5
BNF and context senstive grammars

• BNF can define context sensitivity
• lhs of production can have multiple symbols
• eg
• ltLgt ltAgt mod ltAgt ltAgt ltAgt
• ltAgt mod ltAgt ltintgt ltintgt
• ltAgt ltAgt ltlvalgt ltexpgt
• ltexpgt ltintgt

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Classes of BNF definitions

• Theoretical result only
• (Not used in practical language definition)
• Various restrictions can be placed on (pure) BNF
• Regular expressions Patterns only of the form
• ltnon terminalgt terminal ltnon terminalsgt
• Context-free grammars Patterns only of the form
• lt non terminal gt ltany mix of terminals /
  non-terminalsgt
• Context-sensitive grammars Patterns including
• ltany mixgt ltany mixgt

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Context-sensitive grammars again

• We do need to define these
• (almost all real languages require them)
• To include the concept of
• Type errors
• Identifier scoping errors
• Can be defined in BNF
• But hard (impossible) to write/read
• Different techniques are used
• Context-free grammar description, plus
• Type rules, scope rules, maybe other rules
• These narrow the set of strings defined by the CF
  grammar