Topics

• Top down and bottom up parsers
• Bottom up parsers
• LL(k) and LR(k) parsers
• Limitations of BNF Grammars
• Attribute Grammars
• Creating parsers
• Knuth

Top Down and Bottom Up Parsers

• Recursive descent parsers are an example of what is called a top down parsers because the sequence of procedure calls corresponds to the sequence of substutitions that occur when going through the tree from the top down


• Another type of parser corresponds to the sequence of substitutions corresponding to substitutions from the bottom up


• Top down parsers follow the sequence of substitutions of a leftmost derivation


• Bottom up parsers follow the the sequence of substitutions of a rightmost derivation (but the steps are generated in the reverse order of the derivation)

Classes of Grammars and Parsers

• For some grammars it's impossible to build a top down parser


• The class of grammars that have top down parsers are called LL(k) [Left-to-right scan, Leftmost derivation, k symbol lookahead]


• The class of parsers that have bottom up parsers are called LR(k) [Left-to-right scan, Rightmost derivation, k symbol lookahead]


• LR(1) > LL(1)


• For a grammar to be LL(1), we must be able to choose the next production by looking at the next symbol

Limitations of Context Free Grammars

• Bottom Up parsers can parse any BNF (ie context free) Grammar


• Some common syntax rules can't be specified using BNF
• Declare before use


• End statement names: procedure foo ... end foo


• procedure calls match declaration: procedure x(i: integer) ... x(3)

Attribute Grammars

• To overcome limitations, we add attributes to the productions and pass the attributes up and down the tree
• Example:

      PROC -> procedure IDENTIFIER1 is PROCBODY end IDENTIFIER2;
      RULEforPROC: IDENTIFIER1.string =
      IDENTIFIER2.string
   

Creating Parsers

• Lexical analyzers and parsers can be created automatically or by hand:
• Automatically
  • Lex: Grammar -> Lexical Analyzer
  • YACC: Grammar -> Parser
  • BISON
• By hand: Recursive descent parser is easiest, if the grammar is suitable

Develoment of Parsing Algorithms

• Earliest: all by hand; no underlying theory
• Later: top down, operator precedence; little theory
• Knuth:
• clarified top down algs
• invented bottom up alg
• Developed attribute grammars