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Understanding Parse Trees and Ambiguity in CS | Syntax Analysis Guide

Explore parse trees, derivation, ambiguity, EBNF, BNF, syntax graphs, recursive descent, and more in computer science syntax analysis. Learn to build parsers effectively.

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Understanding Parse Trees and Ambiguity in CS | Syntax Analysis Guide

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  1. Syntax One - Hybrid CMSC 331

  2. Parse Trees PS → P | P PS P → e | '(' PS ')' | '<' PS '>' | '[' PS ']' What’s the parse tree for this statement ? < [ ] [ < > ] >

  3. Derivation for < [ ] [ < > ] > PS → P → < PS > → P PS > → < [ PS ] PS >’ → < [P] PS >’ → < [ e] PS > → <‘[ ] PS> → < [ ] P > → < [ ] [ PS ] > → < [ ] [ P] > → < [ ] [‘<PS > ] > → < [ ] [‘<P> ] >’ → < [ ] [<e’> ] > → < [ ] [ < > ] >

  4. Ambiguity • Two parse trees for the same expression • Consider the following grammar String → String + String | String - String | DIGIT What are the two trees for 9 - 5 + 2

  5. String String + DIGIT(2) DIGIT(9) - DIGIT(5) Parse Tree 1

  6. String DIGIT(9) - String DIGIT(5) * DIGIT(2) Parse Tree 2

  7. EBNF - Extended BNF • Like BNF except that • Non-terminals start w/ uppercase • Parens are used for grouping terminals • Braces {} represent zero or more occurrences (iteration ) • Brackets [] represent an optional construct , that is a construct that appears either once or not at all.

  8. EBNF example Exp → Term { ('+' | '-') Term } Term → Factor { ('*' | '/') Factor } Factor → '(' Exp ')' | variable | constant

  9. EBNF/BNF • EBNF and BNF are equivalent • How can {} be expressed in BNF? • How can ( ) be expressed? • How can [ ] be expressed?

  10. EBNF for {} • X-> a { b } g • BNF • X -> a X’ • X’ -> b X’ | g • EBNF for [] • X-> a [b ] g • BNF • X -> a b g | a g

  11. Syntax Graphs Terminal in circles Non- terminals in rectangles; Syntax Graphs - put the terminals in circles or ellipses and put the nonterminals in rectangles; connect with lines with arrowheads e.g., Pascal type declarations type_identifier ( identifier ) , constant .. constant

  12. Recursive Descent • An easy way to build a parser • Example • Does work in the face of left recursion • Purge left recursion

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