Syntax One - Hybrid CMSC 331

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

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

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

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

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

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.

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

EBNF/BNF EBNF and BNF are equivalent How can {} be expressed in BNF?

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

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

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