3. Contextfree grammars & parsing


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1 3. Contextfree grammars & parsing
2 The parsing process sequences of tokens parse tree or syntax tree a / [ / index / ]/= / 4 / + / 2
3 The parsing process sequences of tokens parse tree or syntax tree a / [ / index / ]/= / 4 / + / 2
4 Contextfree grammars Representing lexical structures Regular expressions Representing syntactic structures Contextfree grammars A contextfree grammar is a set of grammar rules.
5 Contextfree grammars A contextfree grammar rule in BNF (Backus Naur form) consists of a string of symbols. exp exp op exp ( exp ) number The first symbol is a name for a structure. The second symbol is which is followed by a string of symbols, each of which is either a token, a name, or.
6 Contextfree grammars Other form of grammar rules exp exp op exp ( exp ) number <exp> ::= <exp> <op> <exp> (<exp>) NUMBER Equivalence of grammar rules exp exp op exp ( exp ) number exp exp op exp exp ( exp ) exp number
7 Grammar and derivations start symbol Grammar: set of grammar rules exp exp op exp ( exp ) number op +  * A derivation is a sequence of replacements of structure names by choices on the righthand sides of grammar rules. exp => exp op exp exp op number exp * number (exp) * number (exp op exp) * number (exp op number ) * number (exp number) * number (number number)* number sentential forms sentence
8 The language defined by a grammar The language defined by a grammar is the set of all strings of token symbols obtained by derivation. Nonterminals and terminals exp exp op exp ( exp ) number op +  *
9 Grammar examples Example 3.1 E ( E ) a Example 3.2 E (E) Example 3.3 E E + a a
10 Grammar examples Example 3.4 statement ifstmt other ifstmt if ( exp ) statement if ( exp ) statement else statement exp 0 1 other if (0) other if (1) other else other if (0) if (0) other if (0) if (1) other else other if (1) other else if (0) other else other
11 Grammar examples Repetition a+ A Aa a A => Aa => Aaa=> Aaaa => aaaa (left recursive) A aa a A => aa => aaa=> aaaa => aaaa (right recursive) A Aα β βα* A αa β α*β
12 Grammar examples Repetition a* A Aa ε A aa ε Example 3.5 A (A)A ε
13 Grammar examples Example 3.4 statement ifstmt other ifstmt if ( exp ) statement if ( exp ) statement else statement exp 0 1 Example 3.6 statement ifstmt other ifstmt if ( exp ) statement elsepart elsepart else statement ε exp 0 1
14 Grammar examples Example 3.7 stmtsequence stmt ; stmtsequence stmt stmt s (add ε ) stmtsequence stmt ; stmtsequence ε stmt s (no ; in the end) {s, s;s, s;s;s, } {ε, s;, s;s;, s;s;s;, } stmtsequence nonemptystmtsequence ε nonemptystmtsequence stmt ; nonemptystmtsequence stmt stmt s {ε, s, s;s, s;s;s, }
15 Parse trees Grammar exp exp op exp ( exp ) number op +  * A derivation for number + number exp => exp op exp number op exp number + exp number + number
16 Parse trees Grammar exp exp op exp ( exp ) number op +  * A parse tree for (343)*42
17 Abstract syntax trees 3+4 Parse tree Abstract syntax tree
18 Abstract syntax trees (343)*42 Parse tree Abstract syntax tree
19 Abstract syntax trees if (0) other else other statement ifstmt other ifstmt if ( exp ) statement if ( exp ) statement else statement exp 0 1 Parse tree
20 Abstract syntax trees if (0) other else other statement ifstmt other ifstmt if ( exp ) statement elsepart elsepart else statement ε exp 0 1 Parse tree
21 Abstract syntax trees if (0) other else other Abstract syntax tree
22 Abstract syntax trees s; s; s stmtsequence stmt ; stmtsequence stmt stmt s Parse tree
23 Abstract syntax trees s; s; s stmtsequence stmt ; stmtsequence stmt stmt s Abstract syntax tree
24 Abstract syntax trees s; s; s stmtsequence stmt ; stmtsequence stmt stmt s Abstract syntax tree
25 Abstract syntax trees s; s; s stmtsequence stmt ; stmtsequence stmt stmt s Abstract syntax tree
26 Abstract syntax trees s; s; s stmtsequence stmt ; stmtsequence stmt stmt s Abstract syntax tree
27 Ambiguity number number * number exp exp op exp ( exp ) number op +  *
28 Ambiguity 34 3 * 42 (precedence) exp exp op exp ( exp ) number op +  *
29 Ambiguity (Associativity) exp exp op exp ( exp ) number op +  *
30 Ambiguity Precedence cascade exp exp addop exp term addop +  term term mulop term factor mulop * factor (exp) number Associativity (left) exp exp addop term term addop +  term term mulop factor factor mulop * factor (exp) number
31 Ambiguity 34 3 * 42 exp exp addop term term addop +  term term mulop factor factor mulop * factor (exp) number
32 Ambiguity exp exp addop term term addop +  term term mulop factor factor mulop * factor (exp) number
33 Ambiguity if (0) if (1) other else other (Dangling else) statement ifstmt other ifstmt if ( exp ) statement if ( exp ) statement else statement exp 0 1 most closely nested rule
34 Ambiguity A new grammar without the dangling else problem. statement matchedstmt unmatchedstmt matchedstmt if ( exp ) matchedstmt else matchedstmt other unmatchedstmt if ( exp ) statement if ( exp ) matchedstmt else unmatchedstmt exp 0 1
35 Ambiguity if (0) if (1) other else other statement matchedstmt unmatchedstmt matchedstmt if ( exp ) matchedstmt else matchedstmt other unmatchedstmt if ( exp ) statement if ( exp ) matchedstmt else unmatchedstmt exp 0 1
36 Ambiguity Other methods to solving dangling else problem Disambiguating rules Bracketing keywords (p. 122) ifstmt if condition then statementsequence end if if condition then statementsequence else statementsequence end if Inessential ambiguity (p. 122)
37 {} Repetition EBNF A Aα β (left recursive) : A β{α} A αa β (right recursive) : A {α}β p. 124 [] Optional ifstmt if ( exp ) statement [ else statement ] ( ) Choice exp exp ( +  * ) exp ( exp ) number
38 Syntax Diagrams Representing EBNF Nonterminals Square or rectangle boxes Terminals round or oval boxes
39 factor ( exp ) number Syntax Diagrams
40 A { B } Syntax Diagrams
41 A [ B ] Syntax Diagrams
42 BNF Syntax Diagrams exp exp addop term term addop +  term term mulop factor factor mulop * factor (exp) number EBNF exp term {addop term} addop +  term factor {mulop factor} mulop * factor (exp) number
43 Syntax Diagrams BNF statement ifstmt other ifstmt if ( exp ) statement if ( exp ) statement else statement exp 0 1 EBNF statement ifstmt other ifstmt if ( exp ) statement [else statement] exp 0 1
44 Syntax Diagrams EBNF statement ifstmt other ifstmt if ( exp ) statement [else statement] exp 0 1
45 Syntax of the TINY language A contextfree grammar for TINY (Fig. 3.6) 1: program is a statement sequence. 2: A statement sequence is a list of statement separated by ;. 3: There are five kinds of statements. 48: if, repeat, assign, read, and write statements. 915: expressions Precedence: *, / > +, > <, =
46 Syntax of the TINY language statement sequence stmtsequence stmtsequence ; statement statement
47 Syntax of the TINY language if statement ifstmt if exp then stmtsequence end if exp then stmtsequence else stmtsequence end
48 Syntax of the TINY language repeat statement repeatstmt repeat stmtsequence until exp
49 Syntax of the TINY language assign statement assignstmt identifier := exp
50 Syntax of the TINY language write statement writestmt write exp
51 Syntax of the TINY language operation comparisonop < = addop +  mulop * /
52 Syntax of the TINY language other statements? readstmt read identifier addop +  mulop * / No syntax trees for grammar rules with only nonterminals on the right hand.
53 Syntax of the TINY language
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