1. Chapter 3: Describing Syntax and Semantics
Lectures # 7

2. Chapter 3 Topics Syntax Graphs Definitions Tokens and lexemes
Formal Definition of Languages
Formal Methods of Describing Syntax
Context Free Grammar (CFG)
Backus-Naur Form (BNF)
Derivation
Parse Trees
An Ambiguous Expression Grammar
Presidency and associativity of grammars
Syntax Graphs
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3. Derivation
A derivation is a repeated application of rules, starting with the start symbol and ending with a sentence. In each step of a derivation, exactly one nonterminal is expanded.
Every string of symbols in a derivation is a sentential form.
A sentential form may contain terminal and nonterminal symbols.
A sentence is a sentential form that has only terminal symbols.
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4. Types of Derivations
Leftmost derivation: a derivation in which the leftmost nonterminal in the sentential form is always the one that is expanded.
Rightmost derivation: a derivation in which the rightmost nonterminal in the sentential form is always the one that is expanded.
A derivation may be neither leftmost nor rightmost.
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5. An Example Grammar
<program>  <stmts> <stmts>  <stmt> | <stmt> ; <stmts> <stmt>  <var> = <expr> <var>  a | b | c | d <expr>  <term> + <term> | <term> - <term> <term>  <var> | const
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6. An Example Derivation
Using the above grammar derive the following sentence:
a = b + const
<program>  <stmts>  <stmt>  <var> = <expr>  a = <expr>  a = <term> + <term>  a = <var> + <term>  a = b + <term>  a = b + const
Sentential Forms
Sentence
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7. Parse Trees
Parse tree is a well-defined representation of a syntactic structure of a sentence.
A parse tree is a tree with the following properties:
1) Root is labeled with the starting symbol;
2) Each leaf is labeled with a terminal symbol (token);
3) Each internal node is labeled with a nonterminal symbol;
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8. Parse Tree vs Derivation
<program>  <stmts>  <stmt>  <var> = <expr>  a = <expr>  a = <term> + <term>  a = <var> + <term>  a = b + <term>  a = b + const
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9. Ambiguous Grammars
A grammar is ambiguous if and only if it generates a sentential form that has 2 or more distinct parse trees.
Example:
Using the sentence const – const/const, prove that the following expression grammar is ambiguous:
<expr>  <expr> <op> <expr> | const
<op>  / | -
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10. An Ambiguous Expression Grammar
The sentence: const – const/const <expr>  <expr> <op> <expr> | const <op>  / | -
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11. Indicating Precedence
If we use the parse tree to indicate precedence levels of the operators, we can avoid ambiguity.
<expr>  <expr> - <term> | <term>
<term>  <term>/const | const
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12. Associativity of Operators
Operator associativity can also be indicated by a grammar.
The following tree is left associative:
<expr>  <expr> + <term> | <term>
<term>  <term> * const | const
Produce the expression:
(3 + 4) + 5
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13. Associativity of Operators (cont.)
Suppose we reverse the order of <expr> and <term> on the RHS of the first rule:
<expr>  <term> + <expr> | <term>
<term>  <term> * const | const
The tree corresponds to:
3 + (4 + 5), meaning + is now right associative.
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14. Rule of thumb for associativity
A left recursive production results in left associativity
E  E + T (+ is left associative)
A right recursive production results in right associativity
E  T + E (+ is right associative)
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15. Extended BNF (EBNF) Optional parts are placed in brackets [ ].
<proc_call>  ident [(<expr_list>)]
BNF: <proc_call>  ident | ident(<expr_list>)
Alternative parts of RHSs are placed inside parentheses and separated via vertical bars.
<term>  <term> (+|-) const
BNF: <term>  <term> + const | <term> - const
Repetitions (0 or more) are placed inside braces { }.
<ident>  letter {letter|digit}
BNF: <ident>  <ident>(letter|digit) | letter
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16. BNF and EBNF BNF <expr>  <expr> + <term>
<term>  <term> * <factor>
| <term> / <factor>
| <factor>
EBNF
<expr>  <term>{(+|-)<term>}
<term>  <factor>{(*|/)<factor>}
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17. Syntax Graphs
Syntax graphs use directed graphs to represent syntax graphically.
Terminals are placed in circles.
Nonterminals are placed in rectangles.
Circles and rectangles are connected with lines with arrowheads.
Pascal type declarations
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