Syntax and Semantics

Syntax and Semantics • The Purpose of Syntax • Problem of Describing Syntax • Formal Methods of Describing Syntax • Derivations and Parse Trees • Sebesta Chapter 3

What is Syntax and Semantics • Syntax and Semantics define a PL • Syntax • form or structureofprogram units • expressions, statements, declarations, etc. • Semantics • meaningofprogram units • expressions, statements, declarations, etc. • Why do we need language definitions? • to design a language • to implementer a compiler/interpreter • to write a program (use the language)

Syntax Elements • A sentence is • a string of characters over some alphabet • A language is • a set of sentences • A lexeme is • the lowest level syntactic unit of a language • e.g.,*, public, totalCount • A token is • a category of lexemes • e.g., identifier

Describing Syntax • Recognizers • read an input string in the alphabet of the language (a sentence) and decide whether it belongs to the language • used in compilers • see Chapter 4 for details • Generators • produce sentences in a language • a sentence is syntactically correct if it can be generated by the generator

Backus-Naur Form (BNF) • BNF is a meta-language • i.e. a language used to describe another language • invented by John Backus todescribe ALGOL 58 • used by Peter Naur to describe ALGOL 60 • BNF is equivalent to context-free grammars • a BNF grammar is defined by • a set of terminal symbols, • a set of nonterminal symbols • a set of rules • a start symbol (one of the terminal symbols)

BNF Elements • terminal symbols • are the lexemes of the target PL • e.g., while, ( , ) • nonterminal symbols • represent classes of syntactic structures • they act like syntactic variables • e.g., <statement> • rules • define how a nonterminal symbol can by developed into a sequence of nonterminal and terminal symbols • e.g., <while_stmt>while(<logic_expr> )<stmt>

BNF Rules • A rule has • a left-hand side (LHS) • then  • a right-hand side (RHS) • There can be several rules for one LHS <stmt> <assignment> <stmt> begin<stmt_list> end • Syntactic lists are described using recursion <ident_list> ident <ident_list> ident,<ident_list> • A grammar is • a finite nonempty set of rules

EBNF • Extended BNF (EBNF) • is most often used • avoids having numerous rules for the same LHS • Extra meta-symbols (in addition to  ) • [… ] • enclosed symbols are optional (1 or 0 times) • e.g., <if_stmt> if ( <exp>) <stmt> [ else <stmt> ] • {…} • enclosed symbols can be repeated (0 to n times) • e.g., <ident_list> ident{,ident} • …|… • choice of one of the symbol sequences separated by | • e.g., <stmt> <assignment> |begin<stmt_list> end • (…) • groups enclosed symbols

BNF vs. EBNF BNF EBNF <expr> <term> {(+|- )<term> } <term> <factor> { (*|/) <factor> } <factor> <exp> [ **<factor> ] <exp> (<expr> )| id <expr> <expr> + <term> <expr> <expr> - <term> <expr> <term> <term> <term> *<factor> <term> <term> /<factor> <term> <factor> <factor> <exp> **<factor> <factor><exp> <exp>(<expr> ) <exp> id

Augmented EBNF • another meta-symbol = (equal) instead of  • meta-symbols for repetitions +means one or more times *means zero or more times <ident> =<letter>+( <letter> |<digit> )* • rules can use iteration instead of recursion • e.g.: • <stmt_list> <stmt> |<stmt> ; <stmt_list> • can be formulated as • <stmt_list> =<stmt> ( ; <stmt>)*

Context-Free Grammar • Context-Free Grammars (CFG) • defined by Noam Chomsky • meant to describe the syntax of natural languages • Context-Free Grammar G = (S, T, N, P) • S = start symbol • T = set of terminal symbols – lexemes and tokens • N = set of non-terminal symbols - abstractions • P = production rules – definition of a LHS abstraction using RHS • A sentence • a sequence of terminal symbols

Derivation • A derivation is • a repeated application of rules • starting with the start symbol • substitution of a nonterminal LHS by the RHS of a rule • ending with a sentence (all terminal symbols) • Every string of symbols in the derivation is • a sentential form • A sentence is • sentential form with only terminal symbols

Derivation Types • A leftmost derivation • leftmost nonterminal in each sententialform is expanded first • A rightmost derivation • rightmost nonterminal is expanded first • A mixed derivation • an arbitrary nonterminal is expanded

Derivation Example <program> begin<stmt_list> end <stmt_list> <stmt> |<stmt> ;<stmt_list> <stmt> <var> =<expr> <expr> <term> +<term> |<term> -<term> <term> <var> |const <var> a|b|c <program> => begin<stmt_list> end => begin<stmt> end => begin<var> =<expr>end => begin a = <expr> end => begin a = <term> +<term> end => begin a = <var> +<term> end => begin a = b + <term> end => begin a = b + const end

Questions In the preceding slide: • Is the derivation a leftmost or a rightmost derivation? • State the "opposite" derivation. • I.e. if it is a leftmost derivation give rightmost one • or vice versa • What are the terminal symbols of the language, what are the nonterminal symbols and what is the start symbol? • Change a rule so that begin a = - b + const end is a legal sentence

Parse Tree • Parse Tree is • a hierarchical representation of a derivation <program> begin <stmt_list> end <stmt> <var> = <expr> a <term> + <term> <var> const b

Two Distinct Parse Trees add-first parse tree multiply-first parse tree a = b + c * d a = b + c * d <assign> <assign> <id> = <id> = <expr> <expr> a a <expr> * <expr> <expr> <expr> + <expr> + <expr> <id> <id> <expr> <expr> * b <id> <id> <id> <id> d c d b c

Precedence Through Grammar • A grammar can enforce the precedence of operators • The parse tree shows how • (low levels are evaluated first) • e.g., <expr> <expr> +<term> |<term> <term> <term> * const | const <expr> <term> <expr> + <term> <term> const * const const

Syntax and Semantics