CMP 339/692 Programming Languages Day 6 Thursday, February 16, 2012

CMP 339/692Programming LanguagesDay 6Thursday,February 16, 2012 Rhys Eric Rosholt Office: Office Phone: Web Site: Email Address: Gillet Hall - Room 304 718-960-8663 http://comet.lehman.cuny.edu/rosholt/ rhys.rosholt @ lehman.cuny.edu

Chapter 3 Describing Syntax and Semantics

Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars Describing the Meanings of Programs: Dynamic Semantics

Review • Language description includes two main components • Syntax • The form of expressions, statements, and program units • Semantics • The meaning of expressions, statements, and program units • Describing syntax is easier than describing semantics • Universally-accepted notations can be used to describe syntax. (e.g. BNF) • No universally-accepted systems have been created for describing semantics.

The General Problem of Describing Syntax: Terminology Definition: A sentence is an ordered string of characters over some alphabet Definition: A language is a set of sentences Definition: A lexeme is the lowest level syntactic unit of a language (e.g., *, sum,begin) Definition: A token is a category of lexemes (e.g., identifier)

Formal Grammars andFormal Languages A formal grammar G = (N,Σ,P,S) is a quad-tuple such that N is a finite set of nonterminal symbols Σis a finite set of terminal symbols, disjoint from N P is a finite set of production rules of the formαNβ → γ S ЄN the start symbol The language of a formal grammar G, denoted as L(G), is the set of all strings over Σ that can be generated by starting with the start symbol S and then applying the production rules in P until no nonterminal symbols are present.

Formal Methodsof Describing Syntax • The most widely known methods for describing programming language syntax: • Backus-Naur Form (BNF) • Context-Free Grammars • Extended BNF (EBNF) • Improves readability and writability • Grammars and Recognizers

Context-Free Grammars • Developed by Noam Chomsky • mid-1950s • Language generators • meant to describe the syntax of natural languages • Defines a class of languages called context-free languages

Formal Definition of Languages Recognizers A device that reads input strings of the language and decides whether the input strings belong to the language Generators A device that generates sentences of a language which are used to compare with the syntax of a particular sentence

Backus-Naur Form (BNF) • Invented by John Backus and Peter Naur • Equivalent to context-free grammars • A metalanguage used to describe another language • Abstractions are used to represent classes of syntactic structures • act like syntactic variables • called nonterminal symbols

BNF Fundamentals • Non-terminals: abstractions • Terminals: lexemes and tokens • Grammar: a collection of rules • Examples of BNF rules: <id_list> -> ident | ident, <id_list> <if_stmt> -> if <logic_expr> then <stmt>

BNF Rules • A rule has • a left-hand side (LHS) • a right-hand side (RHS) • consists of terminal and nonterminal symbols • A grammar is a finite nonempty set of rules • An abstraction (or nonterminal symbol) can have more than one RHS <stmt> -> <single_stmt> | begin <stmt_list> end

Describing Lists • Syntactic lists are described using recursion <id_list> -> ident | ident, <id_list> • A derivation is • a repeated application of rules, • starting with the start symbol, and • ending with a sentence • all terminal symbols

An Example Derivation <program> => <stmts> => <stmt> => <var> = <expr> => a = <expr> => a = <term> + <term> => a = <var> + <term> => a = b + <term> => a = b + const

Derivation • Every string of symbols in the derivation is a sentential form • A sentence is a sentential form that has only terminal symbols • A leftmost derivation is one in which the leftmost nonterminal in each sentential form is the one that is expanded • A derivation may be neither leftmost nor rightmost

Parse Tree A hierarchical representation of a derivation <program> <stmts> <stmt> <var> = <expr> a <term> + <term> <var> const b

Ambiguity in Grammars A grammar is ambiguous if and only if it generates a sentential form that has two or more distinct parse trees

An Ambiguous Expression Grammar <expr>  <expr> <op> <expr> | const <op>  / | - <expr> <expr> <expr> <op> <op> <expr> <expr> <op> <expr> <expr> <op> <expr> <expr> <op> <expr> const - const / const const - const / const

An Unambiguous Expression Grammar If we use the parse tree to indicate precedence levels of the operators, we cannot have ambiguity <expr>  <expr> - <term> | <term> <term>  <term> / const | const <expr> <expr> - <term> <term> <term> / const const const

Associativity of Operators Operator associativity can also be indicated by a grammar. ambiguous: <expr> -> <expr> + <expr> | const unambiguous: <expr> -> <expr> + const | const <expr> <expr> <expr> + const <expr> + const const

Extended BNF Optional parts are placed in brackets [] <proc_call> -> ident [(<expr_list>)] Alternative parts of RHSs are placed inside parentheses and separated via vertical bars <term> → <term>(+|-) const Repetitions (0 or more) are placed inside braces {} <ident> → letter {letter|digit}

BNF and EBNF BNF <expr> -><expr> + <term> | <expr> - <term> | <term> <term> -><term> * <factor> | <term> / <factor> | <factor> EBNF <expr> -><term> {(+|-) <term> } <term> -><factor> {(*|/) <factor> }

The Chomsky Hierarchy

Semantics • The meaning, not the form • Need a language to describe the semantics of languages • Assorted mathematical formalisms • Static Semantics • Attribute Grammars • Dynamic Semantics • Operational Semantics • Axiomatic Semantics • Denotational Semantics

Next ClassThursdayFebruary 23, 2012 Rhys Eric Rosholt Office: Office Phone: Web Site: Email Address: Gillet Hall - Room 304 718-960-8663 http://comet.lehman.cuny.edu/rosholt/ rhys.rosholt @ lehman.cuny.edu

CMP 339/692 Programming Languages Day 6 Thursday, February 16, 2012