UT Dallas CS 4337 - #Sebesta ch03 rev2 - axiomatic semantics - handout (72 pages)

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#Sebesta ch03 rev2 - axiomatic semantics - handout



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#Sebesta ch03 rev2 - axiomatic semantics - handout

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Pages:
72
School:
University of Texas at Dallas
Course:
Cs 4337 - Organization of Programming Languages
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Chapter 3 Describing Syntax and Semantics Introduction Syntax the form or structure of the expressions statements and program units Semantics the meaning of the expressions statements and program units Syntax and semantics provide a language s definition Users of a language definition Other language designers Implementers Programmers the users of the language Copyright 2012 Addison Wesley All rights reserved 1 2 The General Problem of Describing Syntax Terminology 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 sum begin A token is a category of lexemes e g identifier Copyright 2012 Addison Wesley All rights reserved 1 3 Formal Definition of Languages Recognizers A recognition device reads input strings over the alphabet of the language and decides whether the input strings belong to the language Example syntax analysis part of a compiler Detailed discussion of syntax analysis appears in Chapter 4 Generators A device that generates sentences of a language One can determine if the syntax of a particular sentence is syntactically correct by comparing it to the structure of the generator Copyright 2012 Addison Wesley All rights reserved 1 4 BNF and Context Free Grammars Context Free Grammars Developed by Noam Chomsky in the mid 1950s Language generators meant to describe the syntax of natural languages Define a class of languages called context free languages Backus Naur Form 1959 Invented by John Backus to describe the syntax of Algol 58 BNF is equivalent to context free grammars Copyright 2012 Addison Wesley All rights reserved 1 5 BNF Fundamentals In BNF abstractions are used to represent classes of syntactic structures they act like syntactic variables also called nonterminal symbols or just terminals Terminals are lexemes or tokens A rule has a left hand side LHS which is a nonterminal and a right hand side RHS which is a string of terminals and or nonterminals Copyright 2012 Addison Wesley All rights reserved 1 6 BNF Fundamentals continued Nonterminals are often enclosed in angle brackets Examples of BNF rules ident list identifier identifier ident list if stmt if logic expr then stmt Grammar a finite non empty set of rules A start symbol is a special element of the nonterminals of a grammar Copyright 2012 Addison Wesley All rights reserved 1 7 BNF Rules An abstraction or nonterminal symbol can have more than one RHS stmt single stmt begin stmt list end is same as stmt single stmt stmt begin stmt list end Copyright 2012 Addison Wesley All rights reserved 1 8 Describing Lists Syntactic lists are described using recursion ident list ident ident ident list A derivation is a repeated application of rules starting with the start symbol and ending with a sentence all terminal symbols Copyright 2012 Addison Wesley All rights reserved 1 9 An Example Grammar Given Grammar program stmts stmts stmt stmt stmts stmt var expr var a b c d expr term term term term term var const Derivation for a b const Copyright 2012 Addison Wesley All rights reserved 1 10 An Example Derivation program stmts stmt var expr a expr a term term a var term a b term a b const Copyright 2012 Addison Wesley All rights reserved 1 11 Derivations Every string of symbols in a 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 Copyright 2012 Addison Wesley All rights reserved 1 12 Parse Tree A hierarchical representation of a derivation program stmts stmt var expr a term term var const b Copyright 2012 Addison Wesley All rights reserved 1 13 Ambiguity in Grammars A grammar is ambiguous if and only if it generates a sentential form that has two or more distinct parse trees Copyright 2012 Addison Wesley All rights reserved 1 14 An Ambiguous Expression Grammar expr expr op expr op expr expr const expr op expr expr op expr op expr const const Copyright 2012 Addison Wesley All rights reserved expr expr op expr const const const const 1 15 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 Copyright 2012 Addison Wesley All rights reserved const 1 16 Associativity of Operators Operator associativity can also be indicated by a grammar expr expr expr expr expr const const const ambiguous unambiguous expr expr expr expr const const const Copyright 2012 Addison Wesley All rights reserved 1 17 Part 2 BNF Attribute Grammar Copyright 2012 Pearson Education All rights reserved 1 18 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 Copyright 2012 Addison Wesley All rights reserved 1 19 BNF and EBNF BNF expr expr term expr term term term term factor term factor factor EBNF expr term term term factor factor Copyright 2012 Addison Wesley All rights reserved 1 20 Recent Variations in EBNF Alternative RHSs are put on separate lines Use of a colon instead of Use of opt for optional parts Use of oneof for choices Copyright 2012 Addison Wesley All rights reserved 1 21 Attribute Grammars Attribute grammars AGs have additions to CFGs to carry some semantic info on parse tree nodes Primary value of AGs Static semantics specification Compiler design static semantics checking Copyright 2012 Addison Wesley All rights reserved 1 22 Attribute Grammars Definition Definition An attribute grammar is a context free grammar G S N T P with the following additions For each grammar symbol x there is a set A x of attribute values Each rule has a set of functions that define certain attributes of the nonterminals in the rule Each rule has a possibly empty set of predicates to check for attribute consistency Copyright 2012 Addison Wesley All rights reserved 1 23 Attribute Grammars Definition Let X0 X1 Xn be a rule Functions of the form S X0 f A X1 A Xn define synthesized attributes Functions of the form I Xj f A X0 A Xn for i j n define inherited attributes Initially there are intrinsic attributes on the leaves Copyright 2012 Addison Wesley All rights reserved 1 24 Attribute Grammars An Example


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