Chapter 3 Describing Syntax and Semantics PDF

TWELFTH EDITION GLOBAL EDITION Chapter 3 Describing Syntax and Semantics Copyright © 2023 Pearson Education Ltd. All Rights Reserved. Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars...

TWELFTH EDITION GLOBAL EDITION Chapter 3 Describing Syntax and Semantics Copyright © 2023 Pearson Education Ltd. All Rights Reserved. Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars Describing the Meanings of Programs: Dynamic Semantics Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-2 Introduction Syntax: the form or structure of the expressions, statements, and program units – For example, the syntax of a Java while statement is: while (boolean_expr) statement Semantics: the meaning of the expressions, statements, and program units – The semantics of the above statement form is that when the current value of the Boolean expression is true, the embedded statement is executed. – Then control implicitly returns to the Boolean expression to repeat the process. If the Boolean expression is false, control transfers to the statement following the while construct. Syntax and semantics provide a language’s definition – Users of a language definition Other language designers Implementers Programmers (the users of the language) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-3 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) Consider the following Java statement: index = 2 * count + 17; – The lexemes and tokens of this statement are: Lexemes Tokens index identifier = equal_sign 2 int_literal * mult_op count identifier + plus_op 17 int_literal ; semicolon Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-4 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 © 2023 Pearson Education Ltd. All Rights Reserved. 1-5 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 © 2023 Pearson Education Ltd. All Rights Reserved. 1-6 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 A simple Java assignment statement, for example, might be represented by the abstraction (pointed brackets are often used to delimit names of abstractions). The actual definition of can be given by: Altogether, the definition is called a rule, or production. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-7 BNF Fundamentals (continued) Nonterminals are often enclosed in angle brackets – Examples of BNF rules: → identifier | identifier, → if then Grammar: a finite non-empty set of rules A start symbol is a special element of the nonterminals of a grammar Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-8 BNF Rules An abstraction (or nonterminal symbol) can have more than one RHS → | begin end Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-9  Describing Lists Syntactic lists are described using recursion → ident | ident, This defines as either a single token (identifier) or an identifier followed by a comma and another instance of. A derivation is a repeated application of rules, starting with the start symbol and ending with a sentence (all terminal symbols) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-10 An Example Grammar → → | ; → = → a | b | c | d → + | - → | const Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-11 An Example Derivation => => => = => a = => a = + => a = + => a = b + => a = b + const Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-12 A Grammar for a Small Language Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-13 A derivation of a program in this language Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-14 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 © 2023 Pearson Education Ltd. All Rights Reserved. 1-15 Another Example Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-16 Parse Tree One of the most attractive features of grammars is that they naturally describe the hierarchical syntactic structure of the sentences of the languages they define. These hierarchical structures are called parse trees. = a + const Copyright © 2023 Pearson Education Ltd. All Rights Reserved. b 1-17 Example Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-18 Ambiguity in Grammars A grammar is ambiguous if and only if it generates a sentential form that has two or more distinct parse trees Unambigious Ambigious Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-19 Pars Trees for Ambiguous Grammar Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-20 An Ambiguous Expression Grammar → | const → / | - const - const / const const - const / const Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-21 An Unambiguous Expression Grammar If we use the parse tree to indicate precedence levels of the operators, we cannot have ambiguity → - | → / const| const - / const const const Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-22 An Unambiguous Grammar for Expressions The correct ordering is specified by using separate nonterminal symbols to represent the operands of the operators that have different precedence. This requires additional nonterminals and some new rules. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-23 Left-Most vs. Right-Most Derivation Left-Most Derivation Right-Most Derivation. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-24 Unique Parse Tree for the Grammar Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-25 Associativity of Operators When an expression includes two operators that have the same precedence (as * and / usually have) a semantic rule is required to specify which should have precedence. This rule is named associativity. Operator associativity can also be indicated by a grammar -> + | const (ambiguous) -> + const | const (unambiguous) + const + const Copyright © 2023 Pearson Education Ltd. All Rights Reserved. const 1-26  Associativity of Operators (cont) When a grammar rule has its LHS also appearing at the beginning of its RHS, the rule is said to be left recursive. This left recursion specifies left associativity. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-27 Extended BNF Optional parts are placed in brackets [ ] -> ident [()] Alternative parts of RHSs are placed inside parentheses and separated via vertical bars → (+|-) const Repetitions (0 or more) are placed inside braces { } → letter {letter|digit} Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-28 BNF and EBNF BNF → + | - | → * | / | EBNF → {(+ | -) } → {(* | /) } Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-29 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 © 2023 Pearson Education Ltd. All Rights Reserved. 1-30 Grammars and Recognizers Given a context-free grammar, a recognizer for the language generated by the grammar can be algorithmically constructed. A number of software systems have been developed that perform this construction. Such systems allow the quick creation of the syntax analysis part of a compiler One of the first of these syntax analyzer generators is named yacc (yet another compiler compiler). There are now many such systems available. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-31 Static Semantics Nothing to do with meaning Context-free grammars (CFGs) cannot describe all of the syntax of programming languages Categories of constructs that are trouble: - Context-free, but cumbersome (e.g., types of operands in expressions) - Non-context-free (e.g., variables must be declared before they are used) Static semantics is so named because the analysis required to check these specifications can be done at compile time. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-32 Attribute Grammars Attribute grammars (AGs) have additions to CFGs to carry some semantic info on parse tree nodes Attribute grammars are context-free grammars to which have been added attributes, attribute computation functions, and predicate functions. Primary value of AGs: – Static semantics specification – Compiler design (static semantics checking) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-33 Attribute Grammars : Definition Def: 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 (Synthesized, inherited or intrinsic) – 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 © 2023 Pearson Education Ltd. All Rights Reserved. 1-34 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 + | A | B | C actual_type: synthesized for and intrinsic for expected_type: inherited for Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-37 Attribute Grammar (continued) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-38 Attribute Grammars (continued) How are attribute values computed? – If all attributes were inherited, the tree could be decorated in top-down order. – If all attributes were synthesized, the tree could be decorated in bottom-up order. – In many cases, both kinds of attributes are used, and it is some combination of top-down and bottom-up that must be used. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-40 Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-41 The Parse Tree Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-42 The Flow of Attributes Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-43 The fully Attributed Parse Tree Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-44 EXERCISES - 1 Using the grammar in Example 3.2, show a parse tree and a leftmost derivation for the following statement: A = A * (B + (C * A)) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-46 EXERCISES - 2 Describe, in English, the language defined by the grammar given above Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-47 EXERCISES - 3 Which of the following sentences are in the language generated by the grammar given above? a. baab b. bbbab c. bbaaaaaS d. bbaab Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-48 Semantics There is no single widely acceptable notation or formalism for describing semantics Several needs for a methodology and notation for semantics: – Programmers need to know what statements mean – Compiler writers must know exactly what language constructs do – Correctness proofs would be possible – Compiler generators would be possible – Designers could detect ambiguities and inconsistencies Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-49 Operational Semantics Operational Semantics – Describe the meaning of a program by executing its statements on a machine, either simulated or actual. The change in the state of the machine (memory, registers, etc.) defines the meaning of the statement To use operational semantics for a high- level language, a virtual machine is needed Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-50 Operational Semantics A hardware pure interpreter would be too expensive A software pure interpreter also has problems – The detailed characteristics of the particular computer would make actions difficult to understand – Such a semantic definition would be machine- dependent Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-51 Operational Semantics (continued) A better alternative: A complete computer simulation The process: – Build a translator (translates source code to the machine code of an idealized computer) – Build a simulator for the idealized computer Evaluation of operational semantics: – Good if used informally (language manuals, etc.) – Extremely complex if used formally (e.g., VDL), it was used for describing semantics of PL/I. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-52 Operational Semantics (continued) Uses of operational semantics: - Language manuals and textbooks - Teaching programming languages Two different levels of uses of operational semantics: - Natural operational semantics - Structural operational semantics Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-53 Denotational Semantics Based on recursive function theory The most abstract semantics description method Originally developed by Scott and Strachey (1970) Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-54 Denotational Semantics - continued The process of building a denotational specification for a language: - Define a mathematical object for each language entity – Define a function that maps instances of the language entities onto instances of the corresponding mathematical objects The meaning of language constructs are defined by only the values of the program's variables Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-55 Axiomatic Semantics Based on formal logic (predicate calculus) Original purpose: formal program verification Axioms or inference rules are defined for each statement type in the language (to allow transformations of logic expressions into more formal logic expressions) The logic expressions are called assertions Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-56 Axiomatic Semantics (continued) An assertion before a statement (a precondition) states the relationships and constraints among variables that are true at that point in execution An assertion following a statement is a postcondition A weakest precondition is the least restrictive precondition that will guarantee the postcondition Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-57  Program Proof Process The postcondition for the entire program is the desired result – Work back through the program to the first statement. If the precondition on the first statement is the same as the program specification, the program is correct. Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-58 Evaluation of Axiomatic Semantics Developing axioms or inference rules for all of the statements in a language is difficult It is a good tool for correctness proofs, and an excellent framework for reasoning about programs, but it is not as useful for language users and compiler writers Its usefulness in describing the meaning of a programming language is limited for language users or compiler writers Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-59 Denotational Semantics vs Operational Semantics In operational semantics, the state changes are defined by coded algorithms In denotational semantics, the state changes are defined by rigorous mathematical functions Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-60 Summary BNF and context-free grammars are equivalent meta-languages – Well-suited for describing the syntax of programming languages An attribute grammar is a descriptive formalism that can describe both the syntax and the semantics of a language Three primary methods of semantics description – Operation, axiomatic, denotational Copyright © 2023 Pearson Education Ltd. All Rights Reserved. 1-61