syntax semantics

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ICS 32Structure of Prog. Languages



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Describing Syntax andSemantics



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Syntax & Semantics

• What we need: concise yetunderstandable description of aprogramming language

• implementers must understand:

– how the statements are formed

– what they mean



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Syntax & Semantics

• need for a language reference manual

• Syntax : form of its expressions,statements and program units

• Semantics : meaning of those expressionsand program units



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Syntax & Semantics

• Formal Methods of Describing Syntax

– Grammars

– Syntax Diagrams

– Parse Trees

– metalanguage : language used to describeanother language



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Describing Syntax

• Grammar

– constituted by a set of tokens, terminals, non-terminals, productions, and the goal symbol

– describe the hierarchical syntactic structure ofthe sentence of language

– BNF (Backus-Naur Form): one way of writing

grammars



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Describing Syntax

• Backus-Naur Form (BNF)

– method of describing syntax

– originally presented by John Backus (todescribe ALGOL 58)and later modified byPeter Naur

– similar to Chomsky’s Context-free Diagrams

(1950)



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Describing Syntax

• Parts of a Grammar

– a set of tokens

– a set of non-terminal symbols

– a set of rules called productions

– a goal symbol



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Describing Syntax

• Grammar:

– lexemes : small syntactic units (lexicalspecifications)

• e.g. identifiers, constants, operators, and specialwords

– language statements : string of lexemes

– token : a category of lexemes



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Describing Syntax

• Grammar: Symbols

– Goal Symbol

• one of the set of non-terminal symbols

• also referred to as the start symbol

– Terminal Symbols

• symbols that are atomic / non-divisible

• can be combined to form valid constructs in thelanguage



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Describing Syntax

• Grammar: Symbols

– Non-Terminal Symbols

• symbols used to represent intermediate definitions

within the language• defined by productions

• syntactic classes or categories



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Describing Syntax

• Grammar: Productions

– BNF uses abstraction for syntactic structures

<assign> <var>:=<expression>



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Describing Syntax


– LHS: abstraction being defined

– RHS: tokens, lexemes, references to otherabstractions



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Describing Syntax


– a definition of a non-terminal symbol

– has the form

x y

where x is a non-terminal symbol and y is asequence of symbols (non-terminal or

terminal)



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Describing Syntax

• Grammar: Derivation

– sentences of the language are generatedthrough repeated application of the rules,

beginning with a start symbol



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Describing Syntax

• Grammar Production Example

<if_stmt> if <logic_expr> then

<statement_list>

else

<statement_list>



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Describing Syntax

• Rules to form Grammar

– every non-terminal symbol must appear to theleft of the at least one production

– the goal symbol must not appear to the rightof the of any production



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Describing Syntax

• Rules to form Grammar

– a rule is recursive if its LHS appears in itsRHS

<id_list> <identifier>



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Describing Syntax

• Given: Grammar Productions

<program> begin <stmt_list> end

<stmt_list> <stmt> | <stmt> <stmt_list>

<stmt> <var> := <expression>

<var> A | B | C

<expression> <var> + <var>



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Describing Syntax

• Sample Derivation

<program> begin <stmt_list> end

begin <stmt> end

begin <var> := <expression> end

begin <var> := <var> + <var> end

begin A := B + C end



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Describing Syntax

• When does derivation stop?

– by exhaustingly choosing all combinations ofchoices, the entire language can generate



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Describing Syntax

• Syntax Diagrams

– a.k.a. Syntax Graphs / Syntax Charts

– represented by a directed graph

– a separate graph is used for each syntacticunit

– Rectangles: Non-terminal Symbols

– Circles: Terminal Symbols



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Calculator

<expr>

Describing Syntax

• Syntax Diagrams

<expr>

<val>

<opr> <expr>

=



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<val><unsgn>

<sgn> . <unsgn>

Describing Syntax

• Syntax Diagrams



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<unsgn>

<unsgn>

<digit>

Describing Syntax

• Syntax Diagrams

<sign> +

-



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<digit>

0 1 2 3 4 5 .. 9

Describing Syntax

• Syntax Diagrams



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<opr>

+

-

*

/

Describing Syntax

• Syntax Diagrams



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Describing Syntax

• Parse Trees

– parse trees: hierarchical structure

– node: non-terminal symbol

– leaves: terminal symbol



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<program>

begin end<stmt_list>

<stmt>

<var> <expr>

<var> <var>

Derivation of begin A := B + C end

+

:=

A

B C



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Describing Syntax

• Why do we need to describe syntax?

– to express our ideas to a form understandableby the computer

– be acquainted with rules

– transformation/translation

– comparison with other languages



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Describing Semantics

• Informal Description

• Attribute Grammars

• Operational Semantics• Axiomatic Semantics

• Denotational Semantics



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• Informal Description

– uses informal neutral language descriptions

– construed from English language description

– example: when an integer and a double are added, the result is a double



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• Attribute Grammars – the CFG (Context Free Grammar) for the

language is augmented with a set of attributes

and rules for computing those attributes – describe the syntax and static semantics

– Static Semantics: that part of its semanticswhich can be determined without executing its

code



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• Attribute Grammar

– grammars with sets of attribute valuesassociated with a grammar symbol

– attribute computation functions -- howattribute values are computed

– predicate functions -- state some of the syntax

and semantic rules



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• Example of Attribute Grammar

expr term

expr expr ‘+’ term

$$ $1 $2 $3

some attributes of symbols are:t = type

v = values = scope



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to compute the v attribute of $$ the attributegrammar might be the following rule:%($1.t == $3.t){

switch ($1.t) {case INTEGER: $$.t = INTEGER;

$$.v = $1.v.INTEGER + $3.v.INTEGER;

break;

case DOUBLE: ...}

}



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• Operational Semantics

– the semantics of a program language isdescribed by executing its statements on a

machine, either real or simulated – the changes that occur in the machine’s state

when it executes a given statement define themeaning of that statement



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• Example of Operational Semantics

Operational Semantics

expr1;

loop: if expr2 = 0 goto out

…

expr3;

goto loop

out: …

C Statementfor (expr1; expr2; expr3){

…

}



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• Axiomatic Semantics

– prove the correctness of programs

– assertions: preconditions and post-conditions

– only for very simple statements



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• Example of Axiomatic Semantics

{P} S {Q}

where P is the Precondition

S is the statement to be defined

Q is the Postcondition

{x>=5} sum = 2 * x + 1 {sum >=11}



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• Denotational Semantics

– describe the language by execution

– define a mathematical object for each entity

– define a function that maps instances of theentity to the instances of mathematical objects



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• Example of Denotational Semantics<num> ::= <num><digit> | <digit>

<digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

V(‘0‘) = 0 V(‘1’) = 1

V(‘9‘) = 9

V(<num><digit>) = V(<num>)*10 + V(<digit>)



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• Why do we need to describe semantics?

– understanding programs

– transformation/translation

– proving correctness

– comparison with other languages

syntax semantics

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