1.describing syntax and semantics.pptx

7/21/2019 1.Describing Syntax and Semantics.pptx

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Describing Syntax and Semantics

Introduction The General Problem of Describing

Syntax

Formal Methods of Describing Syntax Attribute Grammars

Describing the Meanings of

Programs: Dynamic Semantics


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Describing Syntax andSemantics

Syntax the form or structure of the expressions statements and

program units

describes ho! programs "loo#": their form and structure

Semantics the meaning of the expressions statements and

program units

!hich describes !hat language constructs "do"

$xample: For example the syntax of a %a&a !hile statement

is

while (boolean_expr) statement


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The semantics of this statement formis that !hen the current &alue of the'oolean expression is true the

embedded statement is executed( )ther!ise control continues after

the !hile construct( Then control

implicitly returns to the 'ooleanexpression to repeat the process(


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Steps in a compiler:


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'oth lexical analysis and syntactic analysis deal !ith syntax

!hy separate them in t!o steps in the compiler*

+ $,ciency:

+ design of the lexer is based on a -nite state automaton

!hile the parser is a pushdo!n automaton !hich is morecomplex

+ for a non+optimi.ing compiler about /01 of compile timeis spent in the lexer

+ 2istory:

+ prior to AS3II computers had their o!n character sets+ still di4erent character sets today actually

+ it used to be hat the end+of+line character !as &ery )5Sdependent


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6ho must use language de-nitions*7( )ther language designers

8( Implementers

9( Programmers the users of thelanguage;

A sentence is a string of characters

o&er some

alphabet

A language is a set of sentences

The General Problem of DescribingSyntax


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A lexeme is the lo!est le&el syntactic unit of a language e(g( " sum begin;

A to#en is a category of lexemes e(g( identi-er;

$xample

index < 8 " count = 7/>

The lexemes and to#ens of this statement are

Lexemes Tokens

index identi-er

< e?ual@sign

8 int@literal" mult@op

3ount identi-er

= plus@op

7/ int@literal

> semicolon


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Formal approaches to describing syntax:

1. ecogni!ers " used in compilers

Suppose !e ha&e a language that uses an alphabet B ofcharacters(

To de-ne formally using the recognition method !e !ouldneed to construct a mechanism C called a recognitionde&ice capable of reading strings of characters from thealphabet B(

C !ould indicate !hether a gi&en input string !as or !asnot in

The syntax analysis part of a compiler is a recogni.er forthe language the compiler translates(

The recogni.er need not test all possible strings ofcharacters from some set to determine !hether each is inthe language it need only determine !hether gi&enprograms are in the language(

The syntax analy.er then determines !hether the gi&en

programs are syntactically correct( The structure of syntax analy.ers also #no!n as parsers


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#. $enerators A language generator is a de&ice that

can be used to generate the

sentences of a language(


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Formal %ethods o& DescribingSyntax

discusses the formal language+

generation mechanisms calledgrammars that are commonly usedto describe the syntax of

programming languages


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'ontext"Free $rammars De&eloped by oam 3homs#y in the

mid+7E0s

anguage generators meant todescribe the syntax of naturallanguages

De-ne a class of languages calledcontext+free languages


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3ontext+Free Grammar

In linguistics and computer science a context+freegrammar 3FG; is a formal grammar in !hich e&eryproduction rule is of the form

w

!here is a Hnon+terminal symbol and ! is a Hstringconsisting of terminals and5or non+terminals(

The term Jcontext+freeJ expresses the fact that the non+terminal can al!ays be replaced by ! regardless of

the context in !hich it occurs(

A formal language is context+free if there is a context+free grammar that generates it(


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context+&ree grammar'F$;

Is a set of recursi&e re!riting rules or productions; used togenerate patterns of strings(

A 'F$consists of the follo!ing components:

a set of terminalsymbols !hich are the characters of thealphabet that appear in the strings generated by thegrammar( K 7L

a set of nonterminal symbols !hich are placeholders forpatterns of terminal symbols that can be generated by thenonterminal symbols( K? fL

a set ofproductions!hich are rules for replacing orre!riting; nonterminal symbols on the left side of theproduction; in a string !ith other nonterminal or terminalsymbols on the right side of the production;(

a start symbol !hich is a special nonterminal symbol that

appears in the initial string generated by the grammar(


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The syntax of !hole programminglanguages !ith minor exceptionscan be described by context+free

grammars


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*ac+us ,ormal Form (1--) In&ented by %ohn 'ac#us to describe Algol

0

'F is e?ui&alent to context+free grammars

'F is a meta+language( A meta+languageis a language used to describe anotherlanguage(

In 'F abstractions are used to representclasses of syntactic structures+they act li#esyntactic &ariables also called non+terminalsymbols;


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A 'F descriptionor grammar is acollection of rules consists terminalsand non terminals

e(g(N!hile@stmtO +O !hile Nlogic@exprOdo NstmtO

This is a rule> it describes thestructure of a !hile statement

Nif@stmtO if Nlogic@exprO ;

NstmtO


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A rule has a left+hand side 2S; and aright+hand side C2S; and consists ofterminal and nonterminal symbols

A grammar is a -nite nonempty set of rules

An abstraction or nonterminal symbol; canha&e more than one C2S

NstmtO +O Nsingle@stmtO

Q begin Nstmt@listO end Syntactic lists

described in 'F using recursion

Nident@listO +O identQ ident Nident@listO


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A grammaris a generati&e de&ice forde-ning languages(

The sentences of the language are

generated through a se?uence ofapplications of the rules beginning !itha special nonterminal of the grammarcalled the start symbol(

A deri&ationis a repeated application ofrules starting !ith the start symbol andending !ith a sentence all terminal

symbols;(

Grammars and Deri&ations


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In a grammar for a complete programminglanguage the start symbol represents a

complete program and is often namedNprogramO(


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Deri&ation of a program


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This deri&ation begins !ith the start symbol in this caseNprogramO( The symbol


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A parse tree is a hierarchicalrepresentation of a deri&ation


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)perator Precedence

2o! to remo&e the ambiguity* 'y enforcing 0perator precedence

)perator !ith igher precedence

should be placed lower in the the tree


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Separate rules for di4erent

operators

nambiguous grammar produces a uni2ue parse tree 'ut a single parse tree can ha&e di3erent deri/ations


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eftmost deri&ation

NassignO


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Cightmost deri&ation

NassignO


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'oth of these deri&ations are represented by the sameparse tree(


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Associati&ity of )perators

eft Associati&ity 4e&t recursi/e grammar rule

e(g a=b=c < a=b;=c

e(g( A < ' = 3 = A


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Cight Associati&ity: ight recursi/egrammar rule e(g( a=b=c < a=b=c;


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6hat languages do

SmallTal#: no operator precedence

AP: right+associati&ity !ith no operator precedence

+ Programmers typically add parentheses !hen things aredi,cult to read

if a N x N b; e?ui&( if a N x; N b; Ureturns 7 if b O< 7V

For languages li#e 3 3== and %a&a the number ofprecedence le&els and operators ma#es the grammar huge

+ this ma#es the parse &ery slo!

+ a possibility is to not JencodeJ anyprecedence5associati&ity in the grammar but Wust ha&e atable that says !hat these things are %a&a 3;


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The syntax graph and $'Fdescriptions of the Ada ifstatement


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Three extensions are commonlyincluded in the &arious &ersions of$'F(

The -rst of these denotes an optionalpart of an C2S !hich is delimited bybrac#ets( For example a 3 if+else

statement can be described as Nif@stmtO if NexpressionO;

NstatementO UelseNstatementOV

5xtended *,F


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The second extension is the use ofbraces in an C2S to indicate that theenclosed part can be

Nident@listO Nidenti-erO KNidenti-erOL

This is a replacement of the recursion

by a form of implied iteration> thepart enclosed !ithin braces can beiterated any number of timesrepeated inde-nitely or left outalto ether


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The third common extension deals !ithmultiple+choice options(

6hen a single element must be chosenfrom a group the options are placed inparentheses and separated by the )Coperator Q(

For example

NtermO NtermO " Q 5 Q 1; NfactorO

In 'F a description of this NtermO !ould

re?uire the follo!ing three rules: NtermO NtermO " NfactorO

Q NtermO 5 NfactorO

Q NtermO 1 NfactorO


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Syntax in isp*

+ o expressions in ISP but functionapplicationsY

+ $&erything is parenthesi.ed(

+ o associati&ity o operator precedence(

+ 3ompare !ith the 80 pages of the %a&a manual

+ ThisZs also !hy !riting a ISP interpreter is not&ery di,cult

+ !rite a pure %a&a interpreter !ould beextremely di,cult

+ !riting a byte code interpreter is not that hard


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Static semantics +

IntroductionThere are some characteristics of the structure of

programming languages that are di,cult todescribe !ith 'F and some that are impossible(

In %a&a for example a [oating+point &alue cannotbe assigned to an integer type &ariable althoughthe opposite is legal(

If all of the typing rules of %a&a !ere speci-ed in

'F the grammar !ould become too large to beuseful because the si.e of the grammardetermines the si.e of the syntax analy.er(


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The static semantics of a language is onlyindirectly related to the meaning of programsduring execution> rather it has to do !ith thelegal forms of programs syntax rather thansemantics;(

Static semantics is so named because theanalysis re?uired to chec# these speci-cationscan be done at compile time(

'ecause of the problems of describing staticsemantics !ith 'F a &ariety of more po!erfulmechanisms has been de&ised for that tas#(

)ne such mechanism attribute grammars !asdesigned by \nuth 7E]a; to describe both thesyntax and the static semantics of programs(


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Attribute grammars are a formal approach both to describing

and chec#ing the correctness of the

static semantics rules of a program( Dynamic semantics

!hich is the meaning of expressions

statements and program units


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*asic concepts

Attributes6 !hich are associated !ithgrammar symbols the terminal and non+terminal symbols; are similar to &ariables inthe sense that they can ha&e &alues assigned

to them( Attribute computation &unctions6

sometimes called semantic functions areassociated !ith grammar rules( They are used

to specify ho! attribute &alues are computed( 7redicate &unctions6 !hich state the static

semantic rules of the language are associated!ith grammar rules to chec# for attribute

consistency(


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An attribute grammar is a context+freegrammar G < S T P; !ith thefollo!ing additions:

7( For each grammar symbol x there is aset Ax;of attribute &alues

The set A^; consists of t!o disWoint sets S^;and I^; called synthesi.ed and inherited

attributes respecti&ely( Synthesi!ed attributes are used to pass

semantic information up a parse tree

inherited attributes pass semantic

information do!n and across a tree(

Attribute $rammars De8ned


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8( $ach rule has a set of functions that de-necertain attributes of the non+terminals in the rule

. For a rule ^ ^7 ((( ^n

Semantic functions of the form S^; < fA^7; (((A^n;; 3ompute Synthesi!ed attributes from child nodes;

Semantic functions of the form I^W; < fA^; ((( A^n;; for I N< W N< n

3ompute 9nherited attributes from parent or siblings;

. 7redicate &unctions

. 'oolean expressions on the attribute setKA^; ((( A^n;L


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Intrinsic attributes

9ntrinsic attributes are synthesi.edattributes of leaf nodes !hose &aluesare determined outside the parse

tree(

$ amples of attribute


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The string attribute of Nproc@nameO denoted by Nproc@nameO(stringis the actual string of characters that !ere found immediately follo!ingthe reser&ed !ord procedure by the compiler(

Syntax rule:

Nproc@defO procedure Nproc@nameOU7V Nproc@bodyO end

Nproc@nameOU8V>

Predicate:

the predicate rule states that the name string attribute of theNproc@nameO nonterminal in the subprogram header must match thename string attribute of the Nproc@nameO nonterminal follo!ing theend of the subprogram

Nproc@nameOU7Vstring


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The attributes for the nonterminals in theexample attribute grammar are describedin the follo!ing paragraphs:

actual_typeA synthesized attributeassociated with the nonterminals

and NexprO( It is used to store the actualtype int or real of a &ariable or expression(

expected_typeAn inherited attributeassociated with the nonterminal NexprO( It

is used to store the type either int or realthat is expected for the expression asdetermined by the type of the &ariable onthe left side of the assignment statement(

$xamples of attribute


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$xamples of attributegrammars


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+ only t!o types: int and real int = int is an int

int = real is a real real = real is a real


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A parse tree of the sentence A < A =

'


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3omputing Attribute alues

called decorating the parse tree

If all attributes !ere inherited thiscould proceed in a completely top+

do!n order from the root to thelea&es(

If all the attributes !ere synthesi.ed

it could proceed in a completelybottom+up order from the lea&es tothe root

The follo!ing is an e&aluation of the attributes


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The follo!ing is an e&aluation of the attributesin an order in !hich it is possible to computethem:


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$&aluation


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$&aluation

3hec#ing the static semantic rules of a language is an

essential part of all compilers( $&en if a compiler !riter has ne&er heard of an attribute

grammar it is necessary to use fundamental ideas todesign the chec#s of static semantics rules of the compiler(

)ne of the main di,culties in using an attribute grammar

to describe all of the syntax and static semantics of a realcontemporary programming language is the si.e andcomplexity of the attribute grammar(

The large number of attributes and semantic rules re?uiredfor a complete programming language ma#e such

grammars di,cult to !rite and read( the attribute &alues on a large parse tree are costly to

e&aluate(


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Semantics

There is no single !idely acceptable notation or formalism fordescribing semantics

Semantics description tool is useful for: 'etter understanding the statements of a language

De&eloping more e4ecti&e compiler

Program correctness proofs

;hree approaches 0perational

Axiomatic

Denotational

0perational 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(; de-nes themeaning of the statement


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natural operational semantics

At the highest le&el the interest is in the-nal result of the execution of acomplete program(

structural operational semantics At the lo!est le&el operational

semantics can be used to determine the

precise meaning of a program throughan examination of the completese?uence of state changes that occur!hen the program is executed(

' i P


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'asic Process language is clarity

to design an appropriate intermediate language $&ery construct of the intermediate language must

ha&e an ob&ious and unambiguous meaning(

If the natural operational semantics is used a

&irtual machine an interpreter; must beconstructed for the intermediate language(The &irtual machine can be used to execute either

single statements code segments or !hole programs(

The semantics description can be used !ithout a&irtual machine if the meaning of a single statement isall that is re?uired(

If structural operational semantics is used theintermediate code can be &isually inspected(


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semantics of the 3 &or construct $xample


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$&aluation

Good if used informally language manuals etc(;

$xtremely complex if used formally e(g( iennaDe-nition anguage + D; it !as used fordescribing semantics of P5I P5I stands for

JProgramming anguage 7J( P5I !as anantecedent of the 3programming language!hich essentially replaced it as an all+purposeserious programming language;(

seful for language users and implementors 'ased on algorithms rather than mathematics
http://searchwinit.techtarget.com/definition/Chttp://searchwinit.techtarget.com/definition/C


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It is an approach of formali.ing themeanings of programming languagesby constructing mathematical

obWects called denotations; thatdescribe the meanings ofexpressions from the languages

The method is named denotationalbecause the mathematical objectsdenote the meaning o theircorresponding syntactic entities(

Denotational semantics
http://en.wikipedia.org/wiki/Programming_languagehttp://en.wikipedia.org/wiki/Programming_language


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'uilding Denotational speci8cation fora language: De-ne a ,umber for each grammar symbol

De-ne a &unction !hich con&erts:

Grammar symbol +O corresponding numbers

Denotational /s operational


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Denotational /s operationalsemantics


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The mapping functions of a denotationalsemantics programming languagespeci-cation li#e all functions in

mathematics ha&e a domain and a range(The domainis the collection of &alues that are

legitimate parameters to the function it iscalled the syntactic domain

the rangeis the collection of obWects to !hichthe parameters are mapped it is called thesemantic domain(


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$xample


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$xample

6e !ant to associate a semantic to each 'F


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6e !ant to associate a semantic to each 'Fproduction

6e de-ne a function M@bin that maps the

syntactic obWects in the grammar rules to theobWects in the set of non negati&e integers(


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;he state o& a program


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;he state o& a program )perational semantics:

;he change in the state of the machine Memory registers etc(

The state change is de-ned by coded algorithms Denotational semantics:

;he change in the /alues o& the program


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5xpressions Semantic function: maps expressions to

integer &alue or error;


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Assignment Statements Semantic function: maps state to state


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4ogical 7retest 4oops Semantic function: maps state to state

$xisting functions Mb: maps boolean expression to boolean

&alues true false undef;

Msl: maps statement lists to states


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5/aluation o& denotational


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5/aluation o& denotationalsemantics:

6hen a complete system has been de-nedfor a gi&en language it can be used todetermine the meaning of completeprograms in that language( i(e; Pro&ides arigorous !ay to analy.e programs

3an be used to pro&e the correctness ofprograms

3an be an aid to language design andcompiler generation

'ut too complex for language users


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A i ti S ti


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Axiomatic semanticsis an approachbased on mathematical logicto pro&ingthe correctness of computer programs

Goal: program correctness proo&(i.e) Cather than directly specifying themeaning of a program axiomatic semanticsspeci-es !hat can be pro&en about theprogram(

Axiomatic Semantics
http://en.wikipedia.org/wiki/Mathematical_logichttp://en.wikipedia.org/wiki/Correctness_of_computer_programshttp://en.wikipedia.org/wiki/Correctness_of_computer_programshttp://en.wikipedia.org/wiki/Correctness_of_computer_programshttp://en.wikipedia.org/wiki/Correctness_of_computer_programshttp://en.wikipedia.org/wiki/Mathematical_logic


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In axiomatic semantics there is no model of thestate of a machine or program or model of statechanges that ta#e place !hen the program isexecuted(

The meaning of a program is based onrelationships among program &ariables andconstants !hich are the same for e&eryexecution of the program(

Axiomatic semantics has t!o distinctapplications: program &eri-cation

program semantics speci-cation(


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Approach Specify constraints for each statement

by logical expressions called assertions (orpredicate)

7re"condition: an assertion be&ore a statement

Describes the constraints on the &ariables at thatpoint

7ost"condition: an assertion &ollowing a statement

Describes the ne! constraints on those &ariables

= + t diti


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=ea+est precondition:

The least restricti/e precondition that !illguarantee the postcondition(

Pre+post form otation: KPL S K`L

S:program statement

P:constraints on &ariables '$F)C$ statementexecution called a JpreconditionJ

`: constraints on &ariables AFT$C statementexecution called a JpostconditionJ

5xample: a < b = 7 Ka O 7L )ne possible precondition: Kb O 7L

6ea#est precondition: Kb O L


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An in&erence rule is a method of inferring the truth of oneassertion on the basis of the &alues of other assertions( Thegeneral form of an inference rule is as follo!s:

This rule states that if S7 S8 ( ( ( and Sn are true thenthe truth of S can be inferred(

The top part of an inference rule is called its antecedent>

the bottom part is called its conse2uent(

An axiomis a logical statement that is assumed to be true(Therefore an axiom is an inference rule !ithout anantecedent(

P f 7 &


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Process of 7rogram proo&

Assignment Statements


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et Jx ?x"@5 or ?x"@5B x > 5 ?B P is computed as ` in !hich all occurrences of x

ha&e been replaced by $

+ $xample:

a < b 5 8 + 7 Ka N 7L

the !ea#est precondition is: P < K b 5 8 + 7N 7L !hich reduces to Kb N 88L(


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The usual notation for specifying theaxiomatic semantics of a gi&en statementform is

KPLSK`L !here P is the precondition ` is the

postcondition and S is the statement form(

In the case of the assignment statement

the notation is

e(g( Pro&e the correctness of Kx O 9L x < x + 9


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K x O L

Ans!er: Kx X 9 O L Kx O 9L thus TC$

e(g( 2o! about x @ B x < x + 9 K x O L *Since Kx O 0L Kx O 9L it is still TC$

the rule of conse?uence says that a postconditioncan al!ays be !ea#ened and a precondition canal!ays be strengthened(

Se?uences


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Se?uences The !ea#est precondition for a se?uence of

statements cannot be described by an axiombecause the precondition depends on the particular#inds of statements in the se?uence(

So the precondition can only be described !ith aninference rule(

et S7 and S8 be adWacent program statements( If S7and S8 ha&e the follo!ing pre+ and post+conditions

Th i f l t t th t t t


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The inference rule states that to getthe se?uence precondition the

precondition of the second statementis computed(

This ne! assertion is then used as

the postcondition of the -rststatement !hich can then be usedto compute the precondition of the

-rst statement !hich is also theprecondition of the !hole se?uence(


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Selection


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Selection


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ogical Pretest oops


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ogical Pretest oops

3omputing the !ea#est precondition for a while loop isinherently more di,cult than for a se?uence because thenumber of iterations cannot al!ays be predetermined(

6hen the number of iterations is #no!n the loop can beunrolled and treated as a se?uence(

The principal step in induction is -nding an inducti&ehypothesis(

The corresponding step in the axiomatic semantics of awhile loop is -nding an assertion called a loop in/ariant(loop in&ariant is a condition that is necessarily trueimmediately before and immediately after each iterationof a loop) !hich is crucial to -nding the !ea#estprecondition(


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loop in&ariant 3haracteristics


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loop in&ariant 3haracteristics

P


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To -nd I the loop postcondition ` is used to

compute preconditions for se&eral di4erentnumbers of iterations of the loop body

In general !ea#est precondition is gi&en by!pstatement postcondition; < precondition

A !p function is often called a predicate

trans&ormer because it ta#es a predicate orassertion as a parameter and returns anotherpredicate(

$xample


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p while y NO x do y < y = 7 end Ky < xL

ote: e?ual sign

outside assertions it means the assignment operator(

For .ero iterations

Ky < xL

For one iteration it is

!py < y = 7 Ky < xL; < Ky = 7 < xL or Ky

< x + 7L For t!o iterations it is

!py < y = 7 Ky < x + 7L;


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6e must ensure that our choice satis-esthe four criteria for I for our example loop(

7( P < I P


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9( It must be true that KI and not ';L


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If loop termination can be sho!n theaxiomatic description of the loop iscalled total correctness(

If the other conditions can be metbut termination is not guaranteed itis called partial correctness(

Program Proofs


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Program Proofs


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$&aluation


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$&aluation

De&eloping axioms or inference rules forall of the statements in a language isdi,cult

It is a good tool for correctness proofsand an excellent frame!or# for reasoningabout programs but it is not as useful forlanguage users and compiler !riters

Its usefulness in describing the meaningof a programming language is limited forlanguage users or compiler !riters


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$&aluation of axiomatic semantics: It is hard to de&elop axioms or

inference rules

for all of the statements in alanguage

ice tool for correctness proofs

'ut not for language users andcompiler !riters

Summary


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Summary

1.describing syntax and semantics.pptx

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