Describing Syntax and Semantics

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Describing Syntax and Semantics

• Jianhua Yang
• Department of Math and Computer Science
• Bennett College

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Outline

• The general problem of describing syntax
• Semantics
• Formal methods of describing syntax
• Attribute grammars
• Describing the meanings of programs Dynamic
  Semantics

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3.1 Introduction

• Describing a language
• Syntax
• Semantics
• Example

The syntax of a programming language is the
form of its expressions, statements, and program
units.
is the meaning of those expressions, statements,
and program units
while (ltboolean_exprgt) ltstatementsgt
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3.2 The general problem of describing syntax

• Lexeme
• Token
• Example

A basic unit to form a programming language
A category of its lexemes
Index 2 count 17
Lexemes Tokens index
identifier
equal_sign count
identifier 17
int_literal
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1. Language recognizer

• Lexical analyzer (lexizer)
• Syntax analyzer (Parser)

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2. Language generator

• It is a device that can be used to generate the
  sentences of a language

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3.3 Formal methods of describing syntax

• 1. Backus-Naur Form and Context-Free Grammars
• 2. Extended Backus-Naur Form

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1. BNF and Context-Free Grammars

• Regular grammars
• Context-free grammars

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Origins of BNF

• Algol 58 (John Backus)
• Algol 60 (Peter Naur)

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Fundamentals of BNF

• BNF is a metalanguage which is used to describe
  another language.
• Example
• Rule (production)
• Nonterminal
• Terminal

ltassigngt? ltvargtltexpressiongt
A definition of one abstraction
A abstraction in a BNF description
The lexemes and tokens of the rules are called
terminals
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Example of BNF
Example1 about multiple definition ltif_stmtgt ?
if ltlogic_exprgt then ltstmtgt
if ltlogic_exprgt then ltstmtgt else ltstmtgt
ifltlog_expgt ltstmtgt
Example2 about recursive definition
(ellipsis) ltident_listgt ? identifier
identifier, ltident_listgt
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Grammars and Derivations
Start symbol

• A grammar for a small language
• ltprogramgt ? begin ltstmt_listgt end
• ltstmt_listgt ? ltstmtgt ltstmtgt ltstmt_listgt
• ltstmtgt ? ltvargt ltexpressiongt
• ltvargt ? A B C
• ltexpressiongt ? ltvargt ltvargt ltvargt - ltvargt
• ltvargt

begin ABC BC end
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Grammars and Derivations

• Derivation it is a sentence generation process
• Leftmost derivation the replaced nonterminal is
  always the leftmost nonterminal

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Grammars and Derivations
Each of the strings in the derivation is called a
sentential form

• Leftmost derivation example
• ltprogramgt gtbegin ltstmt_listgt end
• gtbegin ltstmtgt ltstmt_listgt end
• gtbegin ltvargtltexpressiongt ltstmt_listgt end
• gtbegin Altexpressiongt ltstmt_listgt end
• gtbegin Altvargt ltvargt ltstmt_listgt end
• gtbegin AB ltvargt ltstmt_listgt end
• gtbegin AB C ltstmt_listgt end
• gtbegin AB C ltstmtgtend
• gtbegin AB C ltvargtltexpressiongtend
• gtbegin AB C B ltexpressiongt end
• gtbegin AB C B ltvargtend
• gtbegin AB C BC end

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Another derivation example
ltassinggtgtltidgtltexprgt gtAltexprgt gtAltidgtltexprgt
gtAB ltexprgt gtAB (ltexprgt) gtAB
(ltidgtltexprgt) gtAB (Altexprgt) gtAB
(Altidgt) gtAB (AC)

• Grammar
• ltassigngt? ltidgtltexprgt
• ltidgt?ABC
• ltexprgt?ltidgtltexprgt
• ltidgtltexprgt
• ltidgt(ltexprgt)

A B (A C)
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Parse tree
ltassigngt
ltexprgt
ltidgt

ltexprgt
ltidgt

A
(
ltexprgt
)
B
ltidgt

ltexprgt
ltidgt
A
C
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Ambiguity

• It is said to be ambiguous when a grammar that
  generate a sentential form for which there are
  two or more distinct parse trees

Example ABCA
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Ambiguity
ltassigngt
ltexprgt
ltidgt

ltexprgt

A
ltexprgt
id
ltidgt

ltexprgt
B
ltidgt
c
A
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Ambiguity
ltassigngt
ltexprgt
ltidgt

ltexprgt
ltexprgt

A
ltexprgt

ltexprgt
ltidgt
ltidgt
ltidgt
A
C
B
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Operator Precedence

• An unambiguous grammar for expressions
• ltassigngt?ltidgtltexprgt
• ltidgt?A B C
• ltexprgt?ltexprgtlttermgt
• lttermgt
• lttermgt?lttermgtltfactorgt
• ltfactorgt
• ltfactorgt?(ltexprgt)
• ltidgt

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Associativity of Operators

• Does the grammar describe the associativity?
• Left-associative
• Right-associative
• Does the associativity matter for computer
  addition?

Associativity Math, Computer
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Define associativity of a operator

• Left associativity

A rule has its LHS also appearing at the
beginning of its RHS

• Right associativity

A rule has its LHS also appearing at the end of
its RHS

• Example

ltfactorgt?ltexpgtltfactorgt ltexpgt ltexpgt?(ltexprgt)
id
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2. EBNF

• Not a new form
• For overcoming a few minor inconveniences in BNF
• Not enhance the descriptive power of BNF
• Three extensions

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First extension

• With bracket
• ltselectiongt?if (ltexpressiongt)
• thenltstatementgt
• else ltstatementgt

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Second extension

• With braces
• ltident_listgt?ltidentifiergt , ltidentifiergt

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Third extension

• With parentheses
• lttermgt?lttermgt ( / ) ltfactorgt

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Example
BNF ltexprgt?ltexprgtlttermgt ltexprgt-lttermgt
lttermgt lttermgt?lttermgtltfactorgt
lttermgt/ltfactorgt ltfactorgt ltfactorgt?ltexpgtltfacto
rgt ltexpgt ltexpgt?(ltexprgt) id
EBNF ltexprgt?lttermgt(-)lttermgt lttermgt?ltfactorgt(
/)ltfactorgt ltfactorgt?ltexpgtltexpgt ltexpgt?(ltexpr
gt)id
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3.4 Attribute grammar

• Is an extension to a context-free grammar
• Is a device used to describe more of the
  structure of a programming language than can be
  described with a context-free grammar
• Allows certain language rules to be conveniently
  described, such as type compatibility.

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1. Static semantics

• Used to describe type constraints.
• To check the specifications can be done at
  compile time.
• There are some problems to describe static
  semantics with BNF.
• Attribute grammars are a formal approach to both
  describing and checking the correctness of the
  static semantics rules of a program.

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Example

• Problem In Java, a floating-point value cannot
  be assigned to an integer type variable, but the
  opposite is legal.

This restriction can be described in BNF, it
requires additional nonterminals and rules, the
grammar would become too large, and the size of
parser is also too large to be useful.
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Example

• Problem all variables must be declared before
  they are referenced.

It can be proved that this rule cannot be
described by using BNF.
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2. Basic concepts

• Attribute grammars Context-free grammars
• Attributes
• Attributes functions
• Predicate functions.

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Basic concepts
Are associated with grammar symbols. They can be
assigned values.

• Attributes
• Attribute computation functions
• Predicate functions

Also called semantic functions, are associated
with grammar rules.
which state the static semantic rules of the
language, are associated with grammar rules.
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3. Attribute grammars defined

• 1. Associated with each grammar symbol X is a set
  of attributes A(X).

A(X) consists of two disjoint sets S(X) and
I(X). S(X) synthesized attributes are used to
pass semantic information up a parse tree. I(X)
inherited attributes pass semantic information
down and across a tree.
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Attribute grammars defined

• 2. Associated with each grammar rule is a set of
  semantic functions and a possibly empty set of
  predicate functions over the attributes of the
  symbols in the grammar rule

For a rule X0?X1X2Xn S(X0)f(A(X1), ,
A(Xn)) I(Xj)f(A(X0), , A(Xn))
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Attribute grammars defined

• 3. A predicate function has the form of a Boolean
  expression on the union of the attribute set
  A(X0), , A(Xn) and a set of literal attribute
  values.

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4. Intrinsic attributes

• Intrinsic attributes are synthesized attributes
  of leaf nodes whose values are determined outside
  the parse tree.

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5. Examples of Attribute Grammars

• We will show how attribute grammars can be used
  to describe static semantics.
• Example in Ada language, there is a rule that
  the end of an Ada procedure must match the
  procedures name.

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Ada example with Attribute grammars

• Syntax rule ltproc_defgt?procedure ltproc_namegt1
  
• ltproc_bodygtend
  ltproc_namegt2
• Predicate ltproc_namegt1.stringltproc_namegt2.
  string

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Another example

• The only variable names are A, B, C
• The right side of the assignments can either be a
  variable or an expression in the form of a
  variable added to another variable
• The variables can be one of two types int, or
  real
• The type of the expression when the operand types
  are not the same is always real. When they are
  the same, the expression type is that of the
  operands
• The type of the left side of the assignment must
  match the type of the right side
• Assignment is valid only the LHS and the RHS have
  the same type.

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The syntax

• ltassigngt?ltvargtltexprgt
• ltexprgt?ltvargtltvargtltvargt
• ltvargt?A B C

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Semantic rules

• actual_type A synthesized attribute associated
  with the nonterminals ltvargt and ltexprgt.
• expected_type An inherited attribute associated
  with the nonterminal ltexprgt.

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An attribute grammar for simple assignment
statements

• 1. Syntax rule ltassigngt?ltvargt ltexprgt
• Semantic rule ltexprgt.expected_type ?
  ltvargt.actual_type
• 2. Syntax rule ltexprgt?ltvargt1ltvargt2
• semantic rule ltexprgt.actual_type?
  if(ltvargt1.actual_typeint) and
• (ltvargt2.actual_type int)
• then int
• else real
• predicate ltexprgt.actual_typeltexprgt.expecte
  d_type
• 3. Syntax rule ltexprgt?ltvargt
• Semantic rule ltexprgt.actual_type?ltvargt.actual
  _type
• Predicate rule ltexprgt.actual_typeltexprgt.expect
  ed_type
• 4. Syntax rule ltvargt?A B C
• Semantic rule ltvargt.actual_type?look-up(ltvargt.str
  ing)

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A parse tree for this example
ltassigngt
ltexprgt
ltvargt
ltvargt2
ltvargt3

A
A
B

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6. Computing attribute values
ltassigngt
e_t
a_t
ltexprgt
a_t
ltvargt
ltvargt2
ltvargt3
a_t
a_t

A
A
B

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3.5 summary

• BNF and context-free grammars.
• They are equivalent metalanguages in describing
  the syntax of programming languages.
• Attributed grammar
• Static semantics
• Dynamic semantics operational, axiomatic, and
  denotational.