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Attribute Grammars

Attribute Grammar is a

Framework for specifying semantics

and enables Modular specification.http://knoesis.wright.edu/tkprasad/papers/Attribute-Grammars.pdf

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“Correct” Programs(no run-time errors)

Regular (lexer)

Context-free (parser)

Context-sensitive (type-checker)

Hierarchy of approximations

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LanguagesContext-sensitive (type-checker)

Context-free (parser)

Regular (lexer)

Expresssive power

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Semantics of Bit Pattern : 0101110

• Number – 46 (if base 2)

– 101110 (if base 10)

• Fraction– 23/64

• Unary encoding “13”

• ASCII Character “.”

• Switch positions– ON-OFF-ON-…

• Binary string “0101110”

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Motivation for Precise Specification

• Capture subtly different semantics for the same syntax in various languages.Arrays and strings.Parameter passing mechanisms.Scoping rules.Primitive types vs Composite types.Type equivalence.

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Attribute Grammars Formalism for specifying semantics based

on context-free grammars (BNF)Static semantics (context-sensitive aspects)

• Type checking and type inference

• Compatibility between procedure definition and call

• Scope rules

Dynamic semantics

• Associate attributes with terminals and non-terminals

• Associate attribute computation rules with productions

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Synthesized Attributes

N

N

val

val

valNval

valNval

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Derivation Tree

N

N

N

1

1

0

110 ~> 6

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Derivation Tree

N

N

N

1

1

0

110 ~> 6

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Synthesized Attributes

N

N

vallen

vallen

valNvallenNlen

val Nval^ Nlen

lenNlen + 1

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Grammar Syntax Variations

N

N

| NN

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Synthesized Attributes

• Evaluation of a constant expression

• Type Inference

5.0 + 2

• Determination of non-terminals that derive null string or terminal strings

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Inherited Attributes

• Declaration and Use{ int i, j, k; i := i + j + j; }

<assign-stm> <var> := <expr> <var>.env := <assign-stm>.env

<expr>.env := <assign-stm>.env

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Inherited Attributes

• Coercion (automatic type conversion) Code Generation

5.0 + 2 coerce_int_to_real

• Determination of un-initialized variables

• Determination of reachable non-terminals

• Evaluation of an expression containing variables

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• AttributesAttributes A(X)– Synthesized S(X)– Inherited I(X)

• Attribute computation rulesAttribute computation rules (Semantic functions)

X0 -> X1 X2 … Xn

S(X0) = f( I(X0), A(X1), A(X2), …, A(Xn) )

I(Xj) = Gj( I(X0), A(X1), A(X2), …, A(Xj-1))

for all j in 1..n P( A(X0), A(X1), A(X2), …, A(Xn) )

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Information Flow

inherited

synthesized

... ...

computedcomputed

availableavailable

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• Synthesized AttributesSynthesized Attributes

Pass information up the parse tree• Inherited AttributesInherited Attributes

Pass information down the parse tree or from left siblings to the right siblings

• Attribute values assumed to be available from the context.

• Attribute values computed using the semantic rules provided.

The constraints on the attribute evaluation rules permit top-down left-to-right (one-pass) traversal of the parse tree to compute the meaning.

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Static Semantics

E -> n | m

E -> x | y

E -> E1 + E2

E -> E1 * E2

E.type int

E.type real

E.type

if E1.type E2.type

then E1.type

else real

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Executable Specification in Prolog

type(i,int).

type(x,real).

type(+(E,F),T) :- type(E,T), type(F,T).

type(+(E,F),real) :- type(E,T1), type(F,T2), T1 \= T2.

• Type Checking ?- type(+(i,x),real).

• Type Inference ?- type(+(x,x),T).

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Static Semantics

E -> n | m

E -> p | q

E -> if E0 then E1 else E2

E.type int

E.type bool

E.type

if ( E0.type bool ) ( E1.type = E2.type )

then E1.type

else type error

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Fractions

F

N

N

F.val N.valN.pow 1

N.val N.val 1/2^N.pow)N.pow 1 + N.powN.val Nval

N.pow 1 + N.powN.val Nval +

(1/2^N.pow)

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Fractions (Alternate solution)

F

N

N

F.val N.val 2

N.val N.val

N.val Nval 2

N.val Nval 2 + 1

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Applications of Attribute Grammars

• Compiler Generation– Top-down Parsers (LL(1))

• FIRST sets, FOLLOW sets, etc

– Code Generation Computations• Type, Storage determination, etc

• Databases – Optimizing Bottom-up Query Evaluation

(Magic Sets)

• Programming and Definitions

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An Extended Example

• Number of distinct identifiers in a straight-line program.

BNF<exp> ::= <var> | <exp> + <exp><stm> ::= <var> := <exp> | <stm> ; <stm>

Attributes

<var> id

<exp> ids

<stm> ids num

• Semantics specified in terms of sets (of identifiers).

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<exp> ::= <var><exp>.ids = { <var>.id } <exp> ::= <exp1> + <exp2><exp>.ids = <exp>.ids U <exp>.ids

<stm> ::= <var> := <exp><stm>.ids ={ <var>.id } U <exp>.ids<stm>.num = | <stm>.ids |

<stm> ::= <stm1> ; <stm2><stm>.ids = <stm1>.ids U <stm2>.ids

<stm>.num = | <stm>.ids |

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Alternate approach : Using lists

• Attributes envi : list of vars in preceding context

envo : list of vars for following context

dnum : number of new variables

<exp> ::= <var><exp>.envo = if member(<var>.id,<exp>.envi) then <exp>.envi else cons(<var>.id,<exp>.envi)

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<exp> ::= <exp1> + <exp2>

envi envi envi envo envo envo dnum dnum dnum

<exp1>.envi = <exp>.envi <exp2>.envi = <exp1>.envo <exp>.envo = <exp2>.envo <exp>.dnum = length(<exp>.envo)

Attribute Computation Rules