Attribute Grammars

1
Attribute Grammars

• Attribute Grammar is a
• Framework for specifying semantics
• and enables Modular specification.
• http//knoesis.wright.edu/tkprasad/papers/Attribut
  e-Grammars.pdf

2
S
Regular (lexer)
Context-free (parser)
Context-sensitive (type-checker)
3
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

4
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 -gt 0
• N -gt 1
• N -gt N 0
• N -gt N 1

• N . val 0
• N . val 1
• N . val 2 N. val
• N . val 2 N. val 1

7
Derivation Tree
N
N
0
N
1
110 gt 6
1
8
Synthesized Attributes

• N . val 0
• N . len 1
• N . val 1
• N . len 1
• N . val N. val
• N . len N. len 1
• N . val N. val 2 N. len
• N . len N. len 1

• N -gt 0
• N -gt 1
• N -gt 0 N
• N -gt 1 N

9
Inherited Attributes

• Declaration and Use
• int i, j, k
• i i j j
• ltassign-stmgt -gt ltvargt ltexprgt
• ltvargt.env ltassign-stmgt.env
• ltexprgt.env ltassign-stmgt.env

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Inherited Attributes

• Coercion 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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• Attributes A(X)
• Synthesized S(X)
• Inherited I(X)
• Attribute computation rules (Semantic functions)
• X0 -gt 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
computed
available
synthesized
...
...
13

• Synthesized Attributes
• Pass information up the parse tree
• Inherited 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.

14
Static Semantics

• E -gt n m
• E -gt x y
• E -gt E1 E2
• E -gt E1 E2

• E.type int
• E.type real
• if E1.type E2.type
• then E.type E1.type
• else E.type real

15
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 -gt n m
• E -gt p q
• E -gt if E0
• then E1
• else E2

• E.type int
• E.type bool
• if ( E0.type bool ) Ù ( E1.type
  E2.type )
• then E.type E1.type
• else type error

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Fractions

• F.val N.val
• N.pow 1
• N.val 0
• N.val (1/2N.pow)
• N.pow 1 N.pow
• N.val N.val
• N.pow 1 N.pow
• N.val N.val (1/2N.pow)

• F -gt . N
• N -gt 0
• N -gt 1
• N -gt 0 N
• N -gt 1 N

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Fractions (Alternate solution)

• F.val N.val / 2
• N.val 0
• N.val 1
• N.val N.val / 2
• N.val N.val / 2
• 1

• F -gt . N
• N -gt 0
• N -gt 1
• N -gt 0 N
• N -gt 1 N

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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

20
An Extended Example

• Distinct identifiers in a straight-line
  program.
• BNF
• ltexpgt ltvargt ltexpgt ltexpgt
• ltstmgt ltvargt ltexpgt ltstmgt ltstmgt
• Attributes
• ltvargt ? id
• ltexpgt ? ids
• ltstmgt ? ids ? num
• Semantics specified in terms of sets (of
  identifiers).

21

• ltexpgt ltvargt
• ltexpgt.ids ltvargt.id
• ltexpgt ltexp1gt ltexp2gt
• ltexpgt.ids ltexpgt.ids U ltexpgt.ids
• ltstmgt ltvargt ltexpgt
• ltstmgt.ids ltvargt.id U ltexpgt.ids
• ltstmgt.num ltstmgt.ids
• ltstmgt ltstm1gt ltstm2gt
• ltstmgt.ids ltstm1gt.ids U ltstm2gt.ids
• ltstmgt.num ltstmgt.ids

22
Alternate approach Using lists

• Attributes
• ? envi list of vars in preceding context
• ? envo list of vars for following context
• ? dnum number of new variables
• ltexpgt ltvargt
• ltexpgt.envo
• if member(ltvargt.id,ltexpgt.envi)
• then ltexpgt.envi
• else cons(ltvargt.id,ltexpgt.envi)

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Attribute Computation Rules

• ltexpgt ltexp1gt ltexp2gt
• ? envi ? envi ? envi
• ? envo ? envo ? envo
• ? dnum ? dnum ? dnum
• ltexp1gt.envi ltexpgt.envi
• ltexp2gt.envi ltexp1gt.envo
• ltexpgt.envo ltexp2gt.envo
• ltexpgt.dnum length(ltexpgt.envo)