Attribute Grammar

An attribute grammar can describe more of the structure of a programming language than a context free grammar such as BNF.

Static Semantics

Some characteristics of programming languages are difficult or impossible to describe with BNF. Type compatibility rules are difficult to describe. The common rule that all variables must be declared before they are referenced is impossible to specify in BNF. the static semantics of a language has to do with the syntax of a language. They are so named because the analysis required to check the static semantics can be done at compile time.

Basic Concepts

Attribute grammars are grammars to which have been added attributes, attribute computation functions and predicate functions.

Attributes

similar to variables in the sense that they can have values assigned to them

associated with grammar rules

Attribute computation functions

aka semantic functions

associated with grammar rules

specify how attribute values are computed

Predicate functions

associated with grammar rules

state some of the syntax and static semantic rules of the language

Attribute Grammars defined

An attribute grammar is a grammar with the following additional features:

• Associated with each grammar symbol X is a set of attributes A(X). A(X) is made up of two disjoint sets S(X) syntesized and I(X) inherited attributes. Synthesized attributes, S(X) pass semantic information up a parse tree, inherited attributes pass semantic information down a tree.
• Associated with each grammar rule is a set of semantic functions and set of predicate functions over the attributes of the symbol in the grammar rule.
  • For a rule X₀ --> X₁ ... X_n the synthesized attributes of X₀ are computed with semantic functions of the form S(X₀) -->f(A( X₁) ...A( X_n))
  • The value of a synthesized attribute depends only on the values of attributes of its children in the parse tree.
  • Value of an inherited attribute I(X_j) = f(A( X₀) ...A( X_n)) (or f(A( X₀) ...A( X_j-1)) to avoid cirularity)
  • Value of an inherited attribute depends on attribute values of that node's parent node and those of its siblings.
• A Predicate Function has the form of a Boolean expression on the attribute set {A( X₁) ...A( X_n)}.
  • Only derivations allowed are those in which every predicate associated with every nonterminal is true
  • False predicate function value indicates violation of syntax or static semantics rules of the language (compile error).
• Intrinsic Attributes are synthesized attributes of leaf nodes determined outside the parse tree.
  • E.g. type of a variable might come from the symbol table
  • After constructing unattributed parse tree the only attributes with values are the intrinsic attributes of the leaf nodes.
  • Semantic functions can be used to compute the remaining attribute values.

The following is a simple attribute grammar:

actual_type synthesized attribute associated with nonterminals <var> and <expr> Used to store actual type, int or real of a variable or expression. For variables actual type is intrinsic. For expressions actual type is determined from actual types of the child nodes

expected_type: inherited attribute associated with nonterminal <expr>. Used to store the type, int or real, expected for the expression

<assign>--><var>=<expr>

<expr>.expected_type<--<var>.actual_type

<expr>--><var>[2] + var[3]
       

<expr>.actual_type <--
   if (<var>[2].actual_type = int) and
      <var>[3].actual_type=int)
   then int
   else real
   end if

<expr>.actual_type=<expr>.expected_type

<expr>--> <var>

<expr>.actual_type <-- <var>.actual_type

<expr>.actual_type = <expr>.expected type

<var>.actual_type<--look-up(<var>.string)

Parse tree for A=A+B