Inherited and Synthesized Attributes: Syntax-directed definitions may use two kinds of attributes. A synthesized attribute at a parse-tree node is computed from attributes at its children. An inherited attribute at a node is computed from attributes at its parent and/or siblings.
Dependency Graph: Given a parse tree and an SDD, we draw edges among the attribute instances associated with each parse-tree node to denote that the value of the attribute at the head of the edge is computed in terms of the value of the attribute at the tail of the edge.
Cyclic Definitions: In problematic SDD’s, we find that there are some parse trees for which it is impossible to find an order in which we can compute all the attributes at all nodes. These parse trees have cycles in their associated dependency graphs. It is intractable to decide whether an SDD has such circular dependency graphs.
S-Attributed Definitions: In an S-attributed SDD, all attributes are synthesized.
L-Attributed Definitions: In an L-attributed SDD, attributes may be inherited or synthesized. However, inherited attributes at a parse-tree node may depend only on inherited attributes of its parent and on (any) attributes of siblings to its left.
Syntax Trees: Each node in a syntax tree represents a construct; the children of the node represent the meaningful components of the construct.
Implementing S-Attributed SDD’s: An S-attributed definition can be implemented by an SDT in which all actions are at the end of the production (a “postfix”SDT). The actions compute the synthesized attributes of the production head in terms of synthesized attributes of the symbols in the body. If the underlying grammar is LR, then this SDT can be implemented on the LR parser stack.
Eliminating Left Recursion From SDT’s: If an SDT has only side-effects (no attributes are computed), then the standard left-recursion-elimination algorithm for grammars allows us to carry the actions along as if they were terminals. When attributes are computed, we can still eliminate left recursion if the SDT is a postfix SDT.
Implementing L-attributed SDD’s by Recursive-Descent Parsing: If we have an L-attributed definition on a top-down parsable grammar, we can build a recursive-descent parser with no backtracking to implement the translation. Inherited attributes become arguments of the functions for their nonterminals, and synthesized attributes are returned by that function.
Implementing L-Attributed SDD’s on an LL Grammar: Every L-attributed definitions with an underlying LL grammar can be implemented along with the parse. Records to hold the synthesized attributes for a nonterminal are placed below that nonterminal on the stack, while inherited attributes for a nonterminal are stored with that nonterminal on the stack. Action records are also placed on the stack to compute attributes at the appropriate time.
Implementing L-Attributed SDD’s on an LL Grammar, Bottom-Up: An L-attributed definition with an underlying LL grammar can be converted to a translation on an LR grammar and the translation performed in connection with a bottom-up parse. The grammar transformation introduces “marker” nonterminals that appear on the bottom-up parser’s stack and hold inherited attributes of the nonterminal above it on the stack. Synthesized attributes are kept with their nonterminal on the stack.