COMS W4115
Programming Languages and Translators
Lecture 12: Syntax-Directed Translation
March 4, 2013

Lecture Outline

1. The "dangling-else" ambiguity
2. Syntax-directed definitions and translation schemes
3. Synthesized and inherited attributes
4. S-attributed SDDs
5. L-attributed SDDs
6. Reading

1. The "Dangling-Else" Ambiguity

• Consider the following simplified ambiguous grammar for if- and if-else statements:

S' → S
S  → i S e S | i S | a

• Here the symbol i stands for if expr then, the symbol e stands for else, and the symbol a stands for all other productions. We have also added an augmenting production S' → S.
• The canonical collections of sets of LR(0) items for this grammar is as follows:

I0: S' → .S			I3: S → a.
    S  → .iSeS
    S  → .iS			I4: S → iS.eS
    S  → .a			    S → iS.
				
I1: S' → S.			I5: S → iSe.S
				    S → .iSeS				    
I2: S  → i.SeS			    S → .iS
    S  → i.S			    S → .a
    S  → .iSeS
    S  → .iS			I6: S → iSeS.
    S  → .a

• The set of items I4 gives rise to a shift/reduce conflict. The item S → iS.eS calls for a shift on e and since FOLLOW(S} = {e, $}, the item S → iS. calls for a reduction by production S → iS. on e. To associate each e with the closest unelsed if, we should resolve the conflict in favor of shift to state 5.
• See Section 4.8.2 of ALSU for a more detailed discussion.

2. Syntax-Directed Definitions and Translation Schemes

• The syntax analyzer translates its input token stream into an intermediate language representation of the source program, usually an abstract syntax tree (AST).
• A syntax-directed definition can be used to specify this translation.
• A syntax-directed definition (SDD) is a context-free grammar with attributes attached to grammar symbols and semantic rules attached to the productions.
• The semantic rules define values for attributes associated with the symbols of the productions. These values can be computed by creating a parse tree for the input and then making a sequence of passes over the parse tree, evaluating some or all of the rules on each pass. SDDs are useful for specifying translations.
• A syntax-directed translation scheme (SDTS) is a context-free grammar with program fragments, called semantic actions, embedded within production bodies. SDTSs are useful for implementing syntax-directed definitions.

3. Synthesized and Inherited Attributes

• Attributes are values computed at the nodes of a parse tree.
• Synthesized attributes are values that are computed at a node N in a parse tree from attribute values of the children of N and perhaps N itself. Synthesized attributes can be easily computed by a shift-reduce parser that keeps the values of the attributes on the parsing stack. See Sect. 5.4.2 of ALSU.
• An SDD is S-attributed if every attribute is synthesized. S-attributed SDDs are useful for bottom-up parsing.
• Inherited attributes are values that are computed at a node N in a parse tree from attribute values of the parent of N, the siblings of N, and N itself.
• An SDD is L-attributed is every attribute is either synthesized or inherited from the parent or from the left. L-attributed SDDs are useful for top-down parsing. See Sect. 5.2.4 of ALSU for details.

4. Examples of S-Attributed SDDs

• Example 1. Here is an S-attributed SDD translating signed bit strings into decimal numbers. The attributes, BNum.val, Sign.val, List.val, and Bit.val, are all synthesized attributes that represent integers.

   BNum → Sign List      { BNum.val = Sign.val × List.val }
   Sign → +              { Sign.val = +1 }
   Sign → -              { Sign.val = -1 }
   List → List1 Bit      { List.val = 2 × List1.val + Bit.val }
   List → Bit            { List.val = Bit.val }
   Bit  → 0              { Bit.val = 0 }
   Bit  → 1              { Bit.val = 1 }
  

• Example 2. Here are Yacc translation rules implementing the SDD above for translating signed bit strings into decimal numbers. The identifiers $$, $1, $2 and so on in Yacc actions are synthesized attributes.

   BNum : Sign List      { $$ = $1 * $2; }
        ;
   Sign : '+'            { $$ = +1; }
        | '-'            { $$ = -1; }
        ;
   List : List Bit       { $$ = 2*$1 + $2; }
        | Bit
        ;        
   Bit  : '0'            { $$ = 0; }
        | '1'            { $$ = 1; }
        ;
  

• Example 3. Here is an S-attributed SDD based on an SLR(1) grammar that translates arithmetic expressions into ASTs. E has the synthesized attributed E.node and T the synthesized attribute T.node. E.node and T.node point to a node in the AST. The function Node(op, left, right) returns a pointer to a node with three fields: the first labeled op, the second a pointer to a left subtree, and the third a pointer to a right subtree. The function Leaf(op, value) returns a pointer to a node with two fields: the first labeled op, the second the value of the token. See Example 5.11 in ALSU.

   E → E1 + T     { E.node = Node('+', E1.node, T.node); }

   E → T          { E.node = T.node; }

   T → ( E )      { T.node = E.node; }

   T → id         { T.node = Leaf(id, id.entry); }

  

5. Example of an L-Attributed SDD

• Example 4. Here is an L-attributed SDD based on an LL(1) grammar for translating arithmetic expressions into ASTs. See Example 5.12 in ALSU.

   E → T A        { E.node = A.s;
                    A.i = T.node; }

   A → + T A1     { A1.i = Node('+', A.i, T.node);
                    A.s = A1.s; }

   A → ε          { A.s = A.i; }

   T → ( E )      { T.node = E.node; }

   T → id         { T.node = Leaf(id, id.entry); }
  

6. Practice Problems

1. Using Yacc, implement a syntax-directed translator that translates sequences of postfix Polish expressions into infix notation. For example, your translator should map 345+* into 3*(4+5).
2. Optimize your translator so it doesn't generate any redundant parentheses. For example, your translator should still map 345+* into 3*(4+5) but it should map 345*+ into 3+4*5.

7. Reading

• ALSU, Sects. 5.1-5.4