Compiler Design | Syntax Directed Definition

Prerequisite – Introduction to Syntax Analysis, Syntax Directed Translation 
Syntax Directed Definition (SDD) is a kind of abstract specification. It is generalization of context free grammar in which each grammar production X –> a is associated with it a set of production rules of the form s = f(b₁, b₂, ……b_k) where s is the attribute obtained from function f. The attribute can be a string, number, type or a memory location. Semantic rules are fragments of code which are embedded usually at the end of production and enclosed in curly braces ({ }). 

Example:  

E --> E1 + T  { E.val = E1.val + T.val} 

Annotated Parse Tree – The parse tree containing the values of attributes at each node for given input string is called annotated or decorated parse tree. 

Features –  

• High level specification
• Hides implementation details
• Explicit order of evaluation is not specified

Types of attributes – There are two types of attributes: 

1. Synthesized Attributes – These are those attributes which derive their values from their children nodes i.e. value of synthesized attribute at node is computed from the values of attributes at children nodes in parse tree. 

Example:  

E --> E1 + T  { E.val = E1.val + T.val} 

In this, E.val derive its values from E₁.val and T.val 

Computation of Synthesized Attributes –  

• Write the SDD using appropriate semantic rules for each production in given grammar.
• The annotated parse tree is generated and attribute values are computed in bottom up manner.
• The value obtained at root node is the final output.

Example: Consider the following grammar  

S --> E
E --> E1 + T
E --> T
T --> T1 * F
T --> F
F --> digit

The SDD for the above grammar can be written as follow 

Let us assume an input string 4 * 5 + 6 for computing synthesized attributes. The annotated parse tree for the input string is 

For computation of attributes we start from leftmost bottom node. The rule F –> digit is used to reduce digit to F and the value of digit is obtained from lexical analyzer which becomes value of F i.e. from semantic action F.val = digit.lexval. Hence, F.val = 4 and since T is parent node of F so, we get T.val = 4 from semantic action T.val = F.val. Then, for T –> T₁ * F production, the corresponding semantic action is T.val = T₁.val * F.val . Hence, T.val = 4 * 5 = 20 

Similarly, combination of E₁.val + T.val becomes E.val i.e. E.val = E₁.val + T.val = 26. Then, the production S –> E is applied to reduce E.val = 26 and semantic action associated with it prints the result E.val . Hence, the output will be 26. 

2. Inherited Attributes – These are the attributes which derive their values from their parent or sibling nodes i.e. value of inherited attributes are computed by value of parent or sibling nodes. 
Example:  

A --> BCD   { C.in = A.in, C.type = B.type } 

Computation of Inherited Attributes –  

• Construct the SDD using semantic actions.
• The annotated parse tree is generated and attribute values are computed in top down manner.

Example: Consider the following grammar  

S --> T L
T --> int
T --> float
T --> double
L --> L1, id
L --> id

The SDD for the above grammar can be written as follow 

Let us assume an input string int a, c for computing inherited attributes. The annotated parse tree for the input string is 

The value of L nodes is obtained from T.type (sibling) which is basically lexical value obtained as int, float or double. Then L node gives type of identifiers a and c. The computation of type is done in top down manner or preorder traversal. Using function Enter_type the type of identifiers a and c is inserted in symbol table at corresponding id.entry.