Syntax Directed Definition in Compiler Design

Syntax Directed Definitions (SDD) are formal methods of attaching semantic information to the syntactic structure of a programming language. SDDs improve the means of context-free high-level by instances, adding a semantic rule set for every production of the grammar. The rules described in these definitions state how to derive values such as types, memory locations, or fragments of code from the structure of an input object.

Syntax Directed Translation (SDT) is the action of translating a high-level language program into an intermediate language or machine language according to the semantic rules imposed by SDDs. Semantic actions in SDT, act in coordination with the parsing process in order to provide the translation of the input code. These actions are declarative and they are triggered during the parsing phase of the message to yield the result.

What is Syntax Directed Translation?

Syntax Directed Translation (SDT), is a technical manner utilized in semantics and language translation whereby a source language is translated into an intermediate language or a target language through semantic actions, and attributes attached to the grammar. The translation process follows the structure of the grammar, besides the performance of semantic actions is interwoven with the processes of input parsing.

The semantic actions are normally included in the grammatical rules and can be either performed synchronously or asynchronously with the parsing actions. Integrated development systems such as SDT offer tools to compilers such as code generation, lexical analysis, evaluation of expressions, definition, grammar, and checking of types among other services.

What are Annotated Parse Trees?

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

Features of Annotated Parse Trees

• 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. 

Conclusion

Syntax Directed Definitions (SDD) and Syntax Directed Translation (SDT) are essential tools in the design and implementation of compilers and interpreters. They allow for the generation of intermediate code, type-checking, and expression evaluation in a modular and structured manner. By defining attributes and associating them with grammar productions, we can control the semantic processing of programming languages efficiently. Synthesized and inherited attributes form the basis of attribute evaluation, supporting a broad range of programming language features.