Syntax directed translation

Background: Parser uses a CFG(Context-free-Grammar) to validate the input string and produce output for the next phase of the compiler. Output could be either a parse tree or an abstract syntax tree. Now to interleave semantic analysis with the syntax analysis phase of the compiler, we use Syntax Directed Translation. 

Definition 

Syntax Directed Translation has augmented rules to the grammar that facilitate semantic analysis. SDT involves passing information bottom-up and/or top-down the parse tree in form of attributes attached to the nodes. Syntax-directed translation rules use 1) lexical values of nodes, 2) constants & 3) attributes associated with the non-terminals in their definitions. 

In syntax directed translation, along with the grammar we associate some informal notations and these notations are called as semantic rules.

So we can say that

1. Grammar + semantic rule = SDT (syntax directed translation)  

• In syntax directed translation, every non-terminal can get one or more than one attribute or sometimes 0 attribute depending on the type of the attribute. The value of these attributes is evaluated by the semantic rules associated with the production rule.
• In the semantic rule, attribute is VAL and an attribute may hold anything like a string, a number, a memory location and a complex record
• In Syntax directed translation, whenever a construct encounters in the programming language then it is translated according to the semantic rules define in that particular programming language.

The general approach to Syntax-Directed Translation is to construct a parse tree or syntax tree and compute the values of attributes at the nodes of the tree by visiting them in some order. In many cases, translation can be done during parsing without building an explicit tree. 

Example 

E -> E+T | T
T -> T*F | F
F -> INTLIT 

This is a grammar to syntactically validate an expression having additions and multiplications in it. Now, to carry out semantic analysis we will augment SDT rules to this grammar, in order to pass some information up the parse tree and check for semantic errors, if any. In this example, we will focus on the evaluation of the given expression, as we don’t have any semantic assertions to check in this very basic example. 

 

E -> E+T     { E.val = E.val + T.val }   PR#1
E -> T       { E.val = T.val }           PR#2
T -> T*F     { T.val = T.val * F.val }   PR#3
T -> F       { T.val = F.val }           PR#4
F -> INTLIT  { F.val = INTLIT.lexval }   PR#5

For understanding translation rules further, we take the first SDT augmented to [ E -> E+T ] production rule. The translation rule in consideration has val as an attribute for both the non-terminals – E & T. Right-hand side of the translation rule corresponds to attribute values of right-side nodes of the production rule and vice-versa. Generalizing, SDT are augmented rules to a CFG that associate 1) set of attributes to every node of the grammar and 2) set of translation rules to every production rule using attributes, constants, and lexical values. 

Let’s take a string to see how semantic analysis happens – S = 2+3*4. Parse tree corresponding to S would be 

 

To evaluate translation rules, we can employ one depth-first search traversal on the parse tree. This is possible only because SDT rules don’t impose any specific order on evaluation until children’s attributes are computed before parents for a grammar having all synthesized attributes. Otherwise, we would have to figure out the best-suited plan to traverse through the parse tree and evaluate all the attributes in one or more traversals. For better understanding, we will move bottom-up in the left to right fashion for computing the translation rules of our example. 

 

The above diagram shows how semantic analysis could happen. The flow of information happens bottom-up and all the children’s attributes are computed before parents, as discussed above. Right-hand side nodes are sometimes annotated with subscript 1 to distinguish between children and parents. 

Additional Information 

Synthesized Attributes are such attributes that depend only on the attribute values of children nodes. 

Thus [ E -> E+T { E.val = E.val + T.val } ] has a synthesized attribute val corresponding to node E. If all the semantic attributes in an augmented grammar are synthesized, one depth-first search traversal in any order is sufficient for the semantic analysis phase. 

Inherited Attributes are such attributes that depend on parent and/or sibling’s attributes. 

Thus [ Ep -> E+T { Ep.val = E.val + T.val, T.val = Ep.val } ], where E & Ep are same production symbols annotated to differentiate between parent and child, has an inherited attribute val corresponding to node T.