Semantic Analysis — Attribute Grammars, Type Checking

🎯 Learning Objectives

• Define attributes for grammar symbols
• Differentiate S-attributed and L-attributed grammars
• Build a type checker using attribute grammars
• Implement type inference for simple expressions

1. Syntax-Directed Definitions (SDD)

1.1 Intuition

1.2 Attributes

2. S-Attributed Grammars

pseudo
Production         Semantic Rule
E → E₁ + T         E.val = E₁.val + T.val
E → T              E.val = T.val
T → T₁ * F         T.val = T₁.val * F.val
T → F              T.val = F.val
F → ( E )          F.val = E.val
F → num            F.val = num.lexval

3. L-Attributed Grammars

javascript
Run Inline
Production                    Semantic Rule
D → T L                      L.inh = T.type
T → int                      T.type = integer
T → float                    T.type = float
L → L₁, id                   L₁.inh = L.inh
                              id.type = L.inh
L → id                       id.type = L.inh

4. Type Checking

4.1 Type Rules

c
// Type checker for expressions
if (E1.type == int && E2.type == int)
    E.type = int;         // int + int = int
else if (E1.type == float && E2.type == float)
    E.type = float;       // float + float = float
else if (E1.type == int && E2.type == float)
    E.type = float;       // int + float = float (coercion)
else
    ERROR("Type mismatch");

4.2 Type Inference

1. 5 is int → x has type int
2. x + 3.2: int + float → float (coercion)
3. y gets type float

5. 📝 Practice Questions

Q1: What is the difference between synthesized and inherited attributes?

Answer: Synthesized attributes are computed from children (bottom-up). Inherited attributes are passed from parent or left sibling (top-down or left-to-right). SDDs with only synthesized attributes are S-attributed; those with inherited attributes but limited to left-to-right flow are L-attributed. Q2: Why can S-attributed SDDs be evaluated during LR parsing?

Answer: LR parsers process input bottom-up, reducing productions from leaves to root. When a production is reduced, all children have been fully evaluated (their synthesized attributes are available). The parent's attributes can be computed immediately. Q3: Write an SDD for translating infix to postfix notation.

Answer:

pseudo
E → E₁ + T   E.code = E₁.code || T.code || "+"
E → T        E.code = T.code
T → num      T.code = num.lexval
T → (E)      T.code = E.code

Q4: How does a type checker handle type conversion between int and float?

Answer: The type checker inserts implicit conversion (coercion). In an expression mixing int and float, the int is converted to float before the operation. The result type is float. Some languages (like C) also allow explicit casts to override default behavior. Q5: What is a symbol table and how is it used during semantic analysis?

Answer: A symbol table maps identifier names to their attributes (type, scope, memory location). During semantic analysis, when an identifier is encountered, the type checker looks up its declared type in the symbol table to verify consistent usage.

6. 🔗 Cross-References

• Week 3 - LL Parsing: L-attributed during top-down parsing
• Week 4 - LR Parsing: S-attributed during bottom-up parsing
• Week 6 - Symbol Table: Storing attribute information Join Discord PreviousLR ParsingNextIntermediate Code