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Semantic Analysis II

Semantic Analysis II. x86 executable. exe. IC Program. ic. IC compiler. Compiler. We saw: Scope Symbol tables. Lexical Analysis. Syntax Analysis Parsing. AST. Symbol Table etc. Inter. Rep. (IR). Code Generation. Today: Type checking. assigned type doesn’t match declared type.

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Semantic Analysis II

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  1. Semantic Analysis II

  2. x86 executable exe ICProgram ic IC compiler Compiler We saw: • Scope • Symbol tables LexicalAnalysis Syntax Analysis Parsing AST SymbolTableetc. Inter.Rep.(IR) CodeGeneration Today: • Type checking

  3. assigned type doesn’t match declared type relational operator applied to non-int type a is not a subtype of b argument list doesn’t match formal parameters Examples of type errors 1 < true int a; a = true; class A {…}class B extends A { void foo() { A a; B b; b = a; }} void foo(int x) { int y; foo(5,7);}

  4. Types • Type • Set of possible values (and operations) • boolean = {true,false} • int = {-231..231-1} • void = {} • Type safety • Type usage adheres to formally defined typing rules

  5. Type judgments • e : T • e is a well-typed expression of type T • Examples • 2 : int • 2 * (3 + 4) : int • true : bool • “Hello” : string

  6. Type judgments • E e : T • In the context E,e is a well-typed expression of T • Examples: • b:bool, x:int  b:bool • x:int  1 + x < 4:bool • foo:int->string, x:int  foo(x) : string

  7. Typing rules Premise [Name] Conclusion [Name] Conclusion

  8. Typing rules for expressions E e1 : int E e2 : int [+] E e1+e2 : int

  9. Expression rules E  true : bool E  false : bool E int-literal : int E string-literal : string E  e1 : int E  e2 : int op  { +, -, /, *, %} E  e1 op e2 : int E  e1 : int E  e2 : int rop { <=,<, >, >=} E  e1 rop e2 : bool

  10. More expression rules E  e1 : bool E  e2 : bool lop  { &&,|| } E  e1 lop e2 : bool E  e1 : int E  e1 : bool E - e1 : int E ! e1 : bool E  e1 : T[] E  e1 : T[] E  e2 : int E  e1 : int E  e1[e2] : T E  e1.length : int E new T[e1] : T[] E  e:C (id : T)  C E  e.id : T E new T() : T

  11. Subtyping • Inheritance induces subtyping relation ≤ • S ≤ T  values(S)  values(T) • “A value of type S may be used wherever a value of type T is expected”

  12. Subtyping • For all types: • For reference types: A ≤ A A extends B {…} A ≤ B B ≤ C A ≤ B A ≤ C null ≤ A

  13. Examples • int ≤ int ? • null ≤ A ? • null ≤ string ? • string ≤ null ? • null ≤ boolean ? • null ≤ boolean[] ? • A[] ≤ B[] ?

  14. Examples • int ≤ int ? • null ≤ A ? • null ≤ string ? • string ≤ null ? • null ≤ boolean ? • null ≤ boolean[] ? • A[] ≤ B[] ? “Subtyping is not covariant for array types: if A is a subtype of B then A[ ] is not a subtype of B[ ]. Instead, array subtyping is type invariant, which means that each array type is only a subtype of itself.”

  15. Expression rules with subtyping E  e1 : T1 E  e2 : T2 T1 ≤ T2 or T2 ≤ T1op  {==,!=} E  e1 op e2 : bool

  16. Rules for method invocations E  e0 : T1 …  Tn Tr E  ei : T’i T’i ≤ Ti for all i=1..n E  e0(e1, … ,en): Tr (m : static T1 …  Tn Tr)  CE  ei : T’i T’i ≤ Ti for all i=1..n E  C.m(e1, … ,en): Tr

  17. E  e:bool E  S1 E S2 E  e:bool E  e:bool E  S E  S E if (e) S1 else S2 E while (e) S E if (e) S E break E continue Statement rules • Statements have type void • Judgments of the form E  S • In environment E, S is well typed

  18. Return statements • ret:Tr represents return type of current method E  e:T ret:T’E T≤T’ ret:void  E E return e; E return;

  19. More IC Rules • Declarations • Method • Class • Program • …

  20. Type-checking algorithm • Construct types • Add basic types to a “type table” • Traverse AST looking for user-defined types (classes,methods,arrays) and store in table • Bind all symbols to types

  21. Type-checking algorithm • Traverse AST bottom-up (using visitor) • For each AST node find corresponding rule(there is only one for each kind of node) • Check if rule holds • Yes: assign type to node according to consequent • No: report error

  22. E  e1 : bool E  e2 : bool E  e1 && e2 : bool E  e1 : bool E  e1 : int E  e2 : int E  !e1 : bool E  e1 > e2 : bool E false : bool intLiteral intLiteral boolLiteral E int-literal : int val=45 val=32 val=false Algorithm example … BinopExpr : bool op=AND : bool : bool BinopExpr UnopExpr op=GT op=NEG : int : int : bool 45 > 32 && !false

  23. Semantic analysis flow • Parsing and AST construction • Combine library AST with IC program AST • Construct and initialize global type table • Construct class hierarchy and verify the hierarchy is tree • Phase 1: Symbol table construction • Assign enclosing-scope for each AST node • Phase 2: Scope checking • Resolve names • Check scope rules using symbol table • Phase 3: Type checking • Assign type for each AST node • Phase 4: Remaining semantic checks

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