Points-to Analysis using Types

Transcription

1 CS618: Program Analysis I st Semester Points-to Analysis using Types Amey Karkare karkare@cse.iitk.ac.in karkare@cse.iitb.ac.in Department of CSE, IIT Kanpur/Bombay karkare, CSE, IITK/B CS618 1/10

2 Reference Papers Bjarne Steensgaard: Points-to Analysis in Almost Linear Time. POPL 1996 Manuvir Das: Unification-based pointer analysis with directional assignments. PLDI 2000 karkare, CSE, IITK/B CS618 2/10

3 Language S ::= x = y karkare, CSE, IITK/B CS618 3/10

4 Language S ::= x = y x = &y karkare, CSE, IITK/B CS618 3/10

5 Language S ::= x = y x = &y x = y karkare, CSE, IITK/B CS618 3/10

6 Language S ::= x = y x = &y x = y x = allocate(y) karkare, CSE, IITK/B CS618 3/10

7 Language S ::= x = y x = &y x = y x = allocate(y) x = y karkare, CSE, IITK/B CS618 3/10

8 Language S ::= x = y x = &y x = y x = allocate(y) x = y x = fun(f 1,...,f n ) returns r in S karkare, CSE, IITK/B CS618 3/10

9 Language S ::= x = y x = &y x = y x = allocate(y) x = y x = fun(f 1,...,f n ) returns r in S x = p(y 1,...,y n ) karkare, CSE, IITK/B CS618 3/10

10 Language S ::= x = y x = &y x = y x = allocate(y) x = y x = fun(f 1,...,f n ) returns r in S x = p(y 1,...,y n ) karkare, CSE, IITK/B CS618 3/10

11 Non standard Types s Symbols karkare, CSE, IITK/B CS618 4/10

12 Non standard Types s Symbols karkare, CSE, IITK/B CS618 4/10

13 Non standard Types s Symbols τ Locations ::= (ϕ, α) karkare, CSE, IITK/B CS618 4/10

14 Non standard Types s Symbols τ Locations ::= (ϕ, α) ϕ Ids ::= {s 1,...,s n } karkare, CSE, IITK/B CS618 4/10

15 Non standard Types s Symbols τ Locations ::= (ϕ, α) ϕ Ids ::= {s 1,...,s n } α Values ::= ptr(τ) karkare, CSE, IITK/B CS618 4/10

16 Non standard Types s Symbols τ Locations ::= (ϕ, α) ϕ Ids ::= {s 1,...,s n } α Values ::= ptr(τ) A denotes type environment. karkare, CSE, IITK/B CS618 4/10

17 Partial Order α 1 α 2 (α 1 = ) (α 1 = α 2 ) karkare, CSE, IITK/B CS618 5/10

18 : Typing Rules A x : (ϕ,α) A y : (ϕ,α ) α α A welltyped(x = y) karkare, CSE, IITK/B CS618 6/10

19 : Typing Rules A x : (ϕ,α) A y : (ϕ,α ) α α A welltyped(x = y) A x : (ϕ,α) A y : τ ptr(τ) α A welltyped(x = &y) karkare, CSE, IITK/B CS618 6/10

20 : Typing Rules A x : (ϕ,α) A y : (ϕ,α ) α α A welltyped(x = y) A x : (ϕ,α) A y : τ ptr(τ) α A welltyped(x = &y) A x : (ϕ,α) A y : (ϕ, ptr(ϕ,α )) α α A welltyped(x = y) karkare, CSE, IITK/B CS618 6/10

21 : Typing Rules A x : (ϕ,α) A y : (ϕ,α ) α α A welltyped(x = y) A x : (ϕ,α) A y : τ ptr(τ) α A welltyped(x = &y) A x : (ϕ,α) A y : (ϕ, ptr(ϕ,α )) α α A welltyped(x = y) A x : (ϕ, ptr(ϕ,α )) A y : (ϕ,α ) α α A welltyped( x = y) karkare, CSE, IITK/B CS618 6/10

22 : Typing Rules A x : (ϕ,α) A y : (ϕ,α ) α α A welltyped(x = y) A x : (ϕ,α) A y : τ ptr(τ) α A welltyped(x = &y) A x : (ϕ,α) A y : (ϕ, ptr(ϕ,α )) α α A welltyped(x = y) A x : (ϕ, ptr(ϕ,α )) A y : (ϕ,α ) α α A welltyped( x = y) A x : τ A welltyped(x = allocate(y)) karkare, CSE, IITK/B CS618 6/10

23 Function Definitions karkare, CSE, IITK/B CS618 7/10

24 Function Definitions Need a new type value: (τ 1...τ n ) τ karkare, CSE, IITK/B CS618 7/10

25 Function Definitions Need a new type value: (τ 1...τ n ) τ karkare, CSE, IITK/B CS618 7/10

26 Function Definitions Need a new type value: (τ 1...τ n ) τ A x : (τ 1...τ n ) τ karkare, CSE, IITK/B CS618 7/10

27 Function Definitions Need a new type value: (τ 1...τ n ) τ A x : (τ 1...τ n ) τ i {1...n}.A f i : τ i karkare, CSE, IITK/B CS618 7/10

28 Function Definitions Need a new type value: (τ 1...τ n ) τ A x : (τ 1...τ n ) τ i {1...n}.A f i : τ i A r : τ karkare, CSE, IITK/B CS618 7/10

29 Function Definitions Need a new type value: (τ 1...τ n ) τ A x : (τ 1...τ n ) τ i {1...n}.A f i : τ i A r : τ s S.A welltyped(s) karkare, CSE, IITK/B CS618 7/10

30 Function Definitions Need a new type value: (τ 1...τ n ) τ A x : (τ 1...τ n ) τ i {1...n}.A f i : τ i A r : τ s S.A welltyped(s) A welltyped(x = fun(f 1,...,f n ) returns r in S ) karkare, CSE, IITK/B CS618 7/10

31 Function Calls A x : τ τ = (ϕ,α) karkare, CSE, IITK/B CS618 8/10

32 Function Calls A x : τ τ = (ϕ,α) karkare, CSE, IITK/B CS618 8/10

33 Function Calls A x : τ τ = (ϕ,α) A p : (τ 1...τ n ) τ τ i = (ϕ i,α i ) karkare, CSE, IITK/B CS618 8/10

34 Function Calls A x : τ τ = (ϕ,α) A p : (τ 1...τ n ) τ τ i = (ϕ i,α i ) i {1...n}.A y i : τ i τ i = (ϕ i,α i ) karkare, CSE, IITK/B CS618 8/10

35 Function Calls A x : τ τ = (ϕ,α) A p : (τ 1...τ n ) τ τ i = (ϕ i,α i ) i {1...n}.A y i : τ i τ i = (ϕ i,α i ) α i α i α α karkare, CSE, IITK/B CS618 8/10

36 Function Calls A x : τ τ = (ϕ,α) A p : (τ 1...τ n ) τ τ i = (ϕ i,α i ) i {1...n}.A y i : τ i τ i = (ϕ i,α i ) α i α i α α A welltyped(x = p(y 1,...,y n )) karkare, CSE, IITK/B CS618 8/10

37 Manuvir Das s One-level Flow-based Analysis α 1 α 2 ptr(τ 1 ) ptr(τ 2 ) karkare, CSE, IITK/B CS618 9/10

38 Manuvir Das s One-level Flow-based Analysis α 1 α 2 ptr(τ 1 ) ptr(τ 2 ) ptr((ϕ,α )) ptr((ϕ,α)) karkare, CSE, IITK/B CS618 9/10

39 Manuvir Das s One-level Flow-based Analysis α 1 α 2 ptr(τ 1 ) ptr(τ 2 ) ptr((ϕ,α )) ptr((ϕ,α)) (ϕ ϕ) (α = α) karkare, CSE, IITK/B CS618 9/10

40 One-level Flow-based Analysis Replace by in Steensgaard s analysis karkare, CSE, IITK/B CS618 10/10

41 One-level Flow-based Analysis Replace by in Steensgaard s analysis Keeps top level pointees separate! karkare, CSE, IITK/B CS618 10/10