1. Coq GC
id:mzp
2010-08-08 GC
1

2. • :
• http://twitter.com/mzp
• http://d.hatena.ne.jp/mzp/
• : SE
• Coq
2

3. :
GC
•
• :
• :
2010(c) nari3
3

4. 4

5. 2010(c) nari3
5

6. M&S
•
•
•
6

7. Coq
7

8. Coq
•
•
•
8

9. Coq (1)
•
• OCaml,Haskell,Scheme
•
9

10. Coq (2)
•
• Twitter reply
• Coq 20
10

11. • GC
• (Safety)[1]
[1]Burdy Gemplus Avenue , L. Burdy “B vs. Coq to prove
a Garbage Collector” 2001
11

12. •
•
• “ ”
Record Mem {A : Type} :=
mkMem {
nodes : set A;
roots : set A;
frees : set A;
next : A -> option A;
marker : A -> mark;
}.
12

13. GC
•
•
:
(* m1 m2 *)
Definition MarkPhase (m1 m2 : Mem) : Prop :=
roots m1 = roots m2 ∧ nodes m1 = nodes m2 ∧
frees m1 = frees m2 ∧ next m1 = next m2 ∧
Included (closuresM m2) (marksM Marked m2).
(* ⊆ *)
:
( )
13

14. •
•
Safety
Lemma MarkPhase_Safety:∀(m1 m2: Mem),
MarkPhase m1 m2 -> (* m1 m2 *)
Safety m1 -> (* m1 Safety *)
Safety m2 ∧ MarksAll m2. (* m2 Safety *)
Safety ( )
14

15. •
• OCaml
Definition mark_phase (m : Mem) : Mem :=
mkMem A (nodes m) (roots m)(frees m)
(fun x =>
if In_dec x (closuresM m) then
Marked
else
Unmarked)
(next m).
( )
15

16. •
•
Lemma mark_phase_correct: ∀ m1 m2,
m2 = mark_phase m1 ->
MarkPhase m1 m2.
( )
16

17. • OCaml
• OCaml
• GC
GC GC
17

18. ...
• Coq - Coq
• 8/29 13:00 @
• http://atnd.org/events/6022
18

19. •
• Burdy Gemplus Avenue , L. Burdy “B vs.
Coq to prove a Garbage Collector” 2001
19