Coq GC provides a formal specification and proof of a garbage collector in the Coq proof assistant. It defines: 1. Mark and sweep phases to mark reachable data and collect unreachable data 2. Proofs that the mark and sweep phases individually and the full GC preserve a safety property and mark all reachable data 3. An implementation of the GC using Coq's specification language to formally define the data structures and algorithms

1. Coq GC
id:mzp
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2. • :
• http://twitter.com/mzp
• http://d.hatena.ne.jp/mzp/
• :
• Coq
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3. Coq
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4. Coq
•
•
• OCaml Haskell
• http://coq.inria.fr
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5. Coq
• 1. Coq
• 2. ” ”
• 3. OCaml Haskell
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6. GC
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7. “ ”GC ?
• GC ” ”
•
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8. 1.
Definition mark_phase {A : Type} (dec : x_dec A) (m : Mem) :=
mkMem A (nodes m)
(roots m) closuresM :
(frees m)
(fun x => if In_dec dec x (closuresM dec m) then
Marked
else Marked
Unmarked)
(next m). Unmarked
Definition sweep_phase {A : Type} (dec : x_dec A) (m : Mem) : Mem :=
let
unmarked := filter_dec
(fun n => mark_dec (GC.marker m n) Unmarked) @@
nodes m
in
mkMem A (nodes m)
(roots m)
(union dec (frees m) unmarked) Unmarked
(fun _ => Unmarked)
(next m).
Definition gc {A : Type} (dec : x_dec A) (m : Mem) : Mem := gc mark_phase
sweep_phase dec (mark_phase dec m). sweep_phase
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9. 2.
Safety:
Lemma SweepPhase_Safety : forall A (dec : x_dec A) (m1 m2 :
Mem (A:=A)),
SweepPhase dec m1 m2 -> Safety dec m1 ->
MarksAll dec m1 -> Safety dec m2. Sweep Safety
Proof.
(snip)
Qed.
Lemma MarkPhase_Safety : forall A (dec : x_dec A) (m1 m2 : Mem
(A:=A)),
MarkPhase dec m1 m2 -> Safety dec m1 -> Safety dec m2 / Mark Safety
MarksAll dec m2.
Proof.
(snip)
Qed.
Theorem GC_Safety: forall A (dec : x_dec A) (m1 m2 : Mem
(A:=A)), GC Safety
GC dec m1 m2 -> Safety dec m1 -> Safety dec m2.
Proof.
(snip)
Qed.
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10. 3.
c b
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11. ...
• github
• http://github.com/mzp/GC
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