Local Reasoning about a Copying Garbage Collector

Local Reasoning about a Copying Garbage Collector (2004)

Cached

Download Links

[www.itu.dk]
[www.itu.dk]

Other Repositories/Bibliography

DBLP

by Lars Birkedal , Noah Torp-smith , John C. Reynolds

Venue:	In 31st ACM POPL
Citations:	58 - 7 self

BibTeX

@INPROCEEDINGS{Birkedal04localreasoning,
    author = {Lars Birkedal and Noah Torp-smith and John C. Reynolds},
    title = {Local Reasoning about a Copying Garbage Collector},
    booktitle = {In 31st ACM POPL},
    year = {2004},
    pages = {220--231},
    publisher = {ACM Press}
}

Years of Citing Articles

Bookmark

OpenURL

Abstract

We present a programming language, model, and logic appropriate for implementing and reasoning about a memory management system. We then state what is meant by correctness of a copying garbage collector, and employ a variant of the novel separation logics [18, 23] to formally specify partial correctness of Cheney's copying garbage collector [8]. Finally, we prove that our implementation of Cheney's algorithm meets its specification, using the logic we have given, and auxiliary variables [19].

Citations

1016	Proof-carrying code - Necula - 1997
583	Separation logic: A logic for shared mutable data structures. Symp. on Logic in - Reynolds - 1994
557	From system F to typed assembly language - Morrisett, Walker, et al. - 1999
381	Safe Kernel Extensions without Run-time Checking - Necula, Lee
287	An Axiomatic Proof Technique for Parallel Programs I - Owicki, Gries - 1976
237	H.: Local Reasoning about Programs that Alter Data Structures - O’Hearn, Reynolds, et al. - 2001
215	A nonrecursive list compacting algorithm - Cheney - 1970
213	Foundational proof-carrying code - Appel - 2001
189	On-the-fly Garbage Collection: An Exercise in Cooperation - Dijkstra, Lamport, et al. - 1978
186	Typed memory management in a calculus of capabilities - Crary, Walker, et al. - 1999
157	Alias types - Smith, Walker, et al. - 2000
124	Resources, concurrency, and local reasoning - OHearn - 2007
88	The Semantics and Proof Theory of the Logic of Bunched Implications - Pym
59	Proving pointer programs in higherorder logic - Mehta, Nipkow - 2005
47	An axiomatic approach to computer programming - Hoare - 1969
46	MM garbage collector for C - Wang - 1989
37	Algorithms for on-the-fly garbage collection - Ben-Ari - 1984
31	Local reasoning for stateful programs - Yang
29	Garbage collection for strongly-typed languages using run-time type reconstruction - Aditya, Flood, et al. - 1994
28	Implementing the call-by-value lambda-calculus using a stack of regions - Tofte, Talpin - 1994
25	A type theory for memory allocation and data layout - Petersen, Harper, et al. - 2003
23	Reasoning about hierarchical storage - Ahmed, Jia, et al. - 2003
23	A mechanically verified incremental garbage collector - Russinoff - 1994
20	Program logic and equivalence in the presence of garbage collection - Calcagno, O’Hearn, et al. - 2003
18	Compiler-directed type reconstruction for polymorphic languages - Aditya, Caro - 1993
15	An incremental garbage collection algorithm for multimutator systems - Pixley - 1988
13	Low-level linear memory management - Hawblitzel, Wei, et al. - 2004
10	Typed regions - Monnier, Shao - 2002
8	A Larch specification of copying garbage collection - Nettles - 1992
7	BI-hyperdoctrines and higher order separation logic - Biering, Birkedal, et al. - 2005
2	Local Reasoning, Separation and Aliasing. Submitted to the SPACE'04 workshop. Available at http://www.cs.mdx.ac.uk/staffpages/r bornat - Bornat
1	Correctness of a garbage collector via local reasoning - Birkedal, Torp-Smith, et al. - 2003
1	Correctness of copydag via local reasoning. Private Communication - Bornat - 2003
1	Ptr(e) ∧ (e ′ , e) ∈ r → e ∈ m (73 - PtrRg
1	Ik on the form A1 ∗· · ·∗Am. Similarly, the conclusion in the derivation has the form I ′ 1 ∧ · · · ∧ Ik ′ where I′ i are pure for i ∈ {1 - TBD, Year
1	x ↦→ y) ∗ (∃y ′ . (x, y ′ ) ∈ tail ∧ x + 4 ↦→ y ′ ))) � AUFWD, where the two implications follow from (36) and (10), respectively - head
1	The third implication is an instance of (14). For FIN, it is easiest to note that the condition scan = offset in the conclusion of the derivation above makes both of the assertions about FIN equivalent to emp. The following derivation takes care of FREE ( - Lemma
1	ϕ \ {(root, free - tail
1	ϕ † ∧ (free − 8 - head
1	ϕ † ∧ x + 4 ↦→ y ′ )) � AUFIN Here, the first implication uses (39), (51), and Lemma 3.9. The second follows from (52), and the third implication follows from purity. Finally, the last implication is an instance of the rule - tail
1	The first of these implications follows from (14), the third follows from (15), the fourth from purity, the fifth from (73), and the last follows from (80 - unknown authors
1	The first of these implications follows from (14), the second is a matter of notation. The third implication is an instance of (15), and the next comes from purity. The sixth implication in the derivation follows from (60), and the last is by (54). This s - unknown authors
1	ϕ \ {(a, free - head
1	ϕ \ {(a, free - tail
1	ϕ † ∧ x + 4 ↦→ y ′ )))) The specification step uses the rule for assignment. Like in Section 6.1 and 6.2.3, we now have to show that the pure part of I follows from the pure part I ′′ p of the conclusion I′′ in the derivation above, and that the separatin - tail
1	ϕ † ) ∧ x + 4 ↦→ y ′ )) implies and that implies ∀∗x - tail