Quantitative Separation Logic and Programs with Lists

Bozga, Marius; Iosif, Radu; Perarnau, Swann

doi:10.1007/978-3-540-71070-7_4

Cited by 15 publications

(20 citation statements)

References 16 publications

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“…loop is entered ∧ϕ loop invariant holds on loop head ∧(y 6 = x 1 ) ∧ x 1 n 1 x 6 ∧ x 1 n 6 y 1 loop body ∧same y 1 ,n 1 ,n 6 ∧ same x 1 ,n 1 ,n 6 rest of the heap remains unchanged ⇒ (x 1 = null) no null-derefernce in the body ∧ϕ 6 loop invariant after executing loop body Here, ϕ 6 denotes the loop-invariant formula ϕ after executing the loop body (label L6), i.e., replacing all occurrences of x 1 , y 1 and n 1 in ϕ by x 6 , y 6 and n 6 , respectively. The formula V C loop defines a relation between three states: on entry to the procedure, at the beginning of a loop iteration and at the end of a loop iteration.…”

Section: Fig 2 Reversementioning

confidence: 99%

A logic of reachable patterns in linked data-structures

Yorsh¹,

Rabinovich²,

Sagiv³

et al. 2007

The Journal of Logic and Algebraic Programming

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We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the neighborhood of a node that is reachable via a regular expression from a designated node. The logic is closed under boolean operations (entailment, negation) and has a finite model property. The key technical result is the proof of decidability. We show how to express precondition, postconditions, and loop invariants for some interesting programs. It is also possible to express properties such as disjointness of data-structures, and low-level heap mutations. Moreover, our logic can express properties of arbitrary data-structures and of an arbitrary number of pointer fields. The latter provides a way to naturally specify postconditions that relate the fields on entry to a procedure to the fields on exit. Therefore, it is possible to use the logic to automatically prove partial correctness of programs performing low-level heap mutations.

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Section: Fig 2 Reversementioning

confidence: 99%

A logic of reachable patterns in linked data-structures

Yorsh¹,

Rabinovich²,

Sagiv³

et al. 2007

The Journal of Logic and Algebraic Programming

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“…In general, the techniques used in proving decidability of Separation Logic are either proof-based ( [16,2]), or model-based ( [5,8]). It is well-known that automata theory, through various automata-logics connections, provides a unifying framework for proving decidability of various logics, such as (W)SkS, Presburger Arithmetic or MSO over certain classes of graphs.…”

Section: Introductionmentioning

confidence: 99%

The Tree Width of Separation Logic with Recursive Definitions

Iosif¹,

Rogalewicz²,

Šimáček³

2013

Lecture Notes in Computer Science

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182

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International audienceSeparation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current results report on techniques to decide satisfiability and validity of entail-ments for Separation Logic(s) over lists (possibly with data). In this paper we establish a more general decidability result. We prove that any Separation Logic formula using rather general recursively defined predicates is decidable for satis-fiability, and moreover, entailments between such formulae are decidable for validity. These predicates are general enough to define (doubly-) linked lists, trees, and structures more general than trees, such as trees whose leaves are chained in a list. The decidability proofs are by reduction to decidability of Monadic Second Order Logic on graphs with bounded tree width

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“…However, [3] gives a small decidable fragment of separation logic on lists which has been further extended in [11] to include a restricted form of arithmetic. Symbolic execution with separation logic has been used in [4,5,8] to prove structural specifications for various list and tree programs.…”

Section: Related Workmentioning

confidence: 99%

Natural proofs for structure, data, and separation

Qiu

Garg

Ștefănescu

et al. 2013

Proceedings of the 34th ACM SIGPLAN Conference on Programming Language Design and Implementation

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We propose natural proofs for reasoning with programs that manipulate data-structures against specifications that describe the structure of the heap, the data stored within it, and separation and framing of sub-structures. Natural proofs are a subclass of proofs that are amenable to completely automated reasoning, that provide sound but incomplete procedures, and that capture common reasoning tactics in program verification. We develop a dialect of separation logic over heaps, called Dryad, with recursive definitions that avoids explicit quantification. We develop ways to reason with heaplets using classical logic over the theory of sets, and develop natural proofs for reasoning using proof tactics involving disciplined unfoldings and formula abstractions. Natural proofs are encoded into decidable theories of first-order logic so as to be discharged using SMT solvers.We also implement the technique and show that a large class of more than 100 correct programs that manipulate data-structures are amenable to full functional correctness using the proposed natural proof method. These programs are drawn from a variety of sources including standard data-structures, the Schorr-Waite algorithm for garbage collection, a large number of low-level C routines from the Glib library and OpenBSD library, the Linux kernel, and routines from a secure verified OS-browser project. Our work is the first that we know of that can handle such a wide range of full functional verification properties of heaps automatically, given pre/post and loop invariant annotations. We believe that this work paves the way for deductive verification technology to be used by programmers who do not (and need not) understand the internals of the underlying logic solvers, significantly increasing their applicability in building reliable systems.

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Quantitative Separation Logic and Programs with Lists

Cited by 15 publications

References 16 publications

A logic of reachable patterns in linked data-structures

A logic of reachable patterns in linked data-structures

The Tree Width of Separation Logic with Recursive Definitions

Natural proofs for structure, data, and separation

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