Automated Mutual Explicit Induction Proof in Separation Logic

Ta, Quang-Trung; Le, Ton Chanh; Khoo, Siau‐Cheng; Chin, Wei-Ngan

doi:10.1007/978-3-319-48989-6_40

Cited by 30 publications

(33 citation statements)

References 34 publications

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“…As of now, SSL does not allow for mutually-recursive inductive predicates. While not impossible in principle, this would require us to explore advanced techniques for inductive proofs (Ta et al 2016) and also generalize the use of tags; we plan to look into this in the future. By limiting the number of unfoldings, via O and C rules, via MaxUnfold, we circumvent a commonly known decidability problem of solving entailments in the presence of general inductive predicates (Antonopoulos et al 2014), but this also prevents some non-unreasonable and perfectly specifiable in SSL programs from being synthesized, e.g., allocating a large constant-size list.…”

Section: Limitations and Discussionmentioning

confidence: 99%

Structuring the synthesis of heap-manipulating programs

Polikarpova

Sergey

2019

Proc. ACM Program. Lang.

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This paper describes a deductive approach to synthesizing imperative programs with pointers from declarative specifications expressed in Separation Logic. Our synthesis algorithm takes as input a pair of assertions-a preand a postcondition-which describe two states of the symbolic heap, and derives a program that transforms one state into the other, guided by the shape of the heap. The program synthesis algorithm rests on the novel framework of Synthetic Separation Logic (SSL), which generalises the classical notion of heap entailment P ⊢ Q to incorporate a possibility of transforming a heap satisfying an assertion P into a heap satisfying an assertion Q. A synthesized program represents a proof term for a transforming entailment statement P Q, and the synthesis procedure corresponds to a proof search. The derived programs are, thus, correct by construction, in the sense that they satisfy the ascribed pre/postconditions, and are accompanied by complete proof derivations, which can be checked independently.We have implemented a proof search engine for SSL in a form the program synthesizer called S SL . For efficiency, the engine exploits properties of SSL rules, such as invertibility and commutativity of rule applications on separate heaps, to prune the space of derivations it has to consider. We explain and showcase the use of SSL on characteristic examples, describe the design of S SL , and report on our experience of using it to synthesize a series of benchmark programs manipulating heap-based linked data structures. Nadia Polikarpova and Ilya Sergeythe proof search is guided by a goal in ordinary logics. In this work, we make this connection explicit and employ it for efficiently synthesizing imperative programs from SL pre-and postconditions.Structuring the Synthesis of Heap-Manipulating Programs :3 (reads as "the assertion P transforms into Q via a program c"), which unifies SL entailment P ⊢ Q and verification {P} c {Q}, with the former expressible as P Q| skip.The central practical contribution is the design and implementation of S SL -a deductive synthesizer for heap-manipulating programs, based on SSL. S SL takes as its input a library of inductive predicates, a (typically empty) list of auxiliary function specifications, and an SL specification of the function to be synthesized. It returns a-possibly recursive, but loop-free-program (in a minimalistic C-like language), which provably satisfies the given specification.Our evaluation shows that S SL can synthesize all structurally-recursive benchmarks from previous work on heap-based synthesis (Qiu and Solar-Lezama 2017), without any sketches and in most cases much faster. To the best of our knowledge, it is also the first synthesizer to automatically discover the implementations of copying linked lists and trees, and flattening a tree to a list.The essence of S SL 's synthesis algorithm is a backtracking search in the space of SSL derivations. Even though the structural constraints (i.e., the shape of the heap) embodied in the synthesis rules already pru...

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Section: Limitations and Discussionmentioning

confidence: 99%

Structuring the synthesis of heap-manipulating programs

Polikarpova

Sergey

2019

Proc. ACM Program. Lang.

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“…Methodology. We compared Harrsh against Songbird [19], the winner of the SID entailment category of this year's separation logic competition, SL-COMP'18; and against Slide [11], the tool that is most closely related to our approach but that is complete only for a subclass of SL btw . Experiments were conducted using the popular benchmarking harness jmh on an Intel® Core™ i7-7500U CPU running at 2.70 GHz with a memory limit of 4 GB.…”

Section: Methodsmentioning

confidence: 99%

Effective Entailment Checking for Separation Logic with Inductive Definitions

Katelaan

Matheja

Zuleger

2019

Tools and Algorithms for the Construction and Analysis of Systems

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Symbolic-Heap Separation logic is a popular formalism for automated reasoning about heap-manipulating programs, which allows the user to give customized data structure definitions.In this paper, we give a new decidability proof for the separation logic fragment of Iosif, Rogalewicz and Simacek. We circumvent the reduction to MSO from their proof and provide a direct model-theoretic construction with elementary complexity. We implemented our approach in the Harrsh analyzer and evaluate its effectiveness. In particular, we show that Harrsh can decide the entailment problem for data structure definitions for which no previous decision procedures have been implemented.

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“…It employs mathematical induction to prove entailments involving userdefined predicates. In addition, Songbird is also equipped with powerful proof techniques, which include a mutual induction proof system [35] and a lemma synthesis framework [36].…”

Section: Songbirdmentioning

confidence: 99%

SL-COMP: Competition of Solvers for Separation Logic

Sighireanu

Pérez

Rybalchenko

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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SL-COMP aims at bringing together researchers interested on improving the state of the art of the automated deduction methods for Separation Logic (SL). The event took place twice until now and collected more than 1K problems for different fragments of SL. The input format of problems is based on the SMT-LIB format and therefore fully typed; only one new command is added to SMT-LIB's list, the command for the declaration of the heap's type. The SMT-LIB theory of SL comes with ten logics, some of them being combinations of SL with linear arithmetics. The competition's divisions are defined by the logic fragment, the kind of decision problem (satisfiability or entailment) and the presence of quantifiers. Until now, SL-COMP has been run on the StarExec platform, where the benchmark set and the binaries of participant solvers are freely available. The benchmark set is also available with the competition's documentation on a public repository in GitHub.

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Automated Mutual Explicit Induction Proof in Separation Logic

Cited by 30 publications

References 34 publications

Structuring the synthesis of heap-manipulating programs

Structuring the synthesis of heap-manipulating programs

Effective Entailment Checking for Separation Logic with Inductive Definitions

SL-COMP: Competition of Solvers for Separation Logic

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