An Analysis of Permutations in Arrays

Perrelle, Valentin; Halbwachs, Nicolas

doi:10.1007/978-3-642-11319-2_21

Cited by 10 publications

(9 citation statements)

References 29 publications

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“…A possible solution could be to allow abstract attributes that extract additional information about the abstracted structures [10,37,49]. For P7, a generalization of the multiset abstraction [36] for data types, could be useful to track e.g., the auxiliary statement count, and show that they decrease using multiset-ordering [22] like in term rewriting. Other techniques [4,13,51] support inferring inductive relational properties for general data-typese.g, binary tree property-but require a pre-specified structure to indicate the places where refinement can happen.…”

Section: Related Workmentioning

confidence: 99%

Verification of high-level transformations with inductive refinement types

Al-Sibahi

Jensen

Dimovski

et al. 2018

Proceedings of the 17th ACM SIGPLAN International Conference on Generative Programming: Concepts and Experiences

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High-level transformation languages like Rascal include expressive features for manipulating large abstract syntax trees: first-class traversals, expressive pattern matching, backtracking and generalized iterators. We present the design and implementation of an abstract interpretation tool, Rabit, for verifying inductive type and shape properties for transformations written in such languages. We describe how to perform abstract interpretation based on operational semantics, specifically focusing on the challenges arising when analyzing the expressive traversals and pattern matching. Finally, we evaluate Rabit on a series of transformations (normalization, desugaring, refactoring, code generators, type inference, etc.) showing that we can effectively verify stated properties.

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Section: Related Workmentioning

confidence: 99%

Verification of high-level transformations with inductive refinement types

Al-Sibahi

Jensen

Dimovski

et al. 2018

Proceedings of the 17th ACM SIGPLAN International Conference on Generative Programming: Concepts and Experiences

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“…The universal quantification is usually over all nodes in a network, or all the elements in the heap or the array (e.g. [35] for heaps and [14,34] for arrays). Furthermore, linked-lists can be formulated using a theory of list reachability which allows deciding inductiveness of universal invariants using effectively proportional logic (EPR) [25].…”

Section: Motivation and Backgroundmentioning

confidence: 99%

Decidability of inferring inductive invariants

et al. 2016

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Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safety invariant for the system. A key ingredient in this approach is coming up with the inductive invariant, which is known as invariant inference. This is a major difficulty, and it is often left for humans or addressed by sound but incomplete abstract interpretation. This paper is motivated by the problem of inductive invariants in shape analysis and in distributed protocols. This paper approaches the general problem of inferring firstorder inductive invariants by restricting the language L of candidate invariants. Notice that the problem of invariant inference in a restricted language L differs from the safety problem, since a system may be safe and still not have any inductive invariant in L that proves safety. Clearly, if L is finite (and if testing an inductive invariant is decidable), then inferring invariants in L is decidable. This paper presents some interesting cases when inferring inductive invariants in L is decidable even when L is an infinite language of universal formulas. Decidability is obtained by restricting L and defining a suitable well-quasi-order on the state space. We also present some undecidability results that show that our restrictions are necessary. We further present a framework for systematically constructing infinite languages while keeping the invariant inference problem decidable. We illustrate our approach by showing the decidability of inferring invariants for programs manipulating linked-lists, and for distributed protocols.

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“…The generated invariants are either universally-quantified firstorder formulas [2,13,15,20] or multiset constraints [2,21].…”

Section: Related Workmentioning

confidence: 99%

On inter-procedural analysis of programs with lists and data

et al. 2011

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We address the problem of automatic synthesis of assertions on sequential programs with singly-linked lists containing data over infinite domains such as integers or reals. Our approach is based on an accurate abstract inter-procedural analysis. Program configurations are represented by graphs where nodes represent list segments without sharing. The data in these list segments are characterized by constraints in abstract domains. We consider a domain where constraints are in a universally quantified fragment of the first-order logic over sequences, as well as a domain constraining the multisets of data in sequences.Our analysis computes the effect of each procedure in a local manner, by considering only the reachable part of the heap from its actual parameters. In order to avoid losses of information, we introduce a mechanism based on unfolding/folding operations allowing to strengthen the analysis in the domain of first-order formulas by the analysis in the multisets domain.The same mechanism is used for strengthening the sound (but incomplete) entailment operator of the domain of first-order formulas. We have implemented our techniques in a prototype tool and we have shown that our approach is powerful enough for automatic (1) generation of non-trivial procedure summaries, (2) pre/postcondition reasoning, and (3) procedure equivalence checking. 1 typedef struct list { 2 int data; 3 struct list *next; 4 } list ; 5 list * quicksort(list *a){ 6 list *left,*right,*pivot,*res,*start; 7 int d; 8 if (a == NULL || a->next == NULL) 9 res = clone(a); 10 else { 11 d = a->data; 12 pivot = create(1); // list of length 1 13 pivot->data = d; 14 start = a->next; 15 split(start,d,&left,&right); 16 left = quicksort(left); 17 right = quicksort(right); 18 res = concat(left,pivot,right); } 19 return res; } Figure 1. The quicksort algorithm on singly-linked lists.

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An Analysis of Permutations in Arrays

Cited by 10 publications

References 29 publications

Verification of high-level transformations with inductive refinement types

Verification of high-level transformations with inductive refinement types

Decidability of inferring inductive invariants

On inter-procedural analysis of programs with lists and data

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