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A Spatial Logic for Concurrency (Part II)
 IN CONCUR2002: CONCURRENCY THEORY (13TH INTERNATIONAL CONFERENCE), LECTURE NOTES IN COMPUTER SCIENCE
, 1998
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Logics for unranked trees: an overview
 Logical Methods in Computer Science 2, Issue 3, Paper 2
, 2006
"... Vol. 2 (3:2) 2006, pp. 1–31 www.lmcsonline.org ..."
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Manipulating Trees with Hidden Labels
 FOSSACS'03
, 2003
"... We define an operational semantics and a type system for manipulating semistructured data that contains hidden information. The data model is simple labeled trees with a hiding operator. Data manipulation is based on pattern matching, with types that track the use of hidden labels. ..."
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Cited by 31 (4 self)
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We define an operational semantics and a type system for manipulating semistructured data that contains hidden information. The data model is simple labeled trees with a hiding operator. Data manipulation is based on pattern matching, with types that track the use of hidden labels.
TQL: A Query Language for Semistructured Data Based on the Ambient Logic
 Mathematical Structures in Computer Science
, 2003
"... this paper we present TQL, a query language for semistructured data that is based on the ambient logic ..."
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Cited by 25 (1 self)
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this paper we present TQL, a query language for semistructured data that is based on the ambient logic
Spatial Logics for Bigraphs
 In Proceedings of ICALP’05, volume 3580 of LNCS
, 2005
"... Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, picalculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper)graph for connections. With the aim of describing bigraphical structur ..."
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Cited by 21 (2 self)
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Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, picalculus, and Petri nets. Bigraphs are built orthogonally on two structures: a hierarchical place graph for locations and a link (hyper)graph for connections. With the aim of describing bigraphical structures, we introduce a general framework for logics whose terms represent arrows in monoidal categories. We then instantiate the framework to bigraphical structures and obtain a logic that is a natural composition of a place graph logic and a link graph logic. We explore the concepts of separation and sharing in these logics and we prove that they generalise some known spatial logics for trees, graphs and tree contexts. 1
Semantic subtyping with an SMT solver
, 2010
"... We study a firstorder functional language with the novel combination of the ideas of refinement type (the subset of a type to satisfy a Boolean expression) and typetest (a Boolean expression testing whether a value belongs to a type). Our core calculus can express a rich variety of typing idioms; ..."
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Cited by 20 (1 self)
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We study a firstorder functional language with the novel combination of the ideas of refinement type (the subset of a type to satisfy a Boolean expression) and typetest (a Boolean expression testing whether a value belongs to a type). Our core calculus can express a rich variety of typing idioms; for example, intersection, union, negation, singleton, nullable, variant, and algebraic types are all derivable. We formulate a semantics in which expressions denote terms, and types are interpreted as firstorder logic formulas. Subtyping is defined as valid implication between the semantics of types. The formulas are interpreted in a specific model that we axiomatize using standard firstorder theories. On this basis, we present a novel typechecking algorithm able to eliminate many dynamic tests and to detect many errors statically. The key idea is to rely on an SMT solver to compute subtyping efficiently. Moreover, interpreting types as formulas allows us to call the SMT solver at runtime to compute instances of types.
On the Boolean Algebra of Shape Analysis Constraints
, 2003
"... Shape analysis is a promising technique for statically verifying and extracting properties of programs that manipulate complex data structures. We introduce a new characterization of constraints that arise in parametric shape analysis based on manipulation of threevalued structures as dataflow fact ..."
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Cited by 18 (10 self)
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Shape analysis is a promising technique for statically verifying and extracting properties of programs that manipulate complex data structures. We introduce a new characterization of constraints that arise in parametric shape analysis based on manipulation of threevalued structures as dataflow facts. We identify an interesting syntactic class of firstorder logic formulas that captures the meaning of threevalued structures under concretization. This class is broader than previously introduced classes, allowing for a greater flexibility in the formulation of shape analysis constraints in program annotations and internal analysis representations. Threevalued structures can be viewed as one possible normal form of the formulas in our class. Moreover, we characterize the meaning of threevalued
Expressiveness and complexity of graph logic
, 2007
"... We investigate the complexity and expressive power of a spatial logic for reasoning about graphs. This logic was previously introduced by Cardelli, Gardner, and Ghelli, and provides the simplest setting in which to explore such results for spatial logics. We study several forms of the logic: the log ..."
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Cited by 17 (1 self)
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We investigate the complexity and expressive power of a spatial logic for reasoning about graphs. This logic was previously introduced by Cardelli, Gardner, and Ghelli, and provides the simplest setting in which to explore such results for spatial logics. We study several forms of the logic: the logic with and without recursion, and with either an exponential or a linear version of the basic composition operator. We study the combined complexity and the expressive power of the four combinations. We prove that, without recursion, the linear and exponential versions of the logic correspond to significant fragments of firstorder (FO) and monadic secondorder (MSO) logics; the two versions are actually equivalent to FO and MSO on graphs representing strings. However, when the two versions are enriched withstyle recursion, their expressive power is sharply increased. Both are able to express PSPACEcomplete problems, although their combined complexity and data complexity still belong to PSPACE.
A Logic You Can Count On
 In POPL 2004 – 31st Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 2004
"... We prove the decidability of the quantifierfree, static fragment of ambient logic, with composition adjunct and iteration, which corresponds to a kind of regular expression language for semistructured data. The essence of this result is a surprising connection between formulas of the ambient logic ..."
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Cited by 16 (0 self)
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We prove the decidability of the quantifierfree, static fragment of ambient logic, with composition adjunct and iteration, which corresponds to a kind of regular expression language for semistructured data. The essence of this result is a surprising connection between formulas of the ambient logic and counting constraints on (nested) vectors of integers.
Existential heap abstraction entailment is undecidable
 In 10th Annual International Static Analysis Symposium (SAS 2003
, 2003
"... Abstract. In this paper we study constraints for specifying properties of data structures consisting of linked objects allocated in the heap. Motivated by heap summary graphs in role analysis and shape analysis we introduce the notion of regular graph constraints. A regular graph constraint is a gra ..."
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Cited by 14 (7 self)
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Abstract. In this paper we study constraints for specifying properties of data structures consisting of linked objects allocated in the heap. Motivated by heap summary graphs in role analysis and shape analysis we introduce the notion of regular graph constraints. A regular graph constraint is a graph representing the heap summary; a heap satisfies a constraint if and only if the heap can be homomorphically mapped to the summary. Regular graph constraints form a very simple and natural fragment of the existential monadic secondorder logic over graphs. One of the key problems in a compositional static analysis is proving that procedure preconditions are satisfied at every call site. For role analysis, precondition checking requires determining the validity of implication, i.e., entailment of regular graph constraints. The central result of this paper is the undecidability of regular graph constraint entailment. The undecidability of the entailment problem is surprising because of the simplicity of regular graph constraints: in particular, the satisfiability of regular graph constraints is decidable. Our undecidability result implies that there is no complete algorithm for statically checking procedure preconditions or postconditions, simplifying static analysis results, or checking that given analysis results are correct. While incomplete conservative algorithms for regular graph constraint entailment checking are possible, we argue that heap specification languages should avoid secondorder existential quantification in favor of explicitly specifying a criterion for summarizing objects.