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.

this paper we present TQL, a query language for semistructured data that is based on the ambient logic

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 three-valued structures as dataflow facts. We identify an interesting syntactic class of first-order logic formulas that captures the meaning of three-valued 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. Three-valued structures can be viewed as one possible normal form of the formulas in our class. Moreover, we characterize the meaning of three-valued structures under "tight concretization". We show that the seemingly minor change from concretization to tight concretization increases the expressive power of three-valued structures in such a way that the resulting constraints are closed under all boolean operations. We call the resulting constraints boolean shape analysis constraints. The main technical contribution of this paper is a natural syntactic characterization of boolean shape analysis constraints as arbitrary boolean combinations of first-order sentences of certain form, and an algorithm for transforming such boolean combinations into the normal form that corresponds directly to three-valued structures.

Abstract. Bigraphs are emerging as an interesting model for concurrent calculi, like CCS, pi-calculus, 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

We prove the decidability of the quantifier-free, 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.

We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases. We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of first-order logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates.

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 second-order 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 second-order existential quantification in favor of explicitly specifying a criterion for summarizing objects.

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 first-order (FO) and monadic second-order (MSO) logics; the two versions are actually equivalent to FO and MSO on graphs representing strings. However, when the two versions are enriched with-style recursion, their expressive power is sharply increased. Both are able to express PSPACE-complete problems, although their combined complexity and data complexity still belong to PSPACE.

In this paper we investigate the quantifier-free fragment of the TQL logic proposed by Cardelli and Ghelli. The TQL logic, inspired from the ambient logic, is the core of a query language for semistructured data represented as unranked and unordered trees. The fragment we consider here, named STL, contains as main features spatial composition and location as well as a fixed point construct. We prove that satisfiability for STL is undecidable. We show also that STL is strictly more expressive than the Presburger monadic second-order logic (PMSO) of Seidl, Schwentick and Muscholl when interpreted over unranked and unordered edge-labelled trees. We define a class of tree automata whose transitions are conditioned by arithmetical constraints; we show then how to compute from a closed STL formula a tree automaton accepting precisely the models of the formula. Finally, still using our tree automata framework, we exhibit some syntactic restrictions over STL formulae that allow us to capture precisely the logics MSO and PMSO. 1

We study a first-order functional language with the novel combination of the ideas of refinement type (the subset of a type to satisfy a Boolean expression) and type-test (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 first-order 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 first-order theories. On this basis, we present a novel type-checking 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 run-time to compute instances of types.