Recursive graph queries are increasingly popular for extracting information from interconnected data found in various domains such as social networks, life sciences, and business analytics. Graph data often come with schema information that describe how nodes and edges are organized. We propose a type inference mechanism that enriches recursive graph queries with relevant structural information contained in a graph schema. We show that this schema information can be useful in order to improve the performance when evaluating recursive graph queries. Furthermore, we prove that the proposed method is sound and complete, ensuring that the semantics of the query is preserved during the schema-enrichment process.

Graph databases have received a lot of attention as they are particularly useful in many applications such as social networks, life sciences and the semantic web. Various languages have emerged to query graph databases, many of which embed forms of recursion which reveal essential for navigating in graphs. The relational model has benefited from a huge body of research in the last half century and that is why many graph databases rely on techniques of relational query engines. Since its introduction, the relational model has seen various attempts to extend it with recursion and it is now possible to use recursion in several SQL or Datalog based database systems. The optimization of recursive queries remains, however, a challenge. We propose mu-RA, a variation of the Relational Algebra equipped with a fixpoint operator for expressing recursive relational queries. mu-RA can notably express unions of conjunctive regular path queries. Leveraging the fact that this fixpoint operator makes recursive terms more amenable to algebraic transformations, we propose new rewrite rules. These rules makes it possible to generate new query execution plans, that cannot be obtained with previous approaches. We present the syntax and semantics of mu-RA, and the rewriting rules that we specifically devised to tackle the optimization of recursive queries. We report on practical experiments that show that the newly generated plans can provide significant performance improvements for evaluating recursive queries over graphs.

Although XQuery is a statically typed, functional query language for XML data, some of its features such as upward and horizontal XPath axes are typed imprecisely. The main reason is that while the XQuery data model allows us to navigate upwards and between siblings from a given XML node, the type model, e.g., regular tree types, can describe only the subtree structure of the given node. To alleviate this limitation, precise forward type inference systems for XQuery were recently proposed using an extended regular type language that can describe not only a given XML node but also its context. In this paper, as a different approach, we propose a novel backward type inference system for XQuery, based on a type language extended with logical formulas. Our backward type inference system provides an exact typing result for XPath axes and a sound typing result for XQuery expressions.

XQuery is a functional language dedicated to XML data querying and manipulation. As opposed to other W3C-standardized languages for XML (e.g. XSLT), it has been intended to feature strong static typing. Currently, however, some expressions of the language cannot be statically typed with any precision. We argue that this is due to a discrepancy between the semantics of the language and its type algebra: namely, the values of the language are (possibly inner) tree nodes, which may have siblings and ancestors in the data. The types on the other hand are regular tree types, as usual in the XML world: they describe sets of trees. The type associated to a node then corresponds to the subtree whose root is that node and contains no information about the rest of the data. This makes navigation expressions using `backward axes,' which return e.g. the siblings of a node, impossible to type. We discuss how to handle this discrepancy by improving the type system. We describe a logic-based language of extended types able to represent inner tree nodes and show how it can dramatically increase the precision of typing for navigation expressions. We describe how inclusion between these extended types and the classical regular tree types can be decided, allowing a hybrid system combining both type languages. The result is a net increase in precision of typing.

We present a sound and complete satisfiability-testing algorithm and its effective implementation for an alternation-free modal μ-calculus with converse, where formulas are cycle-free and are interpreted over finite ordered trees. The time complexity of the satisfiability-testing algorithm is 2 O( n ) in terms of formula size n . The algorithm is implemented using symbolic techniques (BDD). We present crucial implementation techniques and heuristics that we used to make the algorithm as fast as possible in practice. Our implementation is available online and can be used to solve logical formulas of significant size and practical value. We illustrate this in the setting of XML trees.

We consider a type algebra equipped with recursive, product, function, intersection, union, and complement types, together with type variables. We consider the subtyping relation defined by Castagna and Xu [2011] over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality and strength of our solution reside in introducing a logical modeling for the semantic subtyping framework. We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system. This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful in the context of XML.

We consider a type algebra equipped with recursive, product, function, intersection, union, and complement types together with type variables and implicit universal quantification over them. We consider the subtyping relation recently defined by Castagna and Xu over such type expressions and show how this relation can be decided in EXPTIME, answering an open question. The novelty, originality and strength of our solution reside in introducing a logical modeling for the semantic subtyping framework. We model semantic subtyping in a tree logic and use a satisfiability-testing algorithm in order to decide subtyping. We report on practical experiments made with a full implementation of the system. This provides a powerful polymorphic type system aiming at maintaining full static type-safety of functional programs that manipulate trees, even with higher-order functions, which is particularly useful in the context of XML.

Session types allow communication protocols to be specified type-theoretically so that protocol implementations can be verified by static type-checking. We extend previous work on session types for distributed object-oriented languages in three ways. (1) We attach a session type to a class definition, to specify the possible sequences of method calls. (2) We allow a session type (protocol) implementation to be modularized , i.e. partitioned into separately-callable methods. (3) We treat session-typed communication channels as objects, integrating their session types with the session types of classes. The result is an elegant unification of communication channels and their session types, distributed object-oriented programming, and a form of typestates supporting non-uniform objects, i.e. objects that dynamically change the set of available methods. We define syntax, operational semantics, a sound type system, and a correct and complete type checking algorithm for a small distributed class-based object-oriented language. Static typing guarantees that both sequences of messages on channels, and sequences of method calls on objects, conform to type-theoretic specifications, thus ensuring type-safety. The language includes expected features of session types, such as delegation, and expected features of object-oriented programming, such as encapsulation of local state. We also describe a prototype implementation as an extension of Java.

Contracts are behavioral descriptions of Web services. We devise a theory of contracts that formalizes the compatibility of a client with a service, and the safe replacement of a service with another service. The use of contracts statically ensures the successful completion of every possible interaction between compatible clients and services. The technical device that underlies the theory is the filter , which is an explicit coercion preventing some possible behaviors of services and, in doing so, make services compatible with different usage scenarios. We show that filters can be seen as proofs of a sound and complete subcontracting deduction system which simultaneously refines and extends Hennessy's classical axiomatization of the must testing preorder. The relation is decidable, and the decision algorithm is obtained via a cut-elimination process that proves the coherence of subcontracting as a logical system. Despite the richness of the technical development, the resulting approach is based on simple ideas and basic intuitions. Remarkably, its application is mostly independent of the language used to program the services or the clients. We outline the practical aspects of our theory by studying two different concrete syntaxes for contracts and applying each of them to Web services languages. We also explore implementation issues of filters and discuss the perspectives of future research this work opens.

Contracts are behavioural descriptions of Web services. We devise a theory of contracts that formalises the compatibility of a client to a service, and the safe replacement of a service with another service. The use of contracts statically ensures the successful completion of every possible interaction between compatible clients and services.