Mechanizing coinduction and corecursion in higher-order logic

A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive data types, such as lazy lists. Well-founded recursion expresses recursive functions over inductive data types; corecursion expresses functions that yield elements of coinductive data types. The theory rests on a traditional formalization of infinite trees. The theory is intended for use in specification and verification. It supports reasoning about a wide range of computable functions, but it does not formalize their operational semantics and can express noncomputable functions also. The theory is illustrated using finite and infinite lists. Corecursion expresses functions over infinite lists; coinduction reasons about such functions

Secure Querying of Recursive XML Views: A Standard XPath-based Technique

Most state-of-the art approaches for securing XML documents allow users to access data only through authorized views defined by annotating an XML grammar (e.g. DTD) with a collection of XPath expressions. To prevent improper disclosure of confidential information, user queries posed on these views need to be rewritten into equivalent queries on the underlying documents. This rewriting enables us to avoid the overhead of view materialization and maintenance. A major concern here is that query rewriting for recursive XML views is still an open problem. To overcome this problem, some works have been proposed to translate XPath queries into non-standard ones, called Regular XPath queries. However, query rewriting under Regular XPath can be of exponential size as it relies on automaton model. Most importantly, Regular XPath remains a theoretical achievement. Indeed, it is not commonly used in practice as translation and evaluation tools are not available. In this paper, we show that query rewriting is always possible for recursive XML views using only the expressive power of the standard XPath. We investigate the extension of the downward class of XPath, composed only by child and descendant axes, with some axes and operators and we propose a general approach to rewrite queries under recursive XML views. Unlike Regular XPath-based works, we provide a rewriting algorithm which processes the query only over the annotated DTD grammar and which can run in linear time in the size of the query. An experimental evaluation demonstrates that our algorithm is efficient and scales well.Comment: (2011

Synthesis of Recursive ADT Transformations from Reusable Templates

Recent work has proposed a promising approach to improving scalability of program synthesis by allowing the user to supply a syntactic template that constrains the space of potential programs. Unfortunately, creating templates often requires nontrivial effort from the user, which impedes the usability of the synthesizer. We present a solution to this problem in the context of recursive transformations on algebraic data-types. Our approach relies on polymorphic synthesis constructs: a small but powerful extension to the language of syntactic templates, which makes it possible to define a program space in a concise and highly reusable manner, while at the same time retains the scalability benefits of conventional templates. This approach enables end-users to reuse predefined templates from a library for a wide variety of problems with little effort. The paper also describes a novel optimization that further improves the performance and scalability of the system. We evaluated the approach on a set of benchmarks that most notably includes desugaring functions for lambda calculus, which force the synthesizer to discover Church encodings for pairs and boolean operations

A General Approach for Securely Querying and Updating XML Data

Over the past years several works have proposed access control models for XML data where only read-access rights over non-recursive DTDs are considered. A few amount of works have studied the access rights for updates. In this paper, we present a general model for specifying access control on XML data in the presence of update operations of W3C XQuery Update Facility. Our approach for enforcing such updates specifications is based on the notion of query rewriting where each update operation defined over arbitrary DTD (recursive or not) is rewritten to a safe one in order to be evaluated only over XML data which can be updated by the user. We investigate in the second part of this report the secure of XML updating in the presence of read-access rights specified by a security views. For an XML document, a security view represents for each class of users all and only the parts of the document these users are able to see. We show that an update operation defined over a security view can cause disclosure of sensitive data hidden by this view if it is not thoroughly rewritten with respect to both read and update access rights. Finally, we propose a security view based approach for securely updating XML in order to preserve the confidentiality and integrity of XML data.Comment: No. RR-7870 (2012

Foundational Extensible Corecursion

This paper presents a formalized framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under well-behaved operations, including constructors. Corecursive functions that are well behaved can be registered as such, thereby increasing the corecursor's expressiveness. The metatheory is formalized in the Isabelle proof assistant and forms the core of a prototype tool. The corecursor is derived from first principles, without requiring new axioms or extensions of the logic

A Refinement Calculus for Logic Programs

Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic programming language, including executable constructs such as sequential conjunction, disjunction, and existential quantification, as well as specification constructs such as general predicates, assumptions and universal quantification. A declarative semantics is defined for this wide-spectrum language based on executions. Executions are partial functions from states to states, where a state is represented as a set of bindings. The semantics is used to define the meaning of programs and specifications, including parameters and recursion. To complete the calculus, a notion of correctness-preserving refinement over programs in the wide-spectrum language is defined and refinement laws for developing programs are introduced. The refinement calculus is illustrated using example derivations and prototype tool support is discussed.Comment: 36 pages, 3 figures. To be published in Theory and Practice of Logic Programming (TPLP

Labeling Workflow Views with Fine-Grained Dependencies

This paper considers the problem of efficiently answering reachability queries over views of provenance graphs, derived from executions of workflows that may include recursion. Such views include composite modules and model fine-grained dependencies between module inputs and outputs. A novel view-adaptive dynamic labeling scheme is developed for efficient query evaluation, in which view specifications are labeled statically (i.e. as they are created) and data items are labeled dynamically as they are produced during a workflow execution. Although the combination of fine-grained dependencies and recursive workflows entail, in general, long (linear-size) data labels, we show that for a large natural class of workflows and views, labels are compact (logarithmic-size) and reachability queries can be evaluated in constant time. Experimental results demonstrate the benefit of this approach over the state-of-the-art technique when applied for labeling multiple views.Comment: VLDB201