Constraint Handling Rules with Binders, Patterns and Generic Quantification

Constraint Handling Rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the term syntax of constraints is replaced by $\lambda$-tree syntax, in which binding is explicit; and a new $\nabla$ generic quantifier is introduced, which is used to create new fresh constants.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no PDF figure

Initial Algebra Semantics for Cyclic Sharing Tree Structures

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural induction and structural recursion. However, for graphs or "tree-like" structures - trees involving cycles and sharing - it remains unclear what kind of inductive structures exists and how we can faithfully assign a term representation of them. In this paper we propose a simple term syntax for cyclic sharing structures that admits structural induction and recursion principles. We show that the obtained syntax is directly usable in the functional language Haskell and the proof assistant Agda, as well as ordinary data structures such as lists and trees. To achieve this goal, we use a categorical approach to initial algebra semantics in a presheaf category. That approach follows the line of Fiore, Plotkin and Turi's models of abstract syntax with variable binding

Variable binding, symmetric monoidal closed theories, and bigraphs

This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may express binding operations, in a way reminiscent from higher-order abstract syntax. This theory generates an SMC category S(T) whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, which are linear w.r.t. processes. This leads to an alternative category of bigraphs, which we compare to the original.Comment: An introduction to two more technical previous preprints. Accepted at Concur '0

On generic context lemmas for lambda calculi with sharing

This paper proves several generic variants of context lemmas and thus contributes to improving the tools to develop observational semantics that is based on a reduction semantics for a language. The context lemmas are provided for may- as well as two variants of mustconvergence and a wide class of extended lambda calculi, which satisfy certain abstract conditions. The calculi must have a form of node sharing, e.g. plain beta reduction is not permitted. There are two variants, weakly sharing calculi, where the beta-reduction is only permitted for arguments that are variables, and strongly sharing calculi, which roughly correspond to call-by-need calculi, where beta-reduction is completely replaced by a sharing variant. The calculi must obey three abstract assumptions, which are in general easily recognizable given the syntax and the reduction rules. The generic context lemmas have as instances several context lemmas already proved in the literature for specific lambda calculi with sharing. The scope of the generic context lemmas comprises not only call-by-need calculi, but also call-by-value calculi with a form of built-in sharing. Investigations in other, new variants of extended lambda-calculi with sharing, where the language or the reduction rules and/or strategy varies, will be simplified by our result, since specific context lemmas are immediately derivable from the generic context lemma, provided our abstract conditions are met

Discovering, quantifying, and displaying attacks

In the design of software and cyber-physical systems, security is often perceived as a qualitative need, but can only be attained quantitatively. Especially when distributed components are involved, it is hard to predict and confront all possible attacks. A main challenge in the development of complex systems is therefore to discover attacks, quantify them to comprehend their likelihood, and communicate them to non-experts for facilitating the decision process. To address this three-sided challenge we propose a protection analysis over the Quality Calculus that (i) computes all the sets of data required by an attacker to reach a given location in a system, (ii) determines the cheapest set of such attacks for a given notion of cost, and (iii) derives an attack tree that displays the attacks graphically. The protection analysis is first developed in a qualitative setting, and then extended to quantitative settings following an approach applicable to a great many contexts. The quantitative formulation is implemented as an optimisation problem encoded into Satisfiability Modulo Theories, allowing us to deal with complex cost structures. The usefulness of the framework is demonstrated on a national-scale authentication system, studied through a Java implementation of the framework.Comment: LMCS SPECIAL ISSUE FORTE 201