A Type-Directed Negation Elimination

In the modal mu-calculus, a formula is well-formed if each recursive variable occurs underneath an even number of negations. By means of De Morgan's laws, it is easy to transform any well-formed formula into an equivalent formula without negations -- its negation normal form. Moreover, if the formula is of size n, its negation normal form of is of the same size O(n). The full modal mu-calculus and the negation normal form fragment are thus equally expressive and concise. In this paper we extend this result to the higher-order modal fixed point logic (HFL), an extension of the modal mu-calculus with higher-order recursive predicate transformers. We present a procedure that converts a formula into an equivalent formula without negations of quadratic size in the worst case and of linear size when the number of variables of the formula is fixed.Comment: In Proceedings FICS 2015, arXiv:1509.0282

A type system for components

In modern distributed systems, dynamic reconfiguration, i.e., changing at runtime the communication pattern of a program, is chal- lenging. Generally, it is difficult to guarantee that such modifications will not disrupt ongoing computations. In a previous paper, a solution to this problem was proposed by extending the object-oriented language ABS with a component model allowing the programmer to: i) perform up- dates on objects by means of communication ports and their rebinding; and ii) precisely specify when such updates can safely occur in an object by means of critical sections. However, improper rebind operations could still occur and lead to runtime errors. The present paper introduces a type system for this component model that extends the ABS type system with the notion of ports and a precise analysis that statically enforces that no object will attempt illegal rebinding

A Type Language for Calendars

Time and calendars play an important role in databases, on the Semantic Web, as well as in mobile computing. Temporal data and calendars require (specific) modeling and processing tools. CaTTS is a type language for calendar definitions using which one can model and process temporal and calendric data. CaTTS is based on a "theory reasoning" approach for efficiency reasons. This article addresses type checking temporal and calendric data and constraints. A thesis underlying CaTTS is that types and type checking are as useful and desirable with calendric data types as with other data types. Types enable (meaningful) annotation of data. Type checking enhances efficiency and consistency of programming and modeling languages like database and Web query languages

A Type System for Tom

Extending a given language with new dedicated features is a general and quite used approach to make the programming language more adapted to problems. Being closer to the application, this leads to less programming flaws and easier maintenance. But of course one would still like to perform program analysis on these kinds of extended languages, in particular type checking and inference. In this case one has to make the typing of the extended features compatible with the ones in the starting language. The Tom programming language is a typical example of such a situation as it consists of an extension of Java that adds pattern matching, more particularly associative pattern matching, and reduction strategies. This paper presents a type system with subtyping for Tom, that is compatible with Java's type system, and that performs both type checking and type inference. We propose an algorithm that checks if all patterns of a Tom program are well-typed. In addition, we propose an algorithm based on equality and subtyping constraints that infers types of variables occurring in a pattern. Both algorithms are exemplified and the proposed type system is showed to be sound and complete

Topological A-Type Models with Flux

We study deformations of the A-model in the presence of fluxes, by which we mean rank-three tensors with antisymmetrized upper/lower indices, using the AKSZ construction. Generically these are topological membrane models, and we show that the fluxes are related to deformations of the Courant bracket which generalize the twist by a closed 3-from $H$, in the sense that satisfying the AKSZ master equation implies the integrability conditions for an almost generalized complex structure with respect to the deformed Courant bracket. In addition, the master equation imposes conditions on the fluxes that generalize $dH=0$. The membrane model can be defined on a large class of $U(m)$- and $U(m) \times U(m)$-structure manifolds, including geometries inspired by $(1,1)$ supersymmetric $\sigma$-models with additional supersymmetries due to almost complex (but not necessarily complex) structures in the target space. Furthermore, we show that the model can be defined on three particular half-flat manifolds related to the Iwasawa manifold. When only $H$-flux is turned on it is possible to obtain a topological string model, which we do for the case of a Calabi-Yau with a closed 3-form turned on. The simplest deformation from the A-model is due to the $(2,0)+ (0,2)$ component of a non-trivial $b$-field. The model is generically no longer evaluated on holomorphic maps and defines new topological invariants. Deformations due to $H$-flux can be more radical, completely preventing auxiliary fields from being integrated out.Comment: 30 pages. v2: Improved Version. References added. v3: Minor changes, published in JHE