Typing rule-based transformations over topological collections

Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits the field of application. However, as shown by Giavitto and Michel at RULE'02, case-based function definitions can be extended to more general data structures called topological collections. We show in this paper that this extension retains the benefits of the typed discipline of the functional languages. More precisely, we show that topological collections and the rule-based definition of functions associated with them fit in a polytypic extension of mini-ML where type inference is still possible

A formal support to business and architectural design for service-oriented systems

Architectural Design Rewriting (ADR) is an approach for the design of software architectures developed within Sensoria by reconciling graph transformation and process calculi techniques. The key feature that makes ADR a suitable and expressive framework is the algebraic handling of structured graphs, which improves the support for specification, analysis and verification of service-oriented architectures and applications. We show how ADR is used as a formal ground for high-level modelling languages and approaches developed within Sensoria

Polymonadic Programming

Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a -> (a -> M b) -> N b, to compose computations with three different kinds of effects, rather than just one. Polymonads subsume monads and parameterized monads, and can express other constructions, including precise type-and-effect systems and information flow tracking; more generally, polymonads correspond to Tate's productoid semantic model. We show how to equip a core language (called lambda-PM) with syntactic support for programming with polymonads. Type inference and elaboration in lambda-PM allows programmers to write polymonadic code directly in an ML-like syntax--our algorithms compute principal types and produce elaborated programs wherein the binds appear explicitly. Furthermore, we prove that the elaboration is coherent: no matter which (type-correct) binds are chosen, the elaborated program's semantics will be the same. Pleasingly, the inferred types are easy to read: the polymonad laws justify (sometimes dramatic) simplifications, but with no effect on a type's generality.Comment: In Proceedings MSFP 2014, arXiv:1406.153

Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.Comment: 96 page

Towards a Maude tool for model checking temporal graph properties

We present our prototypical tool for the verification of graph transformation systems. The major novelty of our tool is that it provides a model checker for temporal graph properties based on counterpart semantics for quantified m-calculi. Our tool can be considered as an instantiation of our approach to counterpart semantics which allows for a neat handling of creation, deletion and merging in systems with dynamic structure. Our implementation is based on the object-based machinery of Maude, which provides the basics to deal with attributed graphs. Graph transformation systems are specified with term rewrite rules. The model checker evaluates logical formulae of second-order modal m-calculus in the automatically generated CounterpartModel (a sort of unfolded graph transition system) of the graph transformation system under study. The result of evaluating a formula is a set of assignments for each state, associating node variables to actual nodes

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Arbitrary Nesting of Spatial Computations

International audienceModern programming languages allow the definition and the use of arbitrary nested data structures but this is not generally considered in unconventional programming models. In this paper, we present arbitrary nesting in MGS, a spatial comput- ing language. By considering different classes of neighborhood relationships, MGS can emulate several unconventional computing models from a programming point of view. The use of arbitrary nested spatial structures allows a hierarchical form of coupling between them. We propose an extension of the MGS pattern- matching facilities to handle directly nesting. This makes possible the straightforward emulation of a larger class of unconventional programming models

06361 Abstracts Collection -- Computing Media Languages for Space-Oriented Computation

From 03.09.06 to 08.09.06, the Dagstuhl Seminar 06361 ``Computing Media and Languages for Space-Oriented Computation\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available