AbstractÐThis paper investigates temporal changes of topological relationships and thereby integrates two important research areas: First, two-dimensional topological relationships that have been investigated quite intensively and, second, the change of spatial information over time. We investigate spatio-temporal predicates, which describe developments of well-known spatial topological relationships. A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary spatial predicates and sequential composition. We compare our framework with two other possible approaches: one is based on the observation that spatio-temporal objects correspond to three-dimensional spatial objects for which existing topological predicates can be exploited. The other approach is to consider possible transitions between spatial configurations. These considerations help to identify a canonical set of spatio-temporal predicates. Index TermsÐTime in geographic information, spatio-temporal data types, representation of spatio-temporal objects, changes of spatial predicates, developments of spatial objects. 1

Abstract. We introduce a handful of software design patterns for functional logic languages. Following usual approaches, for each pattern we propose a name and we describe its intent, applicability, structure, consequences, etc. Our patterns deal with data type construction, identifier declarations, mappings, search, nondeterminism and other fundamental aspects of the design and implementation of programs. We present some problems and we show fragments of programs that solve these problems using our patterns. The programming language of our examples is Curry. The complete programs are available on-line. 1

The effective use of visual languages requires a precise understanding of their meaning. Moreover, it is impossible to prove properties of visual languages like soundness of transformation rules or correctness results without having a formal language definition. Although this sounds obvious, it is surprising that only little work has been done about the semantics of visual languages, and even worse, there is no general framework available for the semantics specification of different visual languages. We present such a framework that is based on a rather general notion of abstract visual syntax. This framework allows a logical as well as a denotational approach to visual semantics, and it facilitates the formal reasoning about visual languages syntax and semantics for the visual languages VEX, Show and Tell, and Euler Circles. We demonstrate the semantics in action by proving a rule for visual reasoning with Euler Circles and by showing the correctness of a Show and Tell program.

Abstract. Although maps and partitions are ubiquitous in geographical information systems and spatial databases, there is only little work investigating their foundations. We give a rigorous definition for spatial partitions and propose partitions as a generic spatial data type that can be used to model arbitrary maps and to support spatial analysis. We identify a set of three powerful operations on partitions and show that the type of partitions is closed under them. These basic operators are sufficient to express all known application-specific operations. Moreover, many map operations will be considerably generalized in our framework. We also indicate that partitions can be effectively used as a meta-model to describe other spatial data types. 1

. Active patterns apply preprocessing functions to data type values before they are matched. This is of use for unfree data types where more than one representation exists for an abstract value: in many cases there is a specific representation for which function definitions become very simple, and active patterns just allow to assume this specific representation in function definitions. We define the semantics of active patterns and describe their implementation. 1 Introduction Pattern matching is a well-appreciated concept of (functional) programming. It contributes to concise function definitions by implicitly decomposing data type values. In many cases, a large part of a function's definition is only needed to prepare for recursive application and to finally lead to a base case for which the definition itself is rather simple. Such function definitions could be simplified considerably if these preparatory computations could be factorized and given in a separate place. Recognizing t...

We propose a new style of writing graph algorithms in functional languages which is based on an alternative view of graphs as inductively defined data types. We show how this graph model can be implemented efficiently, and then we demonstrate how graph algorithms can be succinctly given by recursive function definitions based on the inductive graph view. We also regard this as a contribution to the teaching of algorithms and data structures in functional languages since we can use the functional-style graph algorithms instead of the imperative algorithms that are dominant today. Keywords: Graphs in Functional Languages, Recursive Graph Algorithms, Teaching Graph Algorithms in Functional Languages

String pattern matching in its different forms is an important topic in theoretical computer science. This thesis concentrates on the problem of regular expression matching with submatch addressing, where the position and extent of the substrings matched by given subexpressions must be provided. The algorithms in widespread use at the time either take exponential worst-case time to find a match, can handle only a subset of all regular expressions, or use space proportional to the length of the input string where constant space would suffice. This thesis proposes a new method for solving the submatch addressing problem using nondeterministic finite automata with transitions augmented by copy-on-write update operations. The resulting algorithm makes a single pass over the input string, always using time linearly proportional to the input. Space consumption depends only on the used regular expression, and not on the input string. To the author's knowledge, this is a new result. A prototype of a POSIX.2 compatible regular expression matcher using the algorithm was done. Benchmarking results indicate that the prototype compares favorably against some popular implementations. Furthermore, absence of exponential or polynomial time worst cases makes it possible to use any regular expression without performance problems, which is not the case with previous implementations or algorithms.

. Despite a lot of recent interest in purely functional data structures, for example [Ada93, Oka95, BO96, Oka96, OB97, Erw97], few have been benchmarked. Of these, even fewer have their performance qualified by how they are used. But how a data structure is used can significantly affect performance. This paper makes three original contributions. (1) We present an algorithm for generating a benchmark according to a given use of data structure. (2) We compare use of an automated tool based on this algorithm, with the traditional technique of hand-picked benchmarks, by benchmarking six implementations of random-access list using both methods. (3) We use the results of this benchmarking to present a decision tree for the choice of random-access list implementation, according to how the list will be used. 1 Motivation Recent years have seen renewed interest in purely functional data structures: sets [Ada93], random-access lists [Oka95], priority queues [BO96], arrays [OB97], gr...

... syntax, much like it is often done for textual languages. Here the focus is on visual programming languages; the impact on visual languages in general is not clear by now. We suggest to use unstructured labeled multi-graphs as abstract visual syntax and show how this facilitates semantics definitions and transformations of visual syntax level makes such manipulations simple and powerful. Moreover, we demonstrate that – in contrast to the traditional monolithic graph definition – an inductive view of graphs provides a very convenient way to move in a structured (and declarative) way through graphs. Again this supports the simplicity of descriptions for transformations and semantics.

Maps are a fundamental metaphor in GIS. We introduce several new operations on maps that go far beyond well-known operations like overlay or reclassification. In particular, we identify and generalize operations that are of practical interest for spatial analysis and that can be useful in many GIS applications. We give a precise definition of these operations based on a formal model of spatial partitions. This provides a theoretical foundation for maps which also serves as a specification for implementations.