... Initial computability, algebraic specifications, and partial algebras. Author: Horst Reichel, Publication: · Book, Initial computability, algebraic specifications, and partial algebras. Oxford University Press, Inc. New York, NY, USA...
more... Initial computability, algebraic specifications, and partial algebras. Author: Horst Reichel, Publication: · Book, Initial computability, algebraic specifications, and partial algebras. Oxford University Press, Inc. New York, NY, USA ©1987 ISBN:0-198-53806-5. 1987 Book. Bibliometrics ...
Since the fundamental work of Lawvere in 1963 [7] it is common to understand a theory as category with additional structure, to understand a model of the theory as a functor preserving the additional structure, and to represent...
moreSince the fundamental work of Lawvere in 1963 [7] it is common to understand a theory as category with additional structure, to understand a model of the theory as a functor preserving the additional structure, and to represent homomorphisms by natural transformations. The resulting model category becomes a suitable subcategory of a functor category. Many different classes of mathematical structures have been described and investigated in this way. The aim of this paper is, to find a functorial model theory for those classes of algebras that appear naturally as semantics of algebraic specifications of parameterized data types, using initial respectively more general free functor semantics, and to extend the functorial model theory to specifications that use as well inductively defined data types as coinductively defined patterns of behavior and their systematic combinations.
Discrete time process algebra with abstraction.- A duration calculus with infinite intervals.- A delegation-based object calculus with subtyping.- Model-checking for real-time systems.- On polynomial ideals, their complexity, and...
moreDiscrete time process algebra with abstraction.- A duration calculus with infinite intervals.- A delegation-based object calculus with subtyping.- Model-checking for real-time systems.- On polynomial ideals, their complexity, and applications.- From a concurrent ?-calculus to the ?-calculus.- Rewriting regular inequalities.- A simple abstract semantics for equational theories.- Processes with multiple entries and exits.- Efficient rewriting in cograph trace monoids.- Effective category and measure in abstract complexity theory.- About planar cayley graphs.- On condorcet and median points of simple rectilinear polygons.- Fast algorithms for maintaining shortest paths in outerplanar and planar digraphs.- r-Domination problems on homogeneously orderable graphs.- Growing patterns in 1D cellular automata.- Petri nets, commutative context-free grammars, and basic parallel processes.- Implementation of a UU-algorithm for primitive recursive tree functions.- Dummy elimination: Making termination easier.- Computing Petri net languages by reductions.- Categorial graphs.- Effective systolic algorithms for gossiping in cycles and two-dimensional grids.- Restarting automata.- Optimal contiguous expression DAG evaluations.- Communication as unification in the Petri Box Calculus.- Distributed catenation and chomsky hierarchy.- The power of frequency computation.- Randomized incremental construction of simple abstract Voronoi diagrams in 3-space.- Properties of probabilistic pushdown automata.- Formal parametric equations.- PRAM's towards realistic parallelism: BRAM's.- Some results concerning two-dimensional turing machines and finite automata.- How hard is to compute the edit distance.- On the synchronization of semi-traces.- Tiling with bars and satisfaction of boolean formulas.- Axiomatizing Petri net concatenable processes.- Functional sorts in data type specifications.
... At the very beginning of research on data types one could observe a simi-lar situation. ... Dually, 〈K, η : F ⇒ J; K〉 is called an injective Kan extension if for each functor H : C1 → C and each natural transformation α : F ⇒ J; H...
more... At the very beginning of research on data types one could observe a simi-lar situation. ... Dually, 〈K, η : F ⇒ J; K〉 is called an injective Kan extension if for each functor H : C1 → C and each natural transformation α : F ⇒ J; H there is a unique natural transformation α ∗ : K ⇒ H ...
Die Objektorientierte Programmierung ist dabei, sich als eine nutzliche Methode zur Strukturierung von Programmen zu etablieren. Urn ihr Potential insbesondere bei groseren Programmen voll zur Geltung kommen zu lassen, ist es...
moreDie Objektorientierte Programmierung ist dabei, sich als eine nutzliche Methode zur Strukturierung von Programmen zu etablieren. Urn ihr Potential insbesondere bei groseren Programmen voll zur Geltung kommen zu lassen, ist es erforderlich, die Methodik und ihre Denkweisen auch in den fruhen Phasen der SW-Entwicklung einzusetzen. Es gibt auch bereits seit einiger Zeit Ansatze fur Objektorientiertes Design und Objektorientierter Analyse. Das Fachgesprach will sich mit dem Einsatz der Objektorientierung in alien Phasen der SW-Entwicklung beschaftigen. Insbesondere sind folgende Aspekte von Interesse: Berichte fuber praktische Erfahrungen mit der Objektorientierung — Einflus der Objektorientierung auf den SW-Entwicklungszyklus Einfluis der Objektorientierung auf die erstellte SW Testbarkeit von 00-SW, Starken und Schwachen von OO-Methoden und — Sprachen.
The most basic assumption of work on algebraic speciication is that software systems are modelled as many{sorted algebras, abstracting away from the concrete details of algorithms and code, and focusing on their functional behavior. This...
moreThe most basic assumption of work on algebraic speciication is that software systems are modelled as many{sorted algebras, abstracting away from the concrete details of algorithms and code, and focusing on their functional behavior. This assumption raises the question whether a software system should be speciied by a single prototype algebra or by a class of algebras with equal external behavior. What external behavior precisely means has to be deened by the semantics of the speciication language. In both cases the similarity type of the algebras, called a signature, gives some very abstract information: the names of the data types and the names, the arities, and result sorts of the operations deened by the system. A single prototype algebra has the advantage that it supplies a constructive understanding of the behavior of the speciied software system. For the description of the prototype algebra we can use very abstract mathematical terms to obtain both a precise and abstract description. But every single model has the serious disadvantage that only some properties of its external behavior are clearly visible. Some other interesting properties may be very hard to detect in the given model but much easier in another one with the same external behavior. This remains true if one considers isomorphic algebras as algebras with equal external behavior. Isomorphism is the narrowest interpretation of equal external behavior which will be discussed in the following in more detail. We compare the quality of two diierent prototype algebras considering the example of term algebras introduced in Section 2.4. The carrier jT (X)j could be deened as the least S{sorted set of words such that x 2 jT (X)j s for all s 2 S and x 2 X s , and t 1 : : :t n f 2 jT (X)j s for all f : s 1 : : : s n ! s in and t 1 2 jT (X)j s1 ; : : :; t n 2 jT (X)j sn. The interpretation of an operation name becomes now the appending of the operation name at the end of the argument sequence. This representation of terms is sometimes called posttx polish notation. This is a very 1
Die Entwicklung sicherer Software ist einerseits ein wachsendes Bedurfnis und andererseits seit vielen Jahren ein vorrangiges Ziel der Softwaretechnologie. Mit dem Fachgesprach sollen der aktuelle Stand bezuglich konzeptueller Ansatze,...
moreDie Entwicklung sicherer Software ist einerseits ein wachsendes Bedurfnis und andererseits seit vielen Jahren ein vorrangiges Ziel der Softwaretechnologie. Mit dem Fachgesprach sollen der aktuelle Stand bezuglich konzeptueller Ansatze, Tools und Entwicklungsumgebungen dargestellt, Erfahrungen bei der Anwendung von Spezifikationssprachen, mit rechnergestutzten Korrektheitsbeweisen, bei der Nutzung lauffahiger Spezifikationen u.a.m. prasentiert werden, die vorhandenen Defizite aufgezeigt und die Moglichkeiten und Voraussetzungen fur eine breite Nutzung in der kommerziellen Softwareentwicklung diskutiert werden.
. The focus of this chapter is the incremental presentation of partial firstorderlogic, seen as a powerful framework where the specification of most data typescan be directly represented in the most natural way. Both model theory and...
more. The focus of this chapter is the incremental presentation of partial firstorderlogic, seen as a powerful framework where the specification of most data typescan be directly represented in the most natural way. Both model theory and logicaldeduction are described in full detail.Alternatives to partiality, like (variants of) error algebras and order-sortednessare also discussed, showing their uses and limitations.Moreover, both
A special kind of partiality of heterogeneous algebraic structures is introduced. Every operator of a heterogeneous operator domain is associated with a set of term equations as necessary and sufficient domain condition.It is shown that...
moreA special kind of partiality of heterogeneous algebraic structures is introduced. Every operator of a heterogeneous operator domain is associated with a set of term equations as necessary and sufficient domain condition.It is shown that some kind of hierarchy condition for the system of domain equations is equivalent to the condition that every injective weak homomorphism is a strong homomorphism which is equivalent to the statement that every bijective weak homomorphism is an isomorphism.On the base of this result the notions of a quasi-variety and of a variety of equationally partial heterogeneous algebras are suggested. The class of all small categories becomes a standard example of a variety of equational partial heterogeneous algebras.