this paper are implemented and used for some example logics and sequent calculus proof search. The core inka is implemented in Allegro Common Lisp. The interface runs on distributed Oz, which is available for Unix and Windows. As a next step we intend to integrate a logic for algorithmic function and predicate definitions as well as the methods to prove their termination as tactics. Termination proofs can be inspected and already proven lemmata can be used during the construction of termination proofs, which are the main advantages wrt. the black box implementation of these methods in the old inka system [8]. References

We propose a method for implementing behavioral interface specifications on the .NET platform. Our interface...

This paper introduces a notion of certified computation whereby an algorithm not only produces a result r for a given input x, but also proves that r is a correct result for x. This can greatly enhance the credibility of the result: if we trust the axioms and inference rules that are used in the proof, then we can be assured that r is correct. Typically, the reasoning used in a certified computation is much simpler than the computation itself. We present and analyze two examples of certifying algorithms. We have developed...

This paper presents a novel model-theoretic account of Harel, Pnueli and Shalev's original step semantics of the visual specification language Statecharts. The graphical syntax of a Statechart is read, directly and structurally, as a formula in propositional logic. This proposition captures all the logical constraints imposed by the diagram on the Statechart's semantics, i.e., the possible sets of transitions that can be taken together to perform a valid Statecharts step, and their effects on Statecharts configurations. The paper's main result shows that the correct semantics is uniquely described by the intuitionistic interpretation of Statecharts formulas, whereas the naive classical interpretation is insufficient. The advocated intuitionistic approach not only gives a correct, clear and direct logical account of Statecharts' semantics, but also permits the integration of Statecharts with formal validation tools, such as theorem provers.

Modern society has a strong need for reliable Information Technology. To warrant correct designs for hardware and software systems, there is a thorough methodology (specification, design based on subspecifications and composition of components, and correctness proofs). Because of the difficulty of making specifications and proofs, the success of this method has been only partial, mainly in the area of hardware design. Presently there is emerging a new technology: Computer Mathematics. It consists of the interactive building of definitions, statements and proofs, such that it can be checked automatically whether the definitions are well-formed and the proofs are correct. Hereby the human user provides the intelligence and the system does part of the craftsmanship. Some forms of computer mathematics is already of use for the design of hardware systems. After the technology will be mature, it may become a tool for the development of mathematics comparable to systems of computer algebra, b...

. We present a sequent calculus which allows the simultaneous elimination of multiple quantifiers. The approach is an improvement over the well-known skolemization in sequent calculus. It allows a lazy handling of instantiations and of the order of certain reductions. Simultaneous quantifier elimination is justified from a semantical as well as from a proof theoretical point of view. 1 Introduction Sequent calculi are a very common search space representation. Originally developed by Gentzen [6] they have been applied in automated deduction, in logic programming, in formal program development, and other areas. During analytic proof search formulas in a sequent are decomposed into sub-formulas in a stepwise manner. The structure of sub-formulas and of formulas which are not decomposed is preserved. The preservation of structure is especially beneficial when user interaction is required. A user can recognize structures which e.g. in the context of formal methods [7] originate from a spe...

We propose and discuss a complete sequent calculus formulation for Signed Interval Logic (SIL) with the chief purpose of improving proof support for SIL in practice. The main theoretical result is a simple characterization of the limit between decidability and undecidability of quantifier-free SIL. We present a mechanization of SIL in the generic proof assistant Isabelle and consider techniques for automated reasoning. Many of the results and ideas of this report are also applicable to traditional (non-signed) interval logic and, hence, to Duration Calculus. 1

We present an algorithm for simplifying Fitch-style natural deduction proofs in classical first-order logic. We formalize Fitch-style natural deduction as a denotational proof language, N DL, with a rigorous syntax and semantics. Based on that formalization, we define an array of simplifying transformations and show them to be terminating and to respect the formal semantics of the language. We also show that the transformations never increase the size or complexity of a deduction—in the worst case, they produce deductions of the same size and complexity as the original. We present several examples of proofs containing various types of superfluous “detours, ” and explain how our procedure eliminates them, resulting in smaller and cleaner deductions. All of the transformations are fully implemented in SML-NJ, and the complete code listing is available. 1.1

This paper presents an approach to formalize COM (Component Object Model). Despite its importance, COM still does not have a formal specification. In order to understand the COM's informal rules better, the COMEL language is being introduced. We formalized some of the important COM's rules and present COMEL's abstract syntax, type system, operational semantics and type soundness. 1 Introduction Microsoft's OLE provides an application integration framework for Microsoft Windows. OLE rests on the Component Object Model (COM), which specifies a programming language independent binary standard for object invocations, plus a number of interfaces for foundational services. COM is all about interoperability of independently deployed components and is used to develop component-based software. COM is language independent. The component software can be developed by independent vendors. Extensions to component software can also be developed and integrated by the client. Currently, COM offers a...

This document describes a formalization of basic number theory including two theorems of Fermat and Wilson. Most of this have (in some context) been formalized before but we present a new generalized approach for handling some central parts, based on concepts which seem closer to the original mathematical intuition and likely to be useful in other (similar) developments. Our formalization has been mechanized in the Isabelle/HOL system. Contents 1 Introduction 2 2 Basic Number Theory 2 2.1 The Chinese Remainder Theorem . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Fermat's Little Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Wilson's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Formalization 8 3.1 Bijection Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Fermat's Little Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.1 BoyerMoore's proof . . . . . . . . . . . . . . . . . . . . ...