This paper investigates the performance of automated theo rem provers in formal software veri cation The challenge for the provers in this application is the large number of up to several hundred axioms in typical software speci cations Both the success rates and the proof times strongly depend on how good the provers are able to nd out the few relevant axioms that are really needed in the proo...

This paper describes WinKE, an interactive proof assistant, which is based on the KE calculus. The software has been designed to serve as a tutoring system supporting the teaching of logic and theorem proving through KE.

Data Model Verification via Theorem Proving

time wall-clock time [d] m em or y [G B y te ] Figure 7.7: Memory requirements over time for ROB001-1: bottom axis denotes abstract time, top axis denotes wall-clock time in days 7.4 Further benefits Besides the smaller memory footprint and some simplifications (e. g. for interreduction) there are some other benefits of the new loop design that are worth discussing. Not all of them are complete...

s a f e t y : t h e o r e m p r o v e r f e e d b a c k Fig. 1. S heme of proving safety statements When a safe data abstra tion is obtained, veri ation of the model against a property an start. First, the abstra t data type and fun tion de nitions are inserted into the system spe i ation substituting the on rete de nitions of the original model. Next, the abstra t model together with the prope...

2 Basics 3 2.1 Words and Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Number Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Automatic Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

This special issue of Mathematical Structures in Computer Science is devoted to the theme of 'Interactive theorem proving and the formalisation of mathematics'. The formalisation of mathematics started at the turn of the 20th century when mathematical logic emerged from the work of Frege and his contemporaries with the invention of the formal notation for mathematical statements called predicat...

We examine an approach for demand-driven cooperative theorem proving. We brieey point out the problems arising from the use of common success-driven cooperation methods, and we propose the application of our approach of requirement-based cooperative theorem proving. This approach allows for a better orientation on current needs of provers in comparison with conventional cooperation concepts. We...

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification...