On the shape of mathematical arguments
On the shape of mathematical arguments
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
The Composition of Event-B Models
ABZ '08 Proceedings of the 1st international conference on Abstract State Machines, B and Z
A formal approach for the development of reactive systems
Information and Software Technology
Combining formal methods for the development of reactive systems
International Journal of Computer Applications in Technology
Validating and animating higher-order recursive functions in b
Rigorous Methods for Software Construction and Analysis
Combining Formal Methods for the Development of Reactive Systems
ACM Transactions on Embedded Computing Systems (TECS) - Special Issue on Modeling and Verification of Discrete Event Systems
Practical theory extension in event-B
Theories of Programming and Formal Methods
| Hi-index | 0.00 |
In this paper, we investigate the possibility to mechanize the proof of some real complex mathematical theorems in B [1]. For this, we propose a little structure language which allows one to encode mathematical structures and their accompanying theorems. A little tool is also proposed, which translates this language into B, so that Atelier B, the tool associated with B, can be used to prove the theorems. As an illustrative example, we eventually (mechanically) prove the Theorem of Zermelo [6] stating that any set can be well-ordered. The present study constitutes a complete reshaping of an earlier (1993) unpublished work (referenced in [4]) done by two of the authors, where the classical theorems of Haussdorf and Zorn were also proved.