Introduction to higher order categorical logic
Introduction to higher order categorical logic
Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Category theory for computing science, 2nd ed.
Category theory for computing science, 2nd ed.
Elementary categories, elementary toposes
Elementary categories, elementary toposes
Algebra of programming
Exploring Specifications with Mathematica
ZUM '95 Proceedings of the 9th International Conference of Z Usres on The Z Formal Specification Notation
Tutorial on the Irish School of the VDM
VDM '91 Proceedings of the 4th International Symposium of VDM Europe on Formal Software Development-Volume 2: Tutorials
Theories of Programming: Top-Down and Bottom-Up and Meeting in the Middle
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume I - Volume I
Scientific Decisions which Characterize VDM
FM '99 Proceedings of the Wold Congress on Formal Methods in the Development of Computing Systems-Volume I - Volume I
Mathematics for formal methods, a proposal for education reform
IW-FM'98 Proceedings of the 2nd Irish conference on Formal Methods
The geometry of distributions in formal methods
2FACS'97 Proceedings of the 2nd BCS-FACS conference on Northern Formal Methods
OO-motivated process algebra: a calculus for CORBA-like systems
ROOM'00 Proceedings of the 2000 international conference on Rigorous Object-Oriented Methods
VDM♣ meets LCF: domain-theoretic and topological aspects of VDM♣
IW-FM'01 Proceedings of the 5th Irish conference on Formal Methods
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The Irish School of Constructive Mathematics (Mc♣), which extends the VDM, exploits an algebraic notation based upon monoids and their morphisms for the purposes of abstract modelling. Its method depends upon an operator calculus. The School hereto eschewed every form of formal language and formal logic, relying solely upon constructive mathematics. In 1995 the School committed itself to the development of the modelling of (computing) systems in full generality. This was achieved by embracing Category Theory and by exploring a geometry of formal methods using techniques of fiber bundles. From fiber bundles to sheaves was a natural step. Concurrently, the School moved from the algebra of monoids to categories, and from categories to topoi. Finally, the constructive nature of the School is now coming to terms with formalism and logic through the (natural) intuitionistic logic inherently manifest through topoi. In this paper we exhibit an accessible bridge from classical formal methods to topos theoretic formal methods in seeking a unifying theory.