An Eclectic View of the Irish School of Constructive Mathematics, from [Lucas 1978] to [Mac an Airchinnigh 2001]

Micheal Mac an Airchinnigh (University of Dublin, Trinity College, Ireland)

Abstract: In this paper I celebrate the evolution of the Vienna Development Method (VDM) along its Irish branch and attempt to tell the story that Peter Lucas played in it.

There are two parts to the paper. In the first part I tell my story of the early day of the origins of the Irish School of the VDM (), beginning with prehistory in 1978 up until the radical decisions of 1995 which led to the Irish School of 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 (alt. toposes). The second part of the paper illustrates, with simple examples, how I introduce topos logic into modelling in 2001.

Keywords: VDM, constructive mathematics, intuitionistic logic, modelling, topos theory

Categories: F.4, G.