and the USA. It is funded by the European Union as well as several national funding organisations, and is running for four years. The joint research will study important aspects-both theoretical as well as applied-of computing with infinite o bjects. A central aim is laying the grounds for the generation of efficient and verified software in engineering applications. A prime example for infinite data is provided by the real numbers, most commonly conceived as infinite sequences of d igits.

more »

... the reals are fundamental in mathematics, any attempt to compute objects of mathematical interest has to be based on an implementation of real numbers. While most applications in science and engineering substitute the reals with floating p oint n umbers o f fi xed finite precision and thus have to deal with truncation and rounding errors, the approach in this project is different: exact real numbers are taken as first-class citizens and while any computation can only exploit a finite portion of its input in finite time, increased precision is always available by continuing the computation process. We will refer to this mode of computing with real numbers as exact real arithmetic or ERA. These ideas are greatly generalised in Weihrauch's type-two theory of effectivity which aims to represent infinite data of any kind as streams of finite d ata. T his p roject a ims t o b ring t ogether t he expertise o f s pecialists in mathematics, logic, and computer science to push the frontiers of our theoretical and practical understanding of computing with infinite objects. Three overarching motivations drive the collaboration: Representation and representability. Elementary cardinality considerations tell us that it is not possible to represent arbitrary mathematical objects in a way that is accessible to computation. We will enlist expertise in topology, logic, and set theory, to address the question of which objects are representable and how they can be represented most efficiently.