Introduction to higher order categorical logic
Introduction to higher order categorical logic
A category-theoretic characterization of functional completeness
Theoretical Computer Science
Categories, types, and structures: an introduction to category theory for the working computer scientist
Basic simple type theory
Computable analysis: an introduction
Computable analysis: an introduction
Term Rewriting Systems
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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In one of the many and fundamental side-remarks made by Turing in his 1950 paper (The Imitation Game paper), an analogy is made between Mechanism and Writing. Turing is aware that his Machine is a writing/re-writing mechanism, but he doesn't go deeper into the comparison. Striding along the history of writing, we shall hint here at the nature and the role of alphabetic writing in the invention of Turing's (and today's) notion of computability. We shall stress that computing is a matter of alphabetic sequence checking and replacement, far away from the physical world, yet related to it once the role of physical measurement is taken into account. Turing Morphogenesis paper, 1952, provides the guidelines for the modern analysis of "continuous dynamics" at the core Turing's late and innovative approach to bio-physical processes.