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This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope.This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 144. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 245. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition