Formal languages and computable semantics for continuous mathematics

In this talk I will first outline Weihrauch's computable analysis, which gives a framework for discussing computability in topology, geometry and analysis based on type-two recursive function theory. I will then discuss some possibilities for a formal language for computable continuous mathematics. Ideally, such a language should be expressive enough to allow formulae to be written in a natural mathematical syntax , but restrictive enough that only 'computable functions' can be constructed.  

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