Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for obtaining certified algorithms in exact real arithmetic. 1

on topological spaces via domain representations