Since the work of Brouwer, Kolmogorov, Goedel, Kleene and many others
we know that constructive proofs have computational meaning. In
Computer Science this idea is known as the
"proofs-as-programs paradigm" or "Curry-Howard correspondence". 
We present examples from computable analysis showing that this
paradigm not only works in principle, but can be used to automatically
synthesise practically relevant certified programs