Applications of “Seemingly Impossible Functional Programs”

What are some practical applications (existing or potential) for Martin Escardo's "Seemingly Impossible Functional Programs"?

For starters, here are a few from:

• Alex Simpson’s Lazy functional algorithms for exact real functionals. Compute maximum value and integral of a real function, with real numbers represented as infinite sequences of digits.

• Verification of real-number programs by checking infinitely many cases.