Note that there are very systematic and natural ways to derive dynamic
programming algorithms in functional languages. In a sense, much of the
work of R. Bird centers this topic. The book "Algebra of Programming"

http://web.comlab.ox.ac.uk/oucl/research/pdt/ap/pubs.html#Bird-deMoor96:Algebra

is one of the cornerstones.

The systematic derivation of dynamic programming algorithms has been
rediscovered in a more direct but less general fashion

   http://bibiserv.techfak.uni-bielefeld.de/adp/