[Haskell-beginners] How to extend fuinctions?

Hi, I have a function Delta and two sets S and A. Delta maps some elements from (S x A) to S. How can I extend Delta to some Delta' such that it assigns to every pair in (S x A) that Delta is not defined for a value not occuring in S? Something like: Delta' = if (Delta s a) /= _Undefined_ then Delta s a else if () n where n is the new value. However Delta' should not assign values to pairs not in (S x A). Note: (S x A) is meant to be the set-crossprroduct. Background: I want to learn Haskell by building a small library for Finite State Automata, Büchi Automata etc. I need this extension of Delta for making automata complete. Regards and thanks for reading, Heinrich