A good example of a formal system would be executables like my Asa H 2.0 lite (see my 10 Feb. 2011 post for a listing).
A good example of an informal description of (roughly) the same system is my graph in my 29 Sept. 2010 post. (One could make it more formal by adding details about what each node of the graph does, or by listing what quantities are sent from one node to another and when.)
A good example of a description that is less formal than executable code but more formal than my graph would be the equation set given in my 2006 paper on Asa H (Trans. Kansas Acad. Sci., Vol 109, # 3/4, pg 159).