The promotion and accumulation strategies in transformational programming

The promotion strategy in transformational programming is a general method for achieving efficiency by exploiting the recursive structure in the dominant term of an algorithmic expression. For it to be carried out successfully, the original problem often has to be generalized by the inclusion of an extra parameter, a technique known as accumulation. These strategies are illustrated by deriving algorithms for two nontrivial problems: (1) determining whether a given digraph is acyclic, and (2) constructing the longest subsequence of a given sequence of vertices that forms a connected path in a given digraph. The derivations also serve to emphasize the usefulness of certain notational devices in applicative expressions, especially infix operators.