A set of new combinator families and a new list representation are proposed in this dissertation. Each of the proposed combinators expresses certain commonly occurring combinations of lists as functions of those lists or elements of lists. Most of these combinators reshape the structure of the input list so that its elements can be manipulated concurrently. The reduction semantics and proofs of correctness for these combinators are given in the form of strings of already known combinators. It has been shown that the proposed combinators and list structure make the execution of functional programs faster on both sequential and parallel architectures.