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An important research goal in software engineering and programming languages is the development of principles underlying the specification of computable problems, the translation of these problems into efficient and correct programs, and the performance analysis of these programs. This paper uncovers some of these principles, which are used to design a problem specification language L1 restricted to problems that can be compiled automatically into programs whose worst case asymptotic time and space complexities are linear in the input/output space. Any problem expressible in L1 can be compiled into a linear cost program. A compiler for L1 has been implemented in the RAPTS transformational programming system.