Parsimony Principles for Software Components and Metalanguages

Abstract: Software is a communication system. The usual topic of communication is program behavior, as encoded by programs. Domain-specific libraries are codebooks, domain-specific languages are coding schemes, and so forth. To turn metaphor into method, we adapt toolsfrom information theory--the study of efficient communication--to probe the efficiency with which languages and libraries let us communicate programs. In previous work we developed an information-theoretic analysis of software reuse in problem domains. This new paper uses information theory to analyze tradeoffs in the design of components, generators, and metalanguages. We seek answers to two questions: (1) How can we judge whether a component is over- or under-generalized? Drawing on minimum description length principles, we propose that the best component yields the most succinct representation of the use cases. (2) If we view a programming language as an assemblage of metalanguages, each providing a complementary style of abstraction, how can these metalanguages aid or hinder us in efficiently describing software? We describe a complex triangle of interactions between the power of an abstraction mechanism, the amount of reuse it enables, and the cognitive difficulty of its use.