For decades my colleague, Guy Blelloch, and I have promoted a grand synthesis of the two “theories” of computer science, combinatorial theory and logical theory. It is only a small exaggeration to say that these two schools of thought work in isolation. The combinatorial theorists concern themselves with efficiency, based on hypothetical translations of high-level algorithms to low-level machines, and have no useful theory of composition, the most important tool for developing large software systems. Logical theorists concern themselves with composition, emphasizing the analysis of the properties of components of systems and how those components are combined; the heart of logic is a theory of composition (entailment). But relatively scant attention is paid to efficiency, and, to a distressingly large extent, the situation is worsening, and not improving.
Guy and I have argued, through our separate and joint work, for the applicability of PL ideas to algorithms design, leading. for example, to the concept of adaptive programming that Umut Acar has pursued aggressively over the last dozen years. And we have argued for the importance of cost analysis, for various measures of cost, at the level of the code that one actually writes, and not how it is compiled. Last spring, prompted by discussions with Anindya Banerjee at NSF in the winter of 2014, I decided to write a position paper on the topic, outlining the scientific opportunities and challenges that would arise in an attempt to unify the two, disparate theories of computing. I circulated the first draft privately in May, and revised it in July to prepare for a conference call among algorithms and PL researchers (sponsored by NSF) to find common ground and isolate key technical challenges to achieving its goals.
There are serious obstacles to be overcome if a grand synthesis of the “two theories” is to be achieved. The first step is to get the right people together to discuss the issues and to formulate a unified vision of what are the core problems, and what are promising directions for short- and long-term research. The position paper is not a proposal for funding, but is rather a proposal for a meeting designed to bring together two largely (but not entirely) disparate communities. In summer of 2014 NSF hosted a three-hour long conference call among a number of researchers in both areas with a view towards hosting a workshop proposal in the near future. Please keep an eye out for future developments.
I am grateful to Anindya Banerjee at NSF for initiating the discussion last winter that led to the paper and discussion, and I am grateful to Swarat Chaudhuri for his helpful comments on the proposal.
[Update: word smithing, corrections, updating, removed discussion of cost models for fuller treatment later, fixed incoherence after revision.]