Warm Fusion for the Masses: Detailing Virtual Data Structure Elimination in Fully Recursive Language

In functional programming, small programs are often combined to construct larger, more complex ones. The component reuse encouraged by this modular style of programming yields many bene ts, but, unfortunately, modular programs also tend to be less e cient than their monolithic counterparts. This is frequently due to the construction of intermediate data structures which \glue" together smaller program components into larger ones. Fusion is the process of removing intermediate data structures from modularly constructed programs. Two particularly successful approaches to achieving fusion in functional languages have emerged in recent years. The rst is a catamorphic fusion technique based on Malcolm's promotion theorems, while the second is a shortcut based on parametricity which fuses compositional programs via canned applications of traditional fold/unfold program transformation steps. Warm fusion combines these to arrive at a third fusion method, in which the potentially exponential application of catamorphic fusion is controlled. In essence, the method uses catamorphic fusion to preprocess programs written in the common recursive style into compositions to which the shortcut applies. The primary purpose of this paper is to report on a prototype implementation of the warm fusion method, together with the maturing of ideas from Launchbury and Sheard's paper ([LS95]) introducing the method that construction of the prototype has entailed. In particular, we treat warm fusion in the context of a fully polymorphic higher-order language, and so resolve an important outstanding issue raised in [LS95]. We also demonstrate that it can be automated to eliminate from programs intermediate data structures other than lists. Our implementation experience suggests that the development of a fully automated tool for fusing recursively de ned programs | suitable for incorporation into a state-of-the-art compiler | should be achievable. A secondary, but nevertheless fundamental, aim of this paper is to o er a detailed and self-contained treatment of the warm fusion method. We provide robust discussions of the historical and technical contexts out of which warm fusion has grown, and present the method in su cient detail to render this paper accessible to readers with modest background in functional programming, regardless of whether or not they have any prior familiarity with program fusion.