Lightweight fusion by fixed point promotion

This paper proposes a lightweight fusion method for general recursive function definitions. Compared with existing proposals, our method has several significant practical features: it works for general recursive functions on general algebraic data types; it does not produce extra runtime overhea (except for possible code size increase due to the success of fusion); and it is readily incorporated in standard inlining optimization. This is achieved by extending the ordinary inlining process with a new fusion law that transforms a term of the form f o (fixgλx.E) to a new fixed point term fixhλx.E′ by promoting the function f through the fixed point operator. This is a sound syntactic transformation rule that is not sensitive to the types of f and g. This property makes our method applicable to wide range of functions including those with multi-parameters in both curried and uncurried forms. Although this method does not guarantee any form of completeness, it fuses typical examples discussed in the literature and others that involve accumulating parameters, either in the tt foldl-like specific forms or in general recursive forms, without any additional machinery. In order to substantiate our claim, we have implemented our method in a compiler. Although it is preliminary, it demonstrates practical feasibility of this method.