Lightweight fusion by fixed point promotion

Abstract

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 overhead (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 • (fix g.λx.E) to a new fixed point term fix h.λx.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 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.

Refunctionalization of abstract abstract machines: bridging the gap between abstract abstract machines and abstract definitional interpreters (functional pearl)

“…Lightweight Fusion. Lightweight fusion as one of the transformation in our paper was presented by Ohori and Sasano [2007]. As shown by Danvy and Millikin [2008a], lightweight fusion can be used to show the equivalence between small-step and big-step abstract machines.…”

“…Notably, this makes explicit another layer of control (Section 3). • Lightweight fusion [Danvy and Millikin 2008a;Ohori and Sasano 2007]: We apply a fusion transformation to the linearized AAM, which combines the single-step function step and the driving function into one, but keeps all the machine state representations intact (Section 4). • Disentanglement: We identify different first-order data types which represent different layers of continuations, and disassemble their handlers into separate functions (Section 5).…”

Positive supercompilation for a higher order call-by-value language

“…The work by Ohori and Sasano [35] cannot fuse two successive applications of the same function, nor mutually recursive functions. We show in the next two examples that our transformation can handle these cases.…”

“…We therefore start our survey of related work with one call-by-value transformation and then look at the related transformations from a call-by-name or callby-need perspective. [35] works by promoting functions through the fix-point operator and guarantees termination by limiting inlining to at most once per function. They implement their transformation in a compiler for a variant of Standard ML and present some benchmarks.…”

“…Ohori and Sasano [35] saw this need and presented a very elegant algorithm for callby-value languages that removes intermediate structures. Their algorithm sacrifices some transformational power for algorithmic simplicity.…”