Abstract program schemes, such as scan or homomorphism, can capture a wide range of data parallel programs. While versatile, these schemes are of limited practical use on their own. A key problem is that the more natural sequential specifications may not have associative combine operators required by these schemes. As a result, they often fail to be immediately identified. To resolve this problem, we propose a method to systematically derive parallel programs from sequential definitions. This method is special in that it can automatically invent auxiliary functions needed by associative combine operators. Apart from a formalisation, we also provide new theorems, based on the notion of context preservation, to guarantee parallelization for a precise class of sequential programs. 1 Introduction It is well-recognised that a key problem of parallel computing remains the development of efficient and correct parallel software. This task is further complicated by the variety of parallel arc...

. Tupling transformation strategy can be used to merge loops together by combining recursive calls and also to eliminate redundant calls for a class of programs. In the latter case, this transformation can produce super-linear speedup. Existing works in deriving a safe and automatic tupling only apply to a very limited class of programs. In this paper, we present a novel parameter analysis, called synchronisation analysis, to solve the termination problem for tupling. With it, we can perform tupling on functions with multiple recursion and accumulative arguments without the risk of non-termination. This significantly widens the scope for tupling, and potentially enhances its usefulness. The analysis is shown to be of polynomial complexity; this makes tupling suitable as a compiler optimisation. 1 Introduction Source-to-source transformation can achieve global optimisation through specialisation for recursive functions. Two well-known techniques are partial evaluation [9] a...

Redundant call elimination has been an important program optimisation process as it can produce super-linear speedup in optimised programs. In this paper, we investigate use of the tupling transformation in achieving this optimisation over a first-order functional language. Standard tupling technique, as described in [6], works excellently in a restricted variant of the language; namely, functions with single recursion argument. We provide a semantic understanding of call redundancy, upon which we construct an analysis for handling the tupling of functions with multiple recursion arguments. The analysis provides a means to ensure termination of the tupling transformation. As the analysis is of polynomial complexity, it makes the tupling suitable as a step in compiler optimisation.