Partial Categorical Multi-Combinators and Church-Rosser Theorems

Categorical Multi-Combinators form a rewriting system developed with the aim of providing efficient implementations of lazy functional languages. The core of the system of Categorical Multi-Combinators consists of only four rewriting laws with a very low pattern-matching complexity. This system allows the equivalent of several b-reductions to be performed at once, as functions form frames with all their arguments. This feature is convenient for most cases of function application, but it does not allow partially parameterised functions to fetch arguments. Presented within this paper are Partial Categorical Multi-Combinators (PCMC), a new rewriting system, which removes this drawback. The computational power of Partial Categorical Multi-Combinators is equivalent to the rewriting system presented in [17], but PCMC uses fewer rewriting laws with a much simpler syntax. These factors made the proofs of the Church-Rosser properties for PCMC far easier than the ones in [17]. This report replaces report no. 7-92.