The Vectorisation Monad

Traditionally a vectorising compiler matches the iterative constructs of a program against a set of predeened templates. If a loop contains no dependency cycles then a map template can be used; other simple dependencies can often be expressed in terms of fold or scan templates. This paper addresses the template matching problem within the context of functional programming. A small collection of program identities are used to specify vectorisable for-loops. By incorporating these program identities within a monad, all well-typed for-loops in which the body of the loop is expressed using the vectorisation monad can be vectorised. This technique enables the elimination of template matching from a vectorising compiler, and the proof of the safety of vectorisation can be performed by a type inference mechanism.