Principal type specialisation

Type specialisation is an approach to program specialisation that works with both a program and its type to produce specialised versions of each. As it combines many powerful features,it appears to be a good framework for automatic program production, -- despite the fact that it was designed originally to express optimal specialisation for interpreters written in typed languages.The original specification of type specialisation used a system of rules expressing it as a generalised type system, rather than the usual view of specialisation as generalised evaluation. That system, while powerful, has some weaknesses not widely recognized -- the most important being the inability to express principal type specialisations (a principal specialisation is one that is "more general" than any other for a given specialisable term, and from which those can be obtained by a suitable notion of instantiation). This inability is a problem when extending type specialisation to deal with polymorphism or modules.This work presents a different formulation of the system specifying type specialisation capturing the notion of principal specialisation for a language with static constructions and polyvariance. It is a step forward in the study of type specialisation for polymorphic languages and lazy languages, and also permits modularity of specialisation, and better implementations.