Projection factorisations in partial evaluation by John Launchbury
By John Launchbury
A partial evaluator is a functionality that takes a software, including the various enter to this system, and produces a brand new application for that reason. This new software is an optimized model of the previous, having taken the enter information under consideration. ahead of partial review, the enter software undergoes research. This binding-time research discovers which values in the application should be computed in the course of partial evaluation--the static values--and which could not--the dynamic values. Partial assessment has lately develop into the focal point of recognition for a quickly expanding variety of researchers as a result of its strength for international software optimization. It offers a close advent and proceeds to a mathematical therapy of the strategy. it's suitable to humans attracted to automated application transformation, software optimization, compilers, software research, and theoretical computing device technology. this can be the 1st entire ebook with regards to partial review.
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Example text
7 x F\6 x) is not, in general, a projection. However, greatest lower bounds do exist in Value p^+ Value for the following reason. Projections are bounded by ID, so the set of projections {/? | /? E 7 A j3 Q 6} is consistent and, hence, its least upper bound exists. This least upper bound is a finitary projection and is greater than all other lower bounds for 7 and 6 and so it is the greatest lower bound. The difference between these different greatest lower bounds becomes irrelevant when we introduce particular finite domains of projections, as in these domains, the usual greatest lower bound of any set of projections from these domains is itself a projection and, moreover, also a member of the same finite domain.
The residual program is, in this sense, "congruent" with the source program. In addition to congruence, the results of binding-time analysis must be finite. As congruent annotations produce a congruent program, so finite annotations lead to a finite residual program. Consider the following example. f x y = if then else y=0 x f (x+1) (y-1) We declare x to be static and y dynamic. This is congruent but not finite. Suppose we specialise f to the value 1 for x. Making the recursive call residual, we obtain the following residual program.
Denotational Semantics f : :R->S 41 x: :T h e j :R x::T h f e : :S C ::S,->S X : :1rh e ::S, x: :T h c, e: :S x::Th e::S Vi . (x: :T,y,: :S, h e,::R) x: :T h case e in C\ y t -> ej I I . . I I c n y n -> e n end: :R Only well-formed and well-typed programs are assigned a meaning. This meaning is defined by the denotational semantics. 3 Denotational Semantics The denotational semantics is fairly standard. There are three semantic domains— one to model values and the other two to model value and function environments respectively.