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Based on Henglein’s efficient binding-time analysis for the lambda calculus (with constants and “fix”) [Hen91], we develop four efficient analyses for use in the preprocessing phase of Similix, a self-applicable partial evaluator for a higher-order subset of Scheme. The analyses developed in this paper are almost-linear in the size of the analysed program. (1) A flow analysis determines possible value flow between lambda-abstractions and function applications and between constructor applications and selector/predicate applications. The flow analysis is not particularly biased towards partial evaluation; the analysis corresponds to the closure analysis of [Bon91b]. (2) A (monovariant) binding-time analysis distinguishes static from dynamic values; the analysis treats both higher-order functions and partially static data structures. (3) A new is-used analysis, not present in [Bon91b], finds a non-minimal bindingtime annotation which is “safe ” in a certain way: a first-order value may only become static if its result is “needed ” during specialization; this “poor man’s generalization ” [Hol88] increases termination of specialization. (4) Finally, an evaluation-order dependency analysis ensures that the order of side-effects is preserved in the residual program. The four analyses are performed

This paper shows how the Improvement Theorem---a semantic condition

The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfold-fold method. Unfortunately the unfold-fold method itself guarantees neither improvement in efficiency nor total-correctness. The correctness problem for unfold-fold is an instance of a strictly more general problem: transformation by locally equivalence-preserving steps does not necessarily preserve (global) equivalence. This paper presents a condition for the total correctness of transformations on recursive programs, which, for the first time, deals with higher-order functional languages (both strict and non-strict) including lazy data structures. The main technical result is an improvement theorem which says that if the local transformation steps are guided by certain optimisation concerns (a fairly natural condition for a transformation), then correctness of the transformation follows. The improvement theorem make...

In program optimisation an analysis determines some information about a portion of a program, which is then used to justify certain transformations on the code. The correctness of the optimisation can be argued monolithically by considering the behaviour of the optimiser and a particular analysis in conjunction. Alternatively, correctness can be established by finding an interface, a semantic property, between the analysis and the transformation. The semantic property provides modularity by giving a specification for a systematic construction of the analysis, and the program transformations are justified via the semantic properties. This paper considers the problem of partial evaluation. The safety of a partial evaluator ("it does not go wrong") has previously been argued in the monolithic style by considering the behaviour of a particular binding-time analysis and program specialiser in conjunction. In this paper we pursue the alternative approach of justifying the binding-time prop...