A common technique for improving the speed of program specialization is to specialize the program specializer itself on the program to be specialized, creating a custom program generator. Much research has been devoted to the problem of generating efficient program generators, which do not perform reductions at program generation time which could instead have been performed when the program generator was constructed. The conventional wisdom holds that only program specializers using binding-time approximations can be specialized into such efficient program generators. This paper argues that this is not the case, and demonstrates that the specialization of a nontrivial online program specializer similar to the original ‘naive MIX’ can indeed yield an efficient program generator. The key to our argument is that, while the use of binding-time information at program generator generation time is necessary for the construction of an efficient custom specializer, the use of explicit binding-time approximation techniques is not. This allows us to distinguish the problem at hand (i.e. the use of binding-time information during program generator generation) from particular solutions to that problem (i.e. offline specialization). We show that, given a careful choice of specializer data structures, and sufficiently powerful specialization techniques, binding-time information can be inferred and utilized without explicit approximations. This allows the construction of efficient, optimizing program generators from online program specializers.

A new program transformation method is presented. It is a further refinement of supercompilation where the supercompiler is not applied directly to the function to be transformed, but to a metafunction, namely an interpreter which computes this function using its definition and an abstract (i.e. including variables) input. It is shown that with this method such tranformations become possible which the direct application of the supercompiler cannot perform. Examples include the merging of iterative loops, function inversion, and transformation of deterministic into non-deterministic algorithms, and vice-versa.

Based on Henglein's efficient binding-time analysis for the lambda calculus (with constants and ‘fix’) (Henglein, 1991), we develop three 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 Bondorf (1991b). (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 Bondorf (1991b), finds a non-minimal binding-time 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’ (Holst, 1988) increases termination of specialization. The three analyses are performed sequentially in the above mentioned order since each depends on results from the previous analyses. The input to all three analyses are constraint sets generated from the program being analysed. The constraints are solved efficiently by a normalizing union/find-based algorithm in almost-linear time. Whenever possible, the constraint sets are partitioned into subsets which are solved in a specific order; this simplifies constraint normalization. The framework elegantly allows expressing both forwards and backwards components of analyses. In particular, the new is-used analysis is of backwards nature. The three constraint normalization algorithms are proved correct (soundness, completeness, termination, existence of a best solution). The analyses have been implemented and integrated in the Similix system. The new analyses are indeed much more efficient than those of Bondorf (1991b); the almost-linear complexity of the new analyses is confirmed by the implementation.

A binding-time analysis is correct if it always produces consistent binding-time information. Consistency prevents partial evaluators from ‘going wrong’. A sufficient and decidable condition for consistency, called well-annotatedness, was first presented by Gomard and Jones. In this paper we prove that a weaker condition implies consistency. Our condition is decidable, subsumes the one of Gomard and Jones, and was first studied by Schwartzbach and the present author. Our result implies the correctness of the binding-time analysis of Mogensen, and it indicates the correctness of the core of the binding-time analyses of Bondorf and Consel. We also prove that all partial evaluators will on termination have eliminated all ‘eliminable’-marked parts of an input which satisfies our condition. This generalizes a result of Gomard. Our development is for the pure λ-calculus with explicit binding-time annotations.

Mogensen has exhibited a very compact partial evaluator for the pure lambda calculus, using binding-time analysis followed by specialization. We give a correctness criterion for this partial evaluator and prove its correctness relative to this specification. We show that the conventional properties of partial evaluators, such as the Futamura projections, are consequences of this specification. By considering both a flow analysis and the transformation it justifies together, this proof suggests a framework for incorporating flow analyses into verified compilers.