This paper concerns the static analysis of programs that perform destructive updating on heap-allocated storage. We give an algorithm that conservatively solves this problem by using a finite shape-graph to approximate the possible “shapes” that heap-allocated structures in a program can take on. In contrast with previous work, our method M even accurate for certain programs that update cyclic data structures. For example, our method can determine that when the input to a program that searches a list and splices in a new element is a possibly circular list, the output is a possibly circular list.

Abstract. Type-directed partial evaluation stems from the residualization of arbitrary static values in dynamic contexts, given their type. Its algorithm coincides with the one for coercing asubtype value into a supertype value, which itself coincides with the one of normalization in the-calculus. Type-directed partial evaluation is thus used to specialize compiled, closed programs, given their type. Since Similix, let-insertion is a cornerstone of partial evaluators for callby-value procedural programs with computational e ects. It prevents the duplication of residual computations, and more generally maintains the order of dynamic side e ects in residual programs. This article describes the extension of type-directed partial evaluation to insert residual let expressions. This extension requires the userto annotate arrowtypes with e ect information. It is achieved by delimiting and abstracting control, comparably to continuation-based specialization in direct style. It enables type-directed partial evaluation of e ectful programs (e.g.,ade nitional lambda-interpreter for an imperative language) that are in direct style. The residual programs are in A-normal form. 1

Binding-time analysis determines when variables and expressions in a program can be bound to their values, distinguishing between early (compile-time) and late (run-time) binding. Binding-time information can be used by compilers to produce more efficient target programs by partially evaluating programs at compile-time. Binding-time analysis has been formulated in abstract interpretation contexts and more recently in a type-theoretic setting. In a type-theoretic setting binding-time analysis is a type inference problem: the problem of inferring a completion of a λ-term e with binding-time annotations such that e satisfies the typing rules. Nielson and Nielson and Schmidt have shown that every simply typed λ-term has a unique completion ê that minimizes late binding in TML, a monomorphic type system with explicit binding-time annotations, and they present exponential time algorithms for computing such minimal completions. 1 Gomard proves the same results for a variant of his two-level λ-calculus without a so-called “lifting ” rule. He presents another algorithm for inferring completions in this somewhat restricted type system and states that it can be implemented in time O(n 3). He conjectures that the completions computed are minimal.

We introduce the notion of a perfect process tree as a model for the full propagation of in forma tion in metacomputation. Starting with constant propagation we construct step-by-step the driving mechanism used in supercompilation which ensures the perfect propagation of information. The concept of a simple supercompiler based on perfect driving coupled with a simple folding strategy is explained. As an example we demonstrate that specializing a naive pattern matcher with respect to a fixed pattern obtains the efficiency of a matcher generated by the Knuth, Morris & Pratt al gorithm.

. This paper identifies and solves a class of problems that arise in binding time analysis and more generally in partial evaluation of programs: the approximation and loss of static information due to dynamic expressions with static subexpressions. Solving this class of problems yields substantial binding time improvements and thus dramatically better results not only in the case of partial evaluation but also for static analyses of programs --- this last point actually is related to a theoretical result obtained by Nielson. Our work can also be interpreted as providing a solution to the problem of conditionally static data, the dual of partially static data. We point out which changes in the control flow of a source program may improve its static data flow. Unfortunately they require one to iterate earlier phases of partial evaluation. We show how these changes are subsumed by transforming the source program into continuation-passing style (CPS). The transformed programs get specializ...

. Multiple program specialization can stage a computation into several computation phases. This paper presents an effective solution for multiple program specialization by generalizing conventional off-line partial evaluation and integrating the "cogen approach" with a multi-level binding-time analysis. This novel "multi-cogen approach" solves two fundamental problems of self-applicable partial evaluation: the generation-time problem and the generator-size problem. The multilevel program generator has been implemented for a higher-order subset of Scheme. Experimental results show a remarkable reduction of generation time and generator size compared to previous attempts of multiple self-application. 1 Introduction Stages of computation arise naturally in many programs, depending on the availability of data or the frequency with which the input changes. Code for later stages can be optimized based on values available in earlier stages. Partial evaluation has received much attention beca...

This paper concerns the use of program slicing to perform a certain kind of program-specialization operation. The specialization operation that slicing performs is different from the specialization operations performed by algorithms for partial evaluation, supercompilation, bifurcation, and deforestation. In particular, we present an example in which the specialized program that we create via slicing could not be created as the result of applying partial evaluation, supercompilation, bifurcation, or deforestation to the original unspecialized program. Specialization via slicing also possesses an interesting property that partial evaluation, supercompilation, and bifurcation do not possess: The latter operations are somewhat limited in the sense that they support tailoring of existing software only according to the ways in which parameters of functions and procedures are used in a program. Because parameters to functions and procedures represent the range of usage patterns that the designer of a piece of software has anticipated, partial evaluation, supercompilation, and bifurcation support specialization only in ways that have already been “foreseen ” by the software’s author. In contrast, the specialization operation that slicing supports permits programs to be specialized in ways

A systematic approach is given for deriving incremental programs from non-incremental programs written in a standard functional programming language. We exploit a number of program analysis and transformation techniques and domain-specific knowledge, centered around effective utilization of caching, in order to provide a degree of incrementality not otherwise achievable by a generic incremental evaluator. 1 Introduction Incremental programs take advantage of repeated computations on inputs that differ only slightly from one another, avoiding unnecessary duplication of common computations. Given a program f and a certain input change \Phi, a program f 0 that computes the value of f(x \Phi y) efficiently by making use of the value of f(x) is called an incremental version of f under \Phi. The parameter y can be regarded as a change ffix to the input x. Methods of incremental computation have widespread applications, e.g., loop optimizations in optimizing compilers [1, 24, 9, 10] and ...

Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). In this paper a binding time analysis for the simply typed lambda calculus is presented. The analysis takes the form of an abstract interpretation and uses a novel formalisation of the problem of binding time analysis, based on the use of partial equivalence relations. A simple proof of correctness is achieved by the use of logical relations. 1 Introduction Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). A binding time analysis performed prior to the partial evaluation process can have several practical benefits (see [...

. A partial evaluator, given a program and a known "static" part of its input data, outputs a specialised or residual program in which computations depending only on the static data have been performed in advance. Ideally the partial evaluator would be a "black box" able to extract nontrivial static computations whenever possible; which never fails to terminate; and which always produces residual programs of reasonable size and maximal efficiency, so all possible static computations have been done. Practically speaking, partial evaluators often fall short of this goal; they sometimes loop, sometimes pessimise, and can explode code size. A partial evaluator is analogous to a spirited horse: while impressive results can be obtained when used well, the user must know what he/she is doing. Our thesis is that this knowledge can be communicated to new users of these tools. This paper presents a series of examples, concentrating on a quite broad and on the whole quite successful application ...