We present a framework for applying memoization selectively. The framework provides programmer control over equality, space usage, and identification of precise dependences so that memoization can be applied according to the needs of an application. Two key properties of the framework are that it is efficient and yields programs whose performance can be analyzed using standard techniques. We describe the framework in the context of a functional language and an implementation as an SML library. The language is based on a modal type system and allows the programmer to express programs that reveal their true data dependences when executed. The SML implementation cannot support this modal type system statically, but instead employs run-time checks to ensure correct usage of primitives.

This paper describes a method for transforming any given set of Datalog rules into an efficient specialized implementation with guaranteed worst-case time and space complexities, and for computing the complexities from the rules. The running time is optimal in the sense that only useful combinations of facts that lead to all hypotheses of a rule being simultaneously true are considered, and each such combination is considered exactly once. The associated space usage is optimal in that it is the minimum space needed for such consideration modulo scheduling optimizations that may eliminate some summands in the space usage formula. The transformation is based on a general method for algorithm design that exploits fixed-point computation, incremental maintenance of invariants, and combinations of indexed and linked data structures. We apply the method to a number of analysis problems, some with improved algorithm complexities and all with greatly improved algorithm understanding and greatly simplified complexity analysis.

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Abstract. This paper describes a general and powerful method for dead code analysis and elimination in the presence of recursive data constructions. We represent partially dead recursive data using liveness patterns based on general regular tree grammars extended with the notion of live and dead, and we formulate the analysis as computing liveness patterns at all program points based on program semantics. This analysis yields a most precise liveness pattern for the data at each program point, which is signi cantly more precise than results from previous methods. The analysis algorithm takes cubic time in terms of the size of the program in the worst case but is very e cient in practice, as shown by our prototype implementation. The analysis results are used to identify and eliminate dead code. The general framework for representing and analyzing properties of recursive data structures using general regular tree grammars applies to other analyses as well. 1

This paper describes a general approach for automatic and accurate space and space-bound analyses for high-level languages, considering stack space, heap allocation and live heap space usage of programs. The approach is based on program analysis and transformations and is fully automatic. The analyses produce accurate upper bounds in the presence of partially known input structures. The analyses have been implemented, and experimental results con rm the accuracy. 1

This paper describes a systematic method for optimizing recursive functions using both indexed and recursive data structures. The method is based on two critical ideas: first, determining a minimal input increment operation so as to compute a function on repeatedly incremented input; second, determining appropriate additional values to maintain in appropriate data structures, based on what values are needed in computation on an incremented input and how these values can be established and accessed. Once these two are determined, the method extends the original program to return the additional values, derives an incremental version of the extended program, and forms an optimized program that repeatedly calls the incremental program. The method can derive all dynamic programming algorithms found in standard algorithm textbooks. There are many previous methods for deriving efficient algorithms, but none is as simple, general, and systematic as ours.

This paper describes a formal derivation of an optimized Ackermann's function following a general and systematic method based on incrementalization. The method identifies an appropriate input increment operation and computes the function by repeatedly performing an incremental computation at the step of the increment. This eliminates repeated subcomputations in executions that follow the straightforward recursive definition of Ackermann's function, yielding an optimized program that is drastically faster and takes extremely little space. This case study uniquely shows the power and limitation of the incrementalization method, as well as both the iterative and recursive nature of computation underlying the optimized Ackermann's function.

This paper presents program analyses and transformations for strengthening invariants for the purpose of efficient computation. Finding the stronger invariants corresponds to discovering a general class of auxiliary information for any incremental computation problem. Combining the techniques with previous techniques for caching intermediate results, we obtain a systematic approach that transforms non-incremental programs into ecient incremental programs that use and maintain useful auxiliary information as well as useful intermediate results. The use of auxiliary information allows us to achieve a greater degree of incrementality than otherwise possible. Applications of the approach include strength reduction in optimizing compilers and finite differencing in transformational programming.

This paper describes the precise specification, design, analysis, implementation, and measurements of an efficient algorithm for solving regular tree grammar based constraints. The particular constraints are for dead-code elimination on recursive data, but the method used for the algorithm design and complexity analysis is general and applies to other program analysis problems as well. The method is centered around Paige's finite differencing, i.e., computing expensive set expressions incrementally, and allows the algorithm to be derived and analyzed formally and implemented easily. We study higherlevel transformations that make the derived algorithm concise and allow its complexity to be analyzed accurately. Although a rough analysis shows that the worst-case time complexity is cubic in program size, an accurate analysis shows that it is linear in the number of live program points and in other parameters, including mainly the arity of data constructors and the number of selector applications into whose arguments the value constructed at a program point might flow. These parameters explain the performance of the analysis in practice. Our implementation also runs two to ten times as fast as a previous implementation of an informally designed algorithm.

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