Catamorphic Approach to Program Analysis
Catamorphic Approach to Program Analysis Mizuhito OGAWA1,2, Zhenjiang HU1,2, Isao SASANO1, Masato TAKEICHI1 1 The University of Tokyo 2 PRESTO 21, Japan Science and Technology Corporation {mizuhito,hu,sasano,takeichi}@ipl.t.u-tokyo.ac.jp Abstract. This paper proposes a new framework for program analysis that regards them as maximum marking problems: mark the codes of a program under a certain condition such that the number of marked nodes is maximum. We show that if one can develop an efficient checking program (in terms of a finite catamorphism) whether marked programs are correctly marked, then an efficient and incremental marking algorithm to analyze control flow of structured programs (say in C or Java with limited numbers of gotos) is obtained for free. To describe catamorphisms on control flow graphs, we present an algebraic construction, called SP Term, for graphs with bounded tree width. The transformation to SP Terms is done efficiently in linear time. We demonstrate that our framework is powerful to describe various kinds of control flow analyses. Especially, for analyses in which some optimality is required (or expected), our approach has a big advantage. Keywords: Catamorphism, Control Flow Graphs, Control Flow Analysis, Functional Programming, Linear Time Algorithm, Program Optimization, Bounded Tree Width 1 Introduction While program transformation plays an important role in optimizing compiler and software engi- neering, implementing program transformation requires various kinds of program analyses to extract program fragments satisfying a certain property; these fragments will then be replaced by equivalent but more efficient constructs. As a simple example, consider the program in Fig.
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