Flow analysis of lazy higher-order functional programs

Abstract

In recent years much interest has been shown in a class of functional languages including HASKELL, lazy ML, SASL/KRC/MIRANDA, ALFL, ORWELL, and PONDER. It has been seen that their expressive power is great, programs are compact, and program manipulation and transformation is much easier than with imperative languages or more traditional applicative ones. Common characteristics: they are purely applicative, manipulate trees as data objects, use pattern matching both to determine control flow and to decompose compound data structures, and use a "lazy" evaluation strategy.In this paper we describe a technique for data flow analysis of programs in this class by safely approximating the behavior of a certain class of term rewriting systems. In particular we obtain "safe" descriptions of program inputs, outputs and intermediate results by regular sets of trees. Potential applications include optimization, strictness analysis and partial evaluation. The technique improves earlier work because of its applicability to programs with higher-order functions, and with either eager or lazy evaluation. The technique addresses the call-by-name aspect of laziness, but not memoization. This paper extends [19] (a chapter in the out-of-print [2]) with proofs that the algorithm terminates and yields safe (i.e., sound or correct) approximations to program behavior. Relevance to this festschrift: John Reynolds' 1969 and 1972 papers developed a related first-order program analysis framework [27], and inspired our method for handling higher-order functions [28].

Termination criteria for tree automata completion

“…The mechanisms used in our work and [39] are very similar. However, using equations, we can tune the approximation more precisely than the fixed "independent attributes" approximation of [39], where all relation between parameters of a function call are lost. In particular, such an approximation is unable to precisely analyze the reverse examples of Section 6.6.…”

“…With regards to static analysis of functional programs using grammars or automata, our contribution is in the scope of data-flow analysis techniques, rather than control-flow analysis. More precisely, we are interested here in predicting the results of a function [39,40,41], rather than predicting the control flow [42]. All those papers, as well as many other ones, deal with higher order functions using either tree grammars (for [39]) or higher-order grammar formalisms (PMRS and HORS).…”

“…More precisely, we are interested here in predicting the results of a function [39,40,41], rather than predicting the control flow [42]. All those papers, as well as many other ones, deal with higher order functions using either tree grammars (for [39]) or higher-order grammar formalisms (PMRS and HORS). The mechanisms used in our work and [39] are very similar.…”

“…All those papers, as well as many other ones, deal with higher order functions using either tree grammars (for [39]) or higher-order grammar formalisms (PMRS and HORS). The mechanisms used in our work and [39] are very similar. However, using equations, we can tune the approximation more precisely than the fixed "independent attributes" approximation of [39], where all relation between parameters of a function call are lost.…”

The essence of program transformation by partial evaluation and driving

“…Examples include program optimization both by deforestation and by partial evaluation; the use and significance of self-application for generating compilers and other program generators; and the use of grammars as a tool in program transformation [31,32,17]. Recent works on driving and supercompilation include [33,14,15,27,24,22,1].…”