Flow analysis and optimization of LISP-like structures

In 12 the authors introduced the concept of binding time optimization and presented a series of data flow analytic methods for determining some of the binding time characteristics of programs. In this paper we extend that work by providing methods for determining the class of shapes which an unbounded data object may assume during execution of a LISP-like program, and describe a number of uses to which that information may be put to improve storage allocation in compilers and interpreters for advanced programming languages.We are concerned chiefly with finding, for each program point and variable a finite description of a set of graphs which includes all the shapes of values the variable could assume at that point during the execution of a program. If this set is small or regular in structure, this information can be used to optimize the program's execution, mainly by use of more efficient storage allocation schemes.In the first part we show how to construct from a program without selective updating a tree grammar whose nonterminals generate the desired sets of graphs; in this case they will all be trees. The tree grammars are of a more general form than is usually studied 8, 19, so we show that they may be converted to the usual form. The resulting tree grammar could naturally be viewed as a recursive type definition 11 of the values the variables may assume. Further, standard algorithms may be employed to test for infiniteness, emptiness or linearity of the tree structure.In the second part selective updating is allowed, so an alternate semantics is introduced which more closely resembles traditional LISP implementations, and which is equivalent to the tree model for programs without selective updating. In this model data objects are directed graphs. We devise a finite approximation method which provides enough information to detect cell sharing and cyclic structures whenever they can possibly occur. This information can be used to recognize when the use of garbage collection or of reference counts may be avoided.The work reported in the second part of this paper extends that of Schwartz 17 and Cousot and Cousot 7. They have developed methods for determining whether the values of two or more variables share cells, while we provide information on the detailed structure of what is shared. The ability to detect cycles is also new. It also extends the work of Kaplan 13, who distinguishes only binary relations among the variables of a program, does not handle cycles, and does not distinguish selectors (so that his analysis applies to nodes representing sets rather than ordered tuples).