Higher-order value flow graphs

Abstract

The concepts of value- and control-flow graphs are important for program analysis of imperative programs. An imperative value flow graph can be constructed by a single pass over the program text. No similar concepts exist for higher-order languages: we propose a method for constructing value flow graphs for typed higher-order functional languages. A higher-order value flow graph is constructed by a single pass over an explicitly typed program. By using standard methods, single source and single use value flow problems can be answered in linear time and all sources-all uses can be answered in quadratic time (in the size of the flow graph, which is equivalent to the size of the explicitly typed program). On simply typed programs, the precision of the resulting analysis is equivalent to closure analysis [10,11,8]. In practice, it is a reasonable assumption that typed programs are only bigger than their untyped equivalent by a constant factor, hence this is an asymptotic improvement over previous algorithms.

We extend the analysis to handle polymorphism, sum types and recursive types. As a consequence, the analysis can handle (explicit) dynamically typed programs. The analysis is polyvariant for polymorphic definitions.