Termination analysis and call graph construction for higher-order functional programs

The analysis and verification of higher-order programs raises the issue of control-flow analysis for higher-order languages. The problem of constructing an accurate call graph for a higher-order program has been the topic of extensive research, and numerous methods for flow analysis, varying in complexity and precision, have been suggested. While termination analysis of higher-order programs has been studied, there has been little examination of the impact of call graph construction on the precision of termination checking. We examine the effect of various control-flow analysis techniques on a termination analysis for higher-order functional programs. We present a termination checking framework and instantiate this with three call graph constructions varying in precision and complexity, and illustrate by example the impact of the choice of call graph construction. Our second aim is to use the resulting analyses to shed light on the relationship between control-flow analyses. We prove precise inclusions between the classes of programs recognised as terminating by the same termination criterion over different call graph analyses, giving one of the first characterisations of expressive power of flow analyses for higher-order programs.