Modular Control-Flow Analysis with Rank 2 Intersection Types

The performance of optimising compilers crucially depends on the availability of controlflow information at compile time. For any first-order imperative program, such information is available via a flowchart constructed from the program text. Consequently, traditional dataflow analyses can be used to perform a series of compile-time program optimisations (Aho et al. 1986). For higher-order programs, however, a control-flow graph is often not evident from the program text. In these programs, even simple control structures like while loops are implemented using functions and computation is hidden under a single operation: function application. Hence, a number of control-flow analyses have been proposed (Jones 1981; Sestoft 1988; Shivers 1991; Jagannathan and Weeks 1995) for higher-order programs, all of which seek to answer the fundamental question: given a program point, what functions can be the result of evaluation at the program point? Given this information, the call-graph of a program can be constructed and a suite of compiler optimisations e.g., closure conversion (Steckler and Wand 1997; Dimock et al. 2001), useless variable elimination (Wand and Siveroni 1999), constant propagation, induction variable elimination (Shivers 1991) etc. can be enabled.