We introduce a class of semantic domains, weak powerdomains , that are intended to serve as value spaces for abstract interpretations in which safety is a concern. We apply them to the analysis of PCF programs. In the classical abstract interpretation approach, abstract domains are constructed explicitly and the abstract semantics is then related to the concrete semantics. In the approach presented here, abstract domains are derived directly from concrete domains. The conditions for deriving the domains are intended to be as general as possible while still guaranteeing that the derived domain has sufficient structure so that it can be used as a basis for computing correct information about the concrete semantics. We prove three main theorems, the last of which ensures the correctness of abstract interpretation of PCF programs given safe interpretations of the constants. This generalizes earlier results obtained for the special case of strictness analysis.
We present a simple method for the general flow analysis of high-order functional programs. The method computes an abstraction of the program's runtime environment via a system of monotonic equations. As the environment can grow unbounded, we exploit patterns in the program's control structure (i.e., the call-tree) to determine some static partition of the environment, and merge points in the environment belonging to the same equivalent-class. High order functions are handled by embedding control information into closures. The method is proven correct with respect to a rewriting system based operational semantics. Various implementation issues are also considered.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.