Abstract. The purpose of this paper is to present four basic methods for interpretation: – simplification-based separate analysis; – worst-case separate analysis; – separate analysis with (user-provided) interfaces; – symbolic relational separate analysis; as well as a fifth category which is essentially obtained by composition of the above separate local analyses together with global analysis methods. 1

In this paper we present a generic constraint domain for symbolic modular analysis. The idea is that the semantics of a module can be approximated by a set of relations symbolically linking the input, output and local variables. We show how this result is correct w.r.t. a trace semantics, and how it can be used to perform an (incremental) modular analysis. We claim that our construction generalizes existing modular analyses by showing how well-known modular analyses can be instantiated in our framework.

discover properties of dynamic and/or mutable structures. We ask, “Is there an equivalent to shape analysis for purely functional programs, and if so, what ‘shapes ’ does it discover? ” By treating binding environments as dynamically allocated structures, by treating bindings as addresses, and by treating value environments as heaps, we argue that we can analyze the “shape ” of higher-order functions. To demonstrate this, we enrich an abstract-interpretive control-flow analysis with principles from shape analysis. In particular, we promote “anodization ” as a way to generalize both singleton abstraction and the notion of focusing, and we promote “binding invariants ” as the analog of shape predicates. Our analysis enables two optimizations known to be beyond the reach of control-flow analysis (globalization and super-β inlining) and one previously unknown optimization (higher-order rematerialization). 1