A Calculational Approach to Control-Flow Analysis by Abstract Interpretation

Abstract

Abstract. We present a derivation of a control-flow analysis by abstract interpretation. Our starting point is a transition system semantics defined as an abstract machine for a small functional language in continuation-passing style. We obtain a Galois connection for abstracting the machine states by composing Galois connections, most notable an independent-attribute Galois connection on machine states and a Galois connection induced by a closure operator associated with a constituentparts relation on environments. We calculate abstract transfer functions by applying the state abstraction to the collecting semantics, resulting in a novel characterization of demand-driven 0-CFA.

Control-flow analysis of function calls and returns by abstract interpretation

“…This analysis has been derived in the same way as the ANF CFA was derived in the previous section, using the stack-less CE-machine of Flanagan et al [9] as operational semantics. Details of the derivation can be found in Midtgaard and Jensen [10]. We prove that the ANF analysis derived in this article achieves the same precision as obtained by first transforming a program into CPS and then using the CPS analysis.…”

“…In an earlier paper Spoto and Jensen [42] investigated class analysis of object-oriented programs as a Galois connection-based abstraction of a trace semantics. In a recent article [10], the authors systematically derived a CPS-based CFA from the collecting semantics of a stack-less machine. While investigating how to derive a corresponding direct-style analysis we discovered the mismatch between the computed return information.…”

“…Preliminary versions of the results reported in this article were published at SAS 2008 [10] and ICFP 2009 [11]. The present article is a revised version A 1 × .…”

Certified Abstract Interpretation with Pretty-Big-Step Semantics

“…Cousot [8] has shown how to systematically derive static analyses for an imperative language using the principles of abstract interpretation. Midtgaard and Jensen [15,16] used a similar approach for calculating control-flow analyses for functional languages from operational semantics in the form of abstract machines. Van Horn and Might [22] show how a series of analyses for functional languages can be derived from abstract machines.…”

Calculating Graph Algorithms for Dominance and Shortest Path

“…Finally, one can observe that E ,≥ is a complete lattice with the meet operation provided by (33), ⊥ E = λv.∞ and ⊤ E = λv.0. This follows, e.g, from realizing that N ∪ {∞}, ≥ is a complete lattice 9 that can be lifted into a complete lattice over functions with the above pointwise operations.…”