No abstract

We present a survey of control-flow analysis of functional programs, which has been the subject of extensive investigation throughout the past 25 years. Analyses of the control flow of functional programs have been formulated in multiple settings and have led to many different approximations, starting with the seminal works of Jones, Shivers, and Sestoft. In this paper we survey control-flow analysis of functional programs by structuring the multitude of formulations and approximations and comparing them. * IT-parken,

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.

interpretation A recent line of work lifts particular verification and analysis methods to Software Product Lines (SPL). In an effort to generalize such case-by-case approaches, we develop a systematic methodology for lifting single-program analyses to SPLs using abstract interpretation. Abstract interpretation is a classical framework for deriving static analyses in a compositional, step-by-step manner. We show how to take an analysis expressed as an abstract interpretation and lift each of the abstract interpretation steps to a family of programs (SPL). This includes schemes for lifting domain types, and combinators for lifting analyses and Galois connections. We prove that for analyses developed using our method, the soundness of lifting follows by construction. The resulting variational abstract interpretation is a conceptual framework for understanding, deriving, and validating static analyses for SPLs. Then we show how to derive the corresponding variational dataflow equations for an example static analysis, a constant propagation analysis. We also describe how to approximate variability by applying variability-aware abstractions to SPL analysis. Finally, we discuss how to efficiently implement our method and present some evaluation results.