A Calculational Approach to Control-Flow Analysis by Abstract Interpretation

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.