CPS Transformation of Flow Information, Part II: Administrative Reductions

Abstract

We characterize the impact of a linear β-reduction on the result of a controlflow analysis. (By "a linear β-reduction" we mean the β-reduction of a linear λ-abstraction, i.e., of a λ-abstraction whose parameter occurs exactly once in its body.)As a corollary, we consider the administrative reductions of a Plotkin-style transformation into continuation-passing style (CPS), and how they affect the result of a constraint-based control-flow analysis and, in particular, the least element in the space of solutions. We show that administrative reductions preserve the least solution.

CPS transformation of flow information

“…Our formulation of the CPS transformation introduces 'administrative redexes' (Plotkin, 1975). In a different paper, Damian & Danvy (2001) have extended our work by showing that least solutions to the 0-CFA constraints are preserved by administrative reductions. Their results apply to any CPS transformation in which the administrative reductions are linear.…”

Syntactic accidents in program analysis: on the impact of the CPS transformation

“…For example, one can use a Plotkin-style CPS transformation with administrative reductions (Plotkin, 1975), or one can stage the CPS transformation as normalization to a monadic normal form followed by introduction of continuations (Hatcliff & Danvy, 1994). Palsberg & Wand (2002) use the former method, which can be extended to account for administrative reductions (Damian, 2001;Damian & Danvy, 2001a). We use the latter method here.…”

“…In that, they implicitly share our concern about syntactic accidents, even though their primary goal was to transfer Wand's pioneer results on the CPS transformation of types (Meyer & Wand, 1985;Wand, 1985) to the CPS transformation of flow types. Since then, we have shown that least solutions are preserved by administrative reductions of CPS-transformed programs (Damian, 2001;Damian & Danvy, 2001a).…”