Effect systems extend classical type systems with effect information. Just as types describe the possible values of expressions, effects describe their possible evaluation behaviors. Effects, which appear in function types, introduce new constraints on the typability of expressions. To increase the exibility and accuracy of e ect systems, we present a new effect system based on subtyping. The subtype relation is induced by a subsumption relation on effects. This subtyping effect system avoids merging effect information together, thus collecting more precise effect information. We introduce a reconstruction algorithm which for any expression already typed with classical types, reconstructs its type and effect based on the subtype relation. The reconstruction algorithm is sound and complete w.r.t. the static semantics.

We present a novel technique for offine partial evaluation of functional languages with an ML-style typing discipline. Our program specialization method comprises a polymorphic binding-time analysis with polymorphic recursion. Based on the region calculus of Tofte and Talpin, we develop a binding-time analysis as a constraint analysis on top of region inference. Our insight is to regard binding times as properties of regions.