Reasoning about Continuations with Control E ects

We present a new static analysis method for rst-class continuations that uses an e ect system to classify the control domain behavior of expressions in a typed polymorphic language. We introduce two new control effects, goto and comefrom, that describe the control ow properties of expressions. An expression that does not have a goto e ect is said to be continuation following because it will always call its passed return continuation. An expression that does not have a comefrom effect is said to be continuation discarding because it will never preserve its return continuation for later use. Unobservable control e ects can be masked by the e ect system. Control e ect soundness theorems guarantee that the e ects computed statically by the e ect system are a conservative approximation of the dynamic behavior of an expression. The e ect system that we describe performs certain kinds of control ow analysis that were not previously feasible. We discuss how this analysis can enable a variety of compiler optimizations, including parallel expression scheduling in the presence of complex control structures, and stack allocation of continuations. The e ect system we describe has been implemented as an extension to the FX-87 programming language. This research was supported by the Defense Advanced Research Projects Agency of the Department of Defense and was monitored by the O ce of Naval Research under contract number N0001483-K-0125. CAI, Ecole des Mines, 60 bvd Saint-Michel, 75272, PARIS, France (E-mail: [email protected]) LCS, Massachusetts Institute of Technology, 545 Technology Square, Cambridge, MA 02139, USA (E-mail: [email protected]) Categories and Subject Descriptions: D.1.3 [Programming Techniques] { Concurrent Programming: E ect systems; D.1.m [Programming Techniques] { Miscellaneous: First-class continuations; D.3.1 [Programming Languages] { Formal De nitions and Theory; D.3.3 [Programming Languages] { Language Constructs: Control structures, e ect systems; D.3.4 [Programming Languages] { Processors: Compilers, optimization. General Terms: Languages, Theory, Veri cation. Additional