Algebraic Reconstruction of Types and E ects

We present the rst algorithm for reconstructing the types and e ects of expressions in the presence of rst class procedures in a polymorphic typed language. E ects are static descriptions of the dynamic behavior of expressions. Just as a type describes what an expression computes, an effect describes how an expression computes. Types are more complicated to reconstruct in the presence of e ects because the algebra of e ects induces complex constraints on both e ects and types. In this paper we show how to perform reconstruction in the presence of such constraints with a new algorithm called algebraic reconstruction, prove that it is sound and complete, and discuss its practical import. This research was supported by DARPA under ONR Contract N00014-89-J-1988.