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Abstract.A tension in language design has been between simple semantics on the one hand, and rich possibilities for side-effects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs. Monads have been used to solve long-standing problems such as adding pointers and assignment, inter-language working, and exception handling to Haskell, without compromising its purely functional semantics. The course introduces monads, effects, and exemplifies their applications in programming (Haskell) and in compilation (MLj). The course presents typed metalanguages for monads and related categorical notions, and then describes how they can be further refined by introducing effects.

In earlier work, we used a typed function calculus, XML, with dependent types to analyze several aspects of the Standard ML type system. In this paper, we introduce a refinement of XML with a clear compile-time/run-time phase dislinclion, and a direct compile-time type checking algorithm.The calculus uses a finer separation of types into universes than XML and enforces the phase distinction using a nonstandard equational theory for module and signature expressions. While unusual from a type-theoretic point of view, the nonsta.ndard equationa. theory arises naturally from the well-known GrotNhendieck construction on an indexed category.