9706572, and the US Air Force under grant F19628-95-C-0050 and a generous fellowship. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.

This paper proposes an operational semantics for value recursion in the context of monadic metalanguages. Our technique for combining value recursion with computational effects works uniformly for all monads. The operational nature of our approach is related to the implementation of recursion in Scheme and its monadic version proposed by Friedman and Sabry, but it defines a different semantics and does not rely on assignments. When contrasted to the axiomatic approach proposed by Erkök and Launchbury, our semantics for the continuation monad invalidates one of the axioms, adding to the evidence that this axiom is problematic in the presence of continuations. 1

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Motivated by some examples from functional programming, we propose a generalization of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that in a Freyd category, these notions are equivalent, generalizing a well-known theorem relating traces and Conway operators in cartesian categories.

Mutual dependencies between objects arise frequently in programs, and programmers must typically resort to manually filling “initialization holes ” to help construct the corresponding object graphs, i.e. null values and/or explicitly mutable locations. This report describes a “base-line ” proposal for a generalized form of value recursion in an ML-like language called initialization graphs, where value recursion is given the simplistic semantics of a graph of lazy computations whose nodes are sequentially forced, with uses of recursive values checked for initialization-soundness at runtime. We then develop examples using this mechanism to show how problematic the issue of value recursion is for ML-like languages, and in particular how sophisticated reactive objects cannot be defined in the language without using initialization holes, and how this forces ML programmers to break abstraction boundaries. At the same time we show how OO languages rely extensively on null pointers during initialization. We propose that a general, semi-safe mechanism allows value recursion to be used in conjunction with existing sophisicated abstract APIs such GUI libraries, and allows freshly defined APIs to be both abstract and yet not require clients to use explicit initialization holes. We propose that the initialization mechanism permits more programs to be expressed in the mutation-free fragment of ML, though we do not formally prove this result. 1

In the interest of designing a recursive module extension to ML that is as simple and general as possible, we study the important subproblem of how to support recursive definitions of effectful expressions. Effects seem to necessitate a Scheme-style backpatching semantics of recursion, which typically results in a performance penalty since all recursive references must check whether or not the recursive variable has been backpatched yet.

In the interest of designing a recursive module extension to ML that is as simple and general as possible, we propose a novel type system for general recursion over effectful expressions. The presence of effects seems to necessitate a backpatching semantics for recursion based on Scheme's. Our type system ensures statically that recursion is well-founded (that the body of a recursive expression will evaluate without attempting to access the undefined recursive variable), which avoids some unnecessary run-time costs associated with backpatching. To ensure well-founded recursion in the presence of multiple recursive variables and separate compilation, we track the usage of individual recursive variables, represented statically by "names". So that our type system may eventually be integrated smoothly into ML's, reasoning involving names is only required inside code that uses our recursive construct and does not need to infect existing ML code.