Machine" [BB90], except that there are no "cooling" and "heating" transitions (the process sets of this semantics can be thought of as perpetually "hot" solutions). The concurrent evaluation relation extends "7\Gamma!" to finite sets of terms (i.e., processes) and adds additional rules for process creation, channel creation, and communication. We assume a set of process identifiers, and define the set of processes and process sets as: ß 2 ProcId process IDs p = hß; ei 2 Proc = (ProcId \Theta Exp) processes P 2 Fin(Proc) process sets We often write a process as hß; E[e]i, where the evaluation context serves the role of the program counter, marking the current state of evaluation. Definition4. A process set P is well-formed if for all hß; ei 2 P the following hold: -- FV(e) = ; (e is closed), and -- there is no e 0 6= e, such that hß; e 0 i 2 P. It is occasionally useful to view well-formed process sets as finite maps from ProcId to Exp. If P is a finite set of process state...

This paper describes eXene, a user interface toolkit implemented in a concurrent extension of Standard ML. The design and use of eXene is inextricably woven with the presence of multiple threads and a high-level language. These features replace the object-oriented design of most toolkits, and provide a better basis for dealing with the complexities of user interfaces, especially concerning such aspects as type safety, extensibility, component reuse and the balance between the user interface and other parts of the program. 1

The powerful abstraction mechanisms of functional programming languages provide the means to develop domain-specific programming languages within the language itself. Typically, this is realised by designing a set of combinators (higher-order reusable programs) for an application area, and by constructing individual applications by combining and coordinating individual combinators. This paper is concerned with a successful example of such an embedded programming language, namely Fudgets, a library of combinators for building graphical user interfaces in the lazy functional language Haskell. The Fudget library has been used to build a number of substantial applications, including a web browser and a proof editor interface to a proof checker for constructive type theory. This paper develops a semantic theory for the non-deterministic stream processors that are at the heart of the Fudget concept. The interaction of two features of stream processors makes the development of such a semantic theory problematic: (i) the sharing of computation provided by the lazy evaluation mechanism of the underlying host language, and (ii) the addition of non-deterministic choice needed to handle the natural concurrency that reactive applications entail We demonstrate that this combination of features in a higher-order functional language can be tamed to provide a tractable semantic theory and induction principles suitable for reasoning about contextual equivalence of Fudgets.

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