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.

The Fudgets system is a toolkit for developing graphical applications in the lazy functional programming language Haskell. In this paper we develop an operational semantics for a subset of this system, inspired by ideas from concurrency theory. A semantic theory based on bisimulation is defined and shown to be a congruence. We consider two applications of this theory: firstly, some equational rules useful for reasoning about Fudget programs are verified; secondly, we show how the operational semantics can be used to check the correctness of implementations of the Fudgets system. 1 Introduction The Fudgets system [11] is one of a number of systems for building graphical applications in lazy functional programming languages such as Haskell [24]. A program in the Fudgets system is composed of a collection of fudgets, which correspond closely to concurrent processes in a process network. Fudgets can communicate with one another and also with the window system, and correspond to graphical...