Funktionale Berechnung in einem uniform nebenläufigen Kalkül mit logischen Variablen

Abstract

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The thesis is written in German, but will be translated soon. English title: Functional Computation in a Uniformly Concurrent Calculus with Logic Variables. We present the delta-calculus, a model of uniformly concurrent computation. It integrates eager and lazy functional computation and describes the intended complexity behavior in both cases. We call concurrent computation uniformly concurrent, if result, termination and complexity are independent from the computation order. We establish theses properties for the delta-calculus by proving its uniform confluence. The delta-calculus extends to models of concurrent computation providing for consumable resources and indeterminism. Such are the gamma-calculus, a foundation of concurrent computation with constraints, and the pi-calculus, a successor of CCS based on channel communication. The delta-calculus is a relational calculus with procedural abstraction and application. It provides for communication over logic variables and for suspension on their instantiation. Both mechanisms come naturally with parallel composition and declaration. We embed the eager and the lazy lamda-calculus into the delta-calculus. Using explicit references we guarantee that functional arguments are evaluated at most once. Explicit references are a special form of logic variables. These are needed too for representing lazy functional control. We prove the adequacy of the embedding of the eager lamda-calculus with respect to termination and complexity. We conjecture that the embedding of the lazy lamda preserves termination and improves complexity.