Non-deterministic Böhm trees
نویسنده
چکیده
Lambda calculus is well established as the formal model of functional programming. Non-determinism is an interesting conceptual issue, often considered in process-calculi. It is interesting to mix lambda-calculus and non-determinism, firstly because programmers use functional programming but also concurrent methods, networks and multi-users systems, secondly as a step towards more complex languages as for example those providing pattern-matching features. That is why we add to an already known language a piece of uncertainty. Thus we are able to study non-determinism by using the tools for lambda-calculus, all its background and the same rigor. In order to remain as general as possible, the considered language will be the untyped lambda-calculus endowed with a simple choice operation between terms. We call it the non-deterministic lambdacalculus. Our motivation is to have a comprehensive study of a basic language with non-determinism, its syntax and its operational and denotational semantics, following and extending the work of de’Liguoro and Piperno [1]. As in [1], we choose a natural and simple non-deterministic lambda calculus, where terms are defined as follows:
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