Abstract
We study the semantics of functional languages on streams such as Turner's SASL or KRC. The basis of these languages is recursive equations for (functions on) finite or infinite sequences. The paper presents a start towards a mathematical (denotational) description of such languages using tools from metric topology. The description is based on the Banach fixed point theorem and a restricted version of a typed lambda calculus. To a system of recursive stream (function) declarations a system of functions is associated in an appropriate topological domain. These functions have to be contracting in certain arguments and non distance increasing in others; a syntax is designed which ensures the right interplay between these conditions. Nondeterminism is handled by considering compact sets of streams, and preservation of compactness is another important technical issue. Not all concepts in a language such as KRC are covered, and some indications on possible extensions of the framework are provided.
Supported in part by ESPRIT project 415: Parallel Architectures and Languages
Supported by the Netherlands Organisation for the Advancement of Pure Research (Z.W.O.), grant 125-20-04.
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de Bakker, J.W., Kok, J.N. (1985). Towards a uniform topological treatment of streams and functions on streams. In: Brauer, W. (eds) Automata, Languages and Programming. ICALP 1985. Lecture Notes in Computer Science, vol 194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015739
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DOI: https://doi.org/10.1007/BFb0015739
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