In the paper a notion of parallel program scheme is introduced. Interpretations of such schemes are defined in two steps: first, independently of instructions meaning, to each scheme a language over the set of all instructions is assigned; second, for a given interpretation of instructions, to each such a language a function is assigned, being the intended interpretation of the scheme. This construction allows to obtain a satisfactory interpretation of parallel components of recursive schemes. The parallel composition of languages is introduced and some properties of this notion are given. It is shown how the theory of recursive procedures can be extended to procedures containing parallel operations. An example shows an application of the above approach.


Parallel Composition Sequential Scheme Execution Sequence Program Scheme Parallel Expression 


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    Strachey, C. and Wadsworth, C., Continuations:A mathematical semantics for handling full jumps, Technical Monograph RPG-11, Oxford University Computing Laboratory (1974)Google Scholar
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    Blikle, A., Equations in the space of languages, CC PAS Reports, Warsaw, (1973)Google Scholar
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    Scott, D. and Strachey, C., Toward a mathematical semantics for computer languages, Technical Monograph RPG-6, Oxford University Computing Laboratory (1971).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Antoni Mazurkiewicz
    • 1
  1. 1.Computation Centre of Polish Academy of SciencesWarsaw, PKiNPoland

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