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The expressive power of Structural Operational Semantics with explicit assumptions

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Types for Proofs and Programs (TYPES 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 806))

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Abstract

We explore the expressive power of the formalism called Natural Operational Semantics, NOS, introduced by Burstall and Honsell for defining the operational semantics of programming languages. This formalism is derived from the Natural Semantics of Despeyroux and Kahn. It arises if we take seriously the possibility of deriving assertions in Natural Semantics under assumptions, i.e. using hypothetico-general premises in the sense of Martin-Löf. We investigate to what extent we can reduce to hypothetical premises the notions of store and environment of Plotkin's Structural Operational Semantics. We use this formalism to define the semantics of a functional language which features commands, blocks, procedures, complex declarations, structures and Abstract Data Types. We give the NOS together with the denotational semantics and prove the adequacy of the former w.r.t. the latter. We discuss some other difficulties which arose in the previous treatment of variables in connection with procedures.

Natural Operational Semantics can be easily encoded in formal systems based on λ-calculus type-checking, such as the Edinburgh Logical Framework. We briefly investigate this and discuss some of the design choices.

Work partially supported by Esprit BRA 6453, Types for Proofs and Programs, and italian MURST 40%, 60% grants.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Udine, via Zanon, 6, I 33100, Udine, Italy

    Marino Miculan

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  1. Marino Miculan
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Henk Barendregt Tobias Nipkow

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© 1994 Springer-Verlag Berlin Heidelberg

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Miculan, M. (1994). The expressive power of Structural Operational Semantics with explicit assumptions. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_80

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  • DOI: https://doi.org/10.1007/3-540-58085-9_80

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