Trace-Based Coinductive Operational Semantics for While

Big-Step and Small-Step, Relational and Functional Styles
  • Keiko Nakata
  • Tarmo Uustalu
Conference paper

DOI: 10.1007/978-3-642-03359-9_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5674)
Cite this paper as:
Nakata K., Uustalu T. (2009) Trace-Based Coinductive Operational Semantics for While. In: Berghofer S., Nipkow T., Urban C., Wenzel M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg

Abstract

We present four coinductive operational semantics for the While language accounting for both terminating and non-terminating program runs: big-step and small-step relational semantics and big-step and small-step functional semantics. The semantics employ traces (possibly infinite sequences of states) to record the states that program runs go through. The relational semantics relate statement-state pairs to traces, whereas the functional semantics return traces for statement-state pairs. All four semantics are equivalent. We formalize the semantics and their equivalence proofs in the constructive setting of Coq.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Keiko Nakata
    • 1
  • Tarmo Uustalu
    • 1
  1. 1.Institute of Cybernetics at Tallinn University of TechnologyTallinnEstonia

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