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Fragments of ML Decidable by Nested Data Class Memory Automata

  • Conrad Cotton-Barratt
  • David Hopkins
  • Andrzej S. Murawski
  • C. -H. Luke Ong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)

Abstract

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a “bad variable” construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment, RML\(^{\rm P-Str}_{2\vdash 1}\), consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument.

Keywords

Type Sequent Free Variable Partial Evaluation Initial Move Nest Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Conrad Cotton-Barratt
    • 1
  • David Hopkins
    • 1
  • Andrzej S. Murawski
    • 2
  • C. -H. Luke Ong
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordOxfordUK
  2. 2.Department of Computer ScienceUniversity of WarwickCoventryUK

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