Guard Your Daggers and Traces: On The Equational Properties of Guarded (Co-)recursion

@inproceedings{Milius2013GuardYD,
  title={Guard Your Daggers and Traces: On The Equational Properties of Guarded (Co-)recursion},
  author={Stefan Milius and Tadeusz Litak},
  booktitle={FICS},
  year={2013}
}
Motivated by the recent interest in models of guarded (co-)recursion we study its equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and Esik. Models of these axioms include both standard (e.g., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees studied by Birkedal et al. We show that the standard result on the satisfaction of all Conway axioms… 

Guard Your Daggers and Traces: Properties of Guarded (Co-)recursion

TLDR
It is shown that the standard result on the satisfaction of all Conway axioms by a unique dagger operation generalizes to the guarded setting and it is proved that guarded trace and guarded fixpoint operators are in one-to-one correspondence.

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