# 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…

## 8 Citations

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

- MathematicsFundam. Informaticae
- 2017

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.

### Sequent Calculus in the Topos of Trees

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### Dual-context calculi for modal logic

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The resulting systems are dual-context systems, in the style pioneered by Girard, Barber, Plotkin, Pfenning, Davies, and others, that derive natural deduction systems for the necessity fragment of various constructive modal logics by exploiting a pattern found in sequent calculi.

### Multimodal Dependent Type Theory

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The consistency of MTT is proved and canonicity is established through an extension of recent type-theoretic gluing techniques, which hold irrespective of the choice of mode theory, and thus apply to a wide variety of modal situations.

### Constructive Modalities with Provability Smack

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I overview the work of the Tbilisi school on intuitionistic modal logics of well-founded/scattered structures and its connections with contemporary Theoretical Computer Science. Fixed-point theorems…

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- Computer ScienceNII Shonan Meet. Rep.
- 2013

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