On flowchart theories Part I. The deterministic case

Ştefănescu, Gheorghe

doi:10.1016/0022-0000(87)90011-0

Cited by 29 publications

(8 citation statements)

References 16 publications

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“…We generalize here the known fact that the double dagger identity can be replaced by the Bekič identity (also known as the pairing identity) among axioms of unguarded Conway theories (see, e.g., [32], [9, Ch. 6.2, 6.8-6.9], [16], [19,Ch.…”

Section: The Bekič Identitymentioning

confidence: 98%

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

Milius

Litak

2017

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Motivated by the recent interest in models of guarded (co-)recursion, we study their equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom andÉsik. 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 by a unique dagger operation generalizes to the guarded setting. We also introduce the notion of guarded trace operator on a category, and we prove that guarded trace and guarded fixpoint operators are in one-to-one correspondence. Our results are intended as first steps leading, hopefully, towards future description of classifying theories for guarded recursion.

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Section: The Bekič Identitymentioning

confidence: 98%

“…For unguarded fixpoint operators, it is well-known that the four Conway axioms are equivalent to dinaturality, the parameter and double dagger identities (D, P, † †), in other words, dinaturality can replace the fixpoint and composition identities (see, e.g., [32], [9, Ch. 6.2, 6.8-6.9], [16], [19,Ch.…”

Section: Dinaturalitymentioning

confidence: 99%

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

Milius

Litak

2017

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“…Algebraic structures based on a central operation of iteration, or feedback -inspired by flowcharts and program schemata -have appeared rather early in computer science, see, e.g., [29,4,89,90,63] and [12], that offers for a thorough exposition of so-called 'iteration theory' and more references. The advent of traced monoidal categories [50], i.e., monoidal categories equipped with a feedback operation completely analogous to the one considered in CM has recently revived interest in using such abstract structures in semantics of computation, as e.g., in [1, 53, 40, 41].…”

Section: Discussionmentioning

confidence: 99%