# Unifying Guarded and Unguarded Iteration

@inproceedings{Goncharov2017UnifyingGA, title={Unifying Guarded and Unguarded Iteration}, author={Sergey Goncharov and Lutz Schr{\"o}der and Christoph Rauch and Maciej Pir{\'o}g}, booktitle={FoSSaCS}, year={2017} }

Models of iterated computation, such as completely iterative monads, often depend on a notion of guardedness, which guarantees unique solvability of recursive equations and requires roughly that recursive calls happen only under certain guarding operations. On the other hand, many models of iteration do admit unguarded iteration. Solutions are then no longer unique, and in general not even determined as least or greatest fixpoints, being instead governed by quasi-equational axioms. Monads that…

## 15 Citations

### Coinductive Resumption Monads: Guarded Iterative and Guarded Elgot

- Computer ScienceCALCO
- 2019

We introduce a new notion of "guarded Elgot monad", that is a monad equipped with a form of iteration. It requires every guarded morphism to have a specified fixpoint, and classical equational laws…

### Guarded Traced Categories

- MathematicsFoSSaCS
- 2018

This work relates structural guardedness, determined by propagating guardedness along the operations of the category, to geometric guardedness phrased in terms of a diagrammatic language, and shows that partial traces in the category of Hilbert spaces are an instance of guarded traces.

### Coinductive resumption monads

- Computer Science
- 2019

A new notion of “guarded Elgot monad” is introduced, that is a monad equipped with a form of Elgot iteration, that requires every guarded morphism to have a specified fixpoint, and classical equational laws of iteration to be satisfied.

### A Semantics for Hybrid Iteration

- MathematicsCONCUR
- 2018

This paper uses an available notion of hybrid monad restricted to the category of sets, and modify it in order to obtain a suitable notion of guarded iteration with guardedness interpreted as progressiveness in time, motivated by the intention to capture Zeno behaviour in an arguably general and feasible way.

### Interaction trees: representing recursive and impure programs in Coq

- Computer ScienceProc. ACM Program. Lang.
- 2020

The termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given in an ITree-based denotational semantics is proved.

### Uniform Elgot Iteration in Foundations

- Computer ScienceICALP
- 2021

This work provides a generic categorical iterationbased notion of partiality, which is arguably the most basic one, and shows that the emerging free structures, which the authors dub uniform-iteration algebras enjoy various desirable properties, in particular, yield an equational lifting monad.

### Interaction Trees

- Computer Science
- 2019

The termination-sensitive correctness of a compiler from a simple imperative source language to an assembly-like target whose meanings are given in an ITree-based denotational semantics is proved.

### Implementing Hybrid Semantics: From Functional to Imperative (Extended Version)

- Computer Science
- 2020

A web-based prototype implementation to evaluate and inspect hybrid programs, in the spirit of GHCi for Haskell and UTop for OCaml, that formally follows the operational semantic rules and establishes a corresponding soundness and adequacy theorem.

### Implementing Hybrid Semantics: From Functional to Imperative

- Computer ScienceICTAC
- 2020

An imperative counterpart of HybCore is introduced, whose semantics is simpler and runnable, and yet intimately related with the semantics of HyBCore at the level of hybrid monads, and a corresponding soundness and adequacy theorem is established.

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