8 research outputs found
Representing Guardedness in Call-By-Value
Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles in various settings. In its most general form, the guardedness discipline applies to general symmetric monoidal categories and further specializes to Cartesian and co-Cartesian categories, where it governs guarded recursion and guarded iteration respectively. Here, even more specifically, we deal with the semantics of call-by-value guarded iteration. It was shown by Levy, Power and Thielecke that call-by-value languages can be generally interpreted in Freyd categories, but in order to represent effectful function spaces, such a category must canonically arise from a strong monad. We generalize this fact by showing that representing guarded effectful function spaces calls for certain parametrized monads (in the sense of Uustalu). This provides a description of guardedness as an intrinsic categorical property of programs, complementing the existing description of guardedness as a predicate on a category
Unguarded Recursion on Coinductive Resumptions
We study a model of side-effecting processes obtained by starting from a
monad modelling base effects and adjoining free operations using a cofree
coalgebra construction; one thus arrives at what one may think of as types of
non-wellfounded side-effecting trees, generalizing the infinite resumption
monad. Correspondingly, the arising monad transformer has been termed the
coinductive generalized resumption transformer. Monads of this kind have
received some attention in the recent literature; in particular, it has been
shown that they admit guarded iteration. Here, we show that they also admit
unguarded iteration, i.e. form complete Elgot monads, provided that the
underlying base effect supports unguarded iteration. Moreover, we provide a
universal characterization of the coinductive resumption monad transformer in
terms of coproducts of complete Elgot monads.Comment: 47 pages, extended version of
http://www.sciencedirect.com/science/article/pii/S157106611500079
How to kill epsilons with a dagger: a coalgebraic take on systems with algebraic label structure
We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or ϵ-transitions. Our approach employs monads with a parametrized fixpoint operator †to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.Funded by the ERDF through the Programme COMPETE and by the Portuguese Foundation for Science and Technology, project ref. FCOMP-01-0124-FEDER-020537 and SFRH/BPD/71956/2010. Acknowledge support by project ANR 12IS0 2001 PACE
Representing Guardedness in Call-by-Value and Guarded Parametrized Monads
Like the notion of computation via (strong) monads serves to classify various
flavours of impurity, including exceptions, non-determinism, probability, local
and global store, the notion of guardedness classifies well-behavedness of
cycles in various settings. In its most general form, the guardedness
discipline applies to general symmetric monoidal categories and further
specializes to Cartesian and co-Cartesian categories, where it governs guarded
recursion and guarded iteration respectively. Here, even more specifically, we
deal with the semantics of call-by-value guarded iteration. It was shown by
Levy, Power and Thielecke that call-by-value languages can be generally
interpreted in Freyd categories, but in order to represent effectful function
spaces, such a category must canonically arise from a strong monad. We
generalize this fact by showing that representing guarded effectful function
spaces calls for certain parametrized monads (in the sense of Uustalu). This
provides a description of guardedness as an intrinsic categorical property of
programs, complementing the existing description of guardedness as a predicate
on a category.Comment: Extended version of
https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.3