A Counterexample to Tensorability of Effects
@inproceedings{Goncharov2011ACT, title={A Counterexample to Tensorability of Effects}, author={Sergey Goncharov and Lutz Schr{\"o}der}, booktitle={Conference on Algebra and Coalgebra in Computer Science}, year={2011} }
Monads are widely used in programming semantics and in functional programming to encapsulate notions of side-effect, such as state, exceptions, input/ output, or continuations. One of their advantages is that they allow for a modular treatment of effects, using composition operators such as sum and tensor. Here, the sum represents the non-interacting combination of effects, while the tensor imposes a high degree of interaction in the shape of a commutation law. Although many important effects…
2 Citations
Powermonads and Tensors of Unranked Effects
- Computer Science2011 IEEE 26th Annual Symposium on Logic in Computer Science
- 2011
The class of uniform effects is introduced, which includes unbounded nondeterminism and continuations, and it is proved that the tensor does always exist if one of the component effects is uniform, thus in particular improving on previous results on tensoring with continuations.
Exploring the Boundaries of Monad Tensorability on Set
- MathematicsLog. Methods Comput. Sci.
- 2013
It is shown that the tensor of two monads need not in general exist by presenting two counterexamples, one of them involving finite powerset (i.e. the theory of join semilattices); it is also shown that tensors with bounded powerset monads do exist from countable powerset upwards.
References
SHOWING 1-10 OF 25 REFERENCES
Powermonads and Tensors of Unranked Effects
- Computer Science2011 IEEE 26th Annual Symposium on Logic in Computer Science
- 2011
The class of uniform effects is introduced, which includes unbounded nondeterminism and continuations, and it is proved that the tensor does always exist if one of the component effects is uniform, thus in particular improving on previous results on tensoring with continuations.
Kleene Monads: Handling Iteration in a Framework of Generic Effects
- Computer ScienceCALCO
- 2009
Kleene monads are introduced, which additionally feature nondeterministic choice and Kleene star, and a metalanguage and a sound calculus are provided for Kleene monad, the metalanguage of control and effects, which is the natural joint extension of Kleene algebra and the metalanguages of effects.
Domain theory
- MathematicsLICS 1995
- 1995
bases were introduced in [Smy77] where they are called “R-structures”. Examples of abstract bases are concrete bases of continuous domains, of course, where the relation≺ is the restriction of the…
The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads
- MathematicsComputation, Meaning, and Logic
- 2007
Notions of Computation Determine Monads
- MathematicsFoSSaCS
- 2002
This work focuses on semantics for global and local state, showing that taking operations and equations as primitive yields a mathematical relationship that reflects their computational relationship.
Handbook of Weighted Automata
- Computer Science
- 2009
This book covers all the main aspects of weighted automata and formal power series methods, ranging from theory to applications, and presents a detailed survey of the state of the art and pointers to future research.