Exponentials with Infinite Multiplicities

@inproceedings{Carraro2010ExponentialsWI,
  title={Exponentials with Infinite Multiplicities},
  author={A. Carraro and T. Ehrhard and A. Salibra},
  booktitle={CSL},
  year={2010}
}
Given a semi-ring with unit which satisfies some algebraic conditions, we define an exponential functor on the category of sets and relations which allows to define a denotational model of differential linear logic and of the lambda-calculus with resources. We show that, when the semi-ring has an element which is infinite in the sense that it is equal to its successor, this model does not validate the Taylor formula and that it is possible to build, in the associated Kleisli cartesian closed… Expand
13 Citations
An Infinitary Model of Linear Logic
The Free Exponential Modality of Probabilistic Coherence Spaces
What is a categorical model of the differential and the resource λ-calculi?
Constructing differential categories and deconstructing categories of games
Essential and relational models †
Constructing Differential Categories and Deconstructing Categories of Games
Normalizing the Taylor expansion of non-deterministic λ-terms, via parallel reduction of resource vectors
  • L. Vaux
  • Computer Science, Mathematics
  • Log. Methods Comput. Sci.
  • 2019
...
1
2
...

References

SHOWING 1-10 OF 22 REFERENCES
Not Enough Points Is Enough
Uniformity and the Taylor expansion of ordinary lambda-terms
Applying Universal Algebra to Lambda Calculus
Domains and lambda-calculi
  • R. Amadio, P. Curien
  • Computer Science, Mathematics
  • Cambridge tracts in theoretical computer science
  • 1998
Extensional Rewriting with Sums
Interpreting a finitary pi-calculus in differential interaction nets
Differential interaction nets
The differential lambda-calculus
...
1
2
3
...