Formulae-as-types for an involutive negation

@article{MunchMaccagnoni2014FormulaeastypesFA,
  title={Formulae-as-types for an involutive negation},
  author={Guillaume Munch-Maccagnoni},
  journal={Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  year={2014}
}
  • Guillaume Munch-Maccagnoni
  • Published 2014
  • Computer Science, Mathematics
  • Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Negation is not involutive in the λC calculus because it does not distinguish captured stacks from continuations. We show that there is a formulae-as-types correspondence between the involutive negation in proof theory, and a notion of high-level access to the stacks studied by Felleisen and Clements. We introduce polarised, untyped, calculi compatible with extensionality, for both of classical sequent calculus and classical natural deduction, with connectives for an involutive negation. The… Expand
A functional functional interpretation
Logical relations for coherence of effect subtyping
Polarised Intermediate Representation of Lambda Calculus with Sums
Compiling With Classical Connectives
An extended type system with lambda-typed lambda-expressions (extended version)
  • Matthias Weber
  • Computer Science, Mathematics
  • Log. Methods Comput. Sci.
  • 2020
Resource Polymorphism
Dialogue Categories and Chiralities
...
1
2
...

References

SHOWING 1-10 OF 12 REFERENCES
A New Deconstructive Logic: Linear Logic
Completeness of Continuation Models for λ μ-Calculus
A type-theoretic foundation of delimited continuations
Call-by-value is dual to call-by-name
An approach to call-by-name delimited continuations
The duality of computation
Realizability in classical logic
Lambda-calculus, types and models
  • J. Krivine
  • Computer Science, Mathematics
  • Ellis Horwood series in computers and their applications
  • 1993
Control reduction theories: the benefit of structural substitution
Separation with Streams in the Λμ-calculus
  • In LICS,
  • 2005
...
1
2
...