Reflexive Scott Domains are Not Complete for the Extensional Lambda Calculus

@article{Carraro2009ReflexiveSD,
  title={Reflexive Scott Domains are Not Complete for the Extensional Lambda Calculus},
  author={A. Carraro and A. Salibra},
  journal={2009 24th Annual IEEE Symposium on Logic In Computer Science},
  year={2009},
  pages={91-100}
}
  • A. Carraro, A. Salibra
  • Published 2009
  • Mathematics, Computer Science
  • 2009 24th Annual IEEE Symposium on Logic In Computer Science
A longstanding open problem is whether there exists a model of the untyped lambda calculus in the category CPO of complete partial orderings and Scott continuous functions, whose theory is exactly the least lambda-theory lambda-beta or the least extensional lambda-theory lambda-beta-eta. In this paper we analyze the class of reflexive Scott domains, the models of lambda-calculus living in the category of Scott domains (a full subcategory of CPO). The following are the main results of the paper… Expand
10 Citations
Minimal lambda-theories by ultraproducts
Unfixing the Fixpoint: The Theories of the λY-Calculus
Easy lambda-terms are not always simple
On Linear Information Systems
Refining Properties of Filter Models: Sensibility, Approximability and Reducibility
Problem 19
Observational Equivalence and Full Abstraction in the Symmetric Interaction Combinators
  • Damiano Mazza
  • Mathematics, Computer Science
  • Log. Methods Comput. Sci.
  • 2009
Models and theories of pure and resource lambda calculi
Scott Is Always Simple

References

SHOWING 1-10 OF 28 REFERENCES
Topological incompleteness and order incompleteness of the lambda calculus
Lambda Theories of Effective Lambda Models
Uncountable Limits and the lambda Calculus
Order-incompleteness and finite lambda reduction models
  • P. Selinger
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2003
Graph lambda theories†
Set-Theoretical and Other Elementary Models of the lambda-Calculus
  • G. Plotkin
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 1993
On the construction of stable models of untyped lambda-calculus
  • R. Kerth
  • Computer Science, Mathematics
  • Theor. Comput. Sci.
  • 2001
Stable Models of Typed lambda-Calculi
...
1
2
3
...