The untyped stack calculus and Bohm's theorem

@inproceedings{Carraro2013TheUS,
  title={The untyped stack calculus and Bohm's theorem},
  author={Alberto Carraro},
  booktitle={Workshop on Logical and Semantic Frameworks with Applications},
  year={2013}
}
  • Alberto Carraro
  • Published in
    Workshop on Logical and…
     28 March 2013
  • Physics
The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu. 
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Background Citations
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2 Citations

Reduction System for Extensional Lambda-mu Calculus

A conservative extension of the Λ μ-calculus is introduced, called Λμ cons, from which the open term model is straightforwardly constructed as a stream model, and for which it can define a reduction system satisfying several fundamental properties such as confluence, subject reduction, and strong normalization.

Extensional Models of Untyped Lambda-mu Calculus

It is proved that the extensional equality of the Lambda-mu calculus is equivalent to equality in stream combinatory algebras, and a combinatory calculus SCL is introduced, which is an abstraction-free system corresponding to the lambdas.

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