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. 

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.

References

SHOWING 1-10 OF 31 REFERENCES

The stack calculus

A functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry–Howard correspondence for Classical Logic can be faithfully encoded and is a sound and complete system for full implicational Classical Logic.

Böhm's Theorem for Resource Lambda Calculus through Taylor Expansion

An equivalence relation is defined on the terms, which is significant that this equivalence extends the usual η-equivalence and is related to Ehrhard's Taylor expansion - a translation mapping terms into series of finite resources.

λμ-calculus and Böhm's theorem

It is shown that Böhm's theorem fails in this calculus, an extension of the λ-calculus that has been introduced by M Parigot to give an algorithmic content to classical proofs.

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.

The lambda calculus - its syntax and semantics

  • H. Barendregt
  • Mathematics
    Studies in logic and the foundations of mathematics
  • 1985

Typing streams in the Λμ-calculus

The meta-theory of untyped Λμ-calculus is investigated by proving confluence of the calculus and characterizing the basic observables for the Separation theorem, and it is proved that strong normalization and type preservation hold.

The Relation Between Computational and Denotational Properties for Scott's Dinfty-Models of the Lambda-Calculus

A prominent feature of the lattice-theoretic approach to the theory of computation due to D. Scott is the construction of solutions for isomorphic domain equations. One of the simplest of these is ...

Standardization and Böhm trees for Λ μ-calculus

Λμ-calculus is an extension of Parigot's λμ-calculus which (i) satis es Separation theorem: it is Böhm-complete, (ii) corresponds to CBN delimited control and (iii) is provided with a stream

Free Deduction: An Analysis of "Computations" in Classical Logic

Cut-elimination is a central tool in proof-theory, but also a way of computing with proofs used for constructing new functional languages. As such it depends on the properties of the deduction system

Separation with Streams in the lambdaµ-calculus

The theorem is proved and it is described how /spl Lambda//spl mu/-calculus can be considered as a calculus of terms and streams and Separation is illustrated in showing how in Parigot's Lambda- mu-calculus it is possible to separate the counter-example used by David & Py.