The untyped stack calculus and Bohm's theorem

@inproceedings{Carraro2012TheUS,
  title={The untyped stack calculus and Bohm's theorem},
  author={Alberto Carraro},
  booktitle={LSFA},
  year={2012}
}
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 lazy lambda calculus in a concurrency scenario

  • D. Sangiorgi
  • Mathematics
    [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science
  • 1992
It is shown that maximal discrimination is obtained when all operators are considered and that this discrimination coincides with the one given by Z+ and that the adoption of certain non-deterministic operators is sufficient and necessary to induce it.

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 ...

Classical logic, continuation semantics and abstract machines

The goal of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator.

Introduction to combinators and λ-calculus

These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions.