# 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} }

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.

## 2 Citations

### Reduction System for Extensional Lambda-mu Calculus

- Mathematics, Computer ScienceRTA-TLCA
- 2014

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

- Mathematics, Computer ScienceCL&C
- 2012

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

- Computer ScienceLSFA
- 2012

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

- MathematicsTLCA
- 2011

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

- Mathematics, PhysicsJournal of Symbolic Logic
- 2001

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

- Mathematics, Computer ScienceCL&C
- 2012

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

- MathematicsStudies in logic and the foundations of mathematics
- 1985

### Typing streams in the Λμ-calculus

- MathematicsTOCL
- 2010

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

- MathematicsSIAM J. Comput.
- 1976

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

- Mathematics
- 2009

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

- Computer ScienceRCLP
- 1991

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

- Computer ScienceLICS
- 2005

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.