The λ-calculus in the π-calculus†

@article{Cai2011TheI,
  title={The $\lambda$-calculus in the $\pi$-calculus†},
  author={Xiaojuan Cai and Yuxi Fu},
  journal={Mathematical Structures in Computer Science},
  year={2011},
  volume={21},
  pages={943 - 996}
}
  • Xiaojuan Cai, Yuxi Fu
  • Published 19 May 2011
  • Computer Science
  • Mathematical Structures in Computer Science
A general approach is proposed for transforming objects to methods on the fly in the framework of the π-calculus. The power of the approach is demonstrated by applying it to generate an encoding of the full lambda calculus in the π-calculus. The encoding is proved to preserve and reflect beta reduction, and is shown to be fully abstract with respect to Abramsky's applicative bisimilarity. 

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References

SHOWING 1-10 OF 37 REFERENCES

The Polyadic π-Calculus: a Tutorial

TLDR
The π-calculus is a model of concurrent computation based upon the notion of naming that is generalized from monadic to polyadic form and semantics is done in terms of both a reduction system and a version of labelled transitions called commitment.

Functions as processes

  • R. Milner
  • Mathematics
    Mathematical Structures in Computer Science
  • 1992
This paper exhibits accurate encodings of the λ-calculus in the π-calculus. The former is canonical for calculation with functions, while the latter is a recent step (Milner et al. 1989) towards a

The Update Calculus (Extended Abstract)

TLDR
The structured operational semantics and the proper bisimulation equivalence and congruence are defined, and the π-calculus turns out to be an asymmetric subcalculus, and a complete axiomatization is given.

A Proof Theoretical Approach to Communication

TLDR
A concurrent computation model, chi calculus, in which communications resemble cut eliminations for classical proofs is investigated, and it is illustrated by showing that it incorporates the operational semantics of the call-by-name lambda calculus.

Spi Calculus Translated to --Calculus Preserving May-Tests

We present a concise and natural encoding of the spi-calculus into the more basic ?-calculus and establish its correctness with respect to a formal notion of testing.This is particularly relevant for

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
TLDR
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.

On the expressiveness of interaction

Spi calculus translated to /spl pi/-calculus preserving may-tests

We present a concise and natural encoding of the spi-calculus into the more basic /spl pi/-calculus and establish its correctness with respect to a formal notion of testing. This is particularly

Pi-Calculus Semantics of Object-Oriented Programming Languages

TLDR
Semantics for a pair of parallel object-oriented programming languages are presented by translation into the π-calculus, a foundation for the study of computational systems with evolving communication structure.

Variations on Mobile Processes

  • Yuxi Fu
  • Computer Science
    Theor. Comput. Sci.
  • 1999