# 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} }

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.

## 14 Citations

### Fully abstract encodings of λ-calculus in HOcore through abstract machines

- Computer Science, Mathematics2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2017

Two fully abstract encodings of the call-byname λ-calculus are presented into HOcore, a minimal higher-order process calculus with no name restriction, to prove full abstraction.

### Fully Abstract Encodings of $\lambda$-Calculus in HOcore through Abstract Machines

- Computer Science, Mathematics
- 2022

This work presents fully abstract encodings of the call-by-name and call- by-value λ calculus into HOcore, a minimal higher-order process calculus with no name restriction, and considers several equivalences on the λ -calculus side that internalize into abstract machines in order to prove full abstraction of theencodings.

### From Computing to Interaction: on the Expressiveness of Asynchronous pi-Calculus

- Computer ScienceInt. J. Found. Comput. Sci.
- 2013

In line with the framework of Theory of Interaction proposed by Yuxi Fu, this work formalizes the asynchronous theory in model independent way and introduces ℂ-...

### The Name-Passing Calculus

- Computer ScienceArXiv
- 2015

A model independent approach is applied to the study of the name-passing calculi, leading to a uniform treatment and simplification of the technical tools and the results presented.

### Simulate Match and Mismatch by Computing in Pi-Calculus

- Computer Science, Mathematics2011 International Conference on Network Computing and Information Security
- 2011

A new approach is proposed that simulate, in the framework of pi-calculus, match and mismatch by computing and transforms-terms to a simpler form without match and mism, which is proved to reserve bisimulation.

### Remark on Some \pi Variants

- MathematicsSETTA
- 2017

Two \(\pi \) variants that restrict the use of received names are studied and the relative expressiveness between the two variants and their relationship to \(\pi\) are revealed in terms of subbisimilarity.

### Theory by Process

- Computer ScienceCONCUR
- 2010

A complete axiomatic system is constructed for the asynchronous theory, which gives rise to a proof system for the weak asynchronous bisimilarity of the asynchronous π.

### Static Semantics of Secret Channel Abstractions

- Computer ScienceNordSec
- 2014

The secret π-calculus extends the π-calculus by adding an hide operator that permits to declare channels as secret. The main aim is confidentiality, which is gained by restricting the access of the…

### Non-deterministic structures of computation

- Mathematics, Computer ScienceMathematical Structures in Computer Science
- 2014

It is proved that, as far as computation is concerned, the effect produced jointly by divergence and non-determinism is model independent for a large class of process models.

## References

SHOWING 1-10 OF 37 REFERENCES

### The Polyadic π-Calculus: a Tutorial

- Computer Science
- 1993

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

- MathematicsMathematical 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)

- Computer ScienceAMAST
- 1997

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

- Computer ScienceICALP
- 1997

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

- Computer Science, MathematicsLICS 2004
- 2004

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

- 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.

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

- Computer Science, MathematicsProceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
- 2004

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

- Computer ScienceTACS
- 1991

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.