## A proof-theoretical approach to communication (1997)

Venue: | Proceedings of ICALP '97, volume 1256 of LNCS |

Citations: | 19 - 4 self |

### BibTeX

@INPROCEEDINGS{Fu97aproof-theoretical,

author = {Yuxi Fu},

title = {A proof-theoretical approach to communication},

booktitle = {Proceedings of ICALP '97, volume 1256 of LNCS},

year = {1997},

pages = {325--335},

publisher = {Springer}

}

### OpenURL

### Abstract

Abstract. The paper investigates a concurrent computation model, chi calculus, in which communications resemble cut eliminations for classical proofs. The algebraic properties of the model are studied. Its relationship to sequential computation is illustrated by showing that it incorporates the operational semantics of the call-by-name lambda calculus. Practically the model has pi calculus as a submodel. 1 Communication as Cut Elimination Concurrent computation is currently an open-ended issue. The situation is in contrast with sequential computation whose operational semantics is formalized by, among others, the λ-calculus ([2]). In retrospect, the λ-calculus can be seen as a fallout of proof theory. Curry-Howard’s proposition-as-type principle allows one to code up constructive proofs as typed terms. At the core of the constructive logic is the minimal logic, whose type theoretical formulation gives rise to, roughly, the simply typed λ-calculus. Now the untyped λ-calculus is obtained from the simply typed λ-calculus by removing all the typing information.

### Citations

1115 |
The Lambda Calculus: Its Syntax and Semantics
- Barendregt
- 1981
(Show Context)
Citation Context ...imination Concurrent computation is currently an open-ended issue. The situation is in contrast with sequential computation whose operational semantics is formalized by, among others, the λ-calculus (=-=[2]-=-). In retrospect, the λ-calculus can be seen as a fallout of proof theory. Curry-Howard’s proposition-as-type principle allows one to code up constructive proofs as typed terms. At the core of the con... |

995 | A calculus of mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ... between π-calculus and χcalculus. We give a first answer in this section. Let P be the set of π-processes defined as follows: P := 0 | m(x).P | mx.P | P |P ′ | (x)P | m(x)∗P . We refer the reader to =-=[6]-=- for background material on π-calculus. There are many bisimulation equivalences on π-processes. What is most relevant in this section is the open bisimilarity defined in [8]. Actually we will use a v... |

313 |
Functions as processes, in
- Milner
- 1990
(Show Context)
Citation Context ... are syntactically the same. The operational semantics of the language can be defined in terms of a labeled transition system. We prefer however a reductional semantics for χ-calculus in the style of =-=[5]-=-: (x)(R|α[x].P |α[y].Q) → (x)(R[y/x]|P [y/x]|Q[y/x]) α(x)∗P |α[y].Q → α(x)∗P |P [y/x]|Q P → P ′ P |Q → P ′ |Q P → P ′ (x)P → (x)P ′sTo help understand the communication rules, we now give some example... |

199 |
Call-by-name, call-by-value and the λ-calculus
- Plotkin
- 1975
(Show Context)
Citation Context ... of whether it captures sequential computation successfully. The issue is often addressed by relating variants of λ-calculus to the model. Our focus in this section is on thescall-by-name λ-calculus (=-=[7]-=-), whose semantics is defined by the following rules: (λx.M)N → M[N/x] M → M ′ MN → M ′ N M → M ′ λx.M → λx.M ′ . The following translation, which is Milner’s encoding of the lazy λ-calculus with modi... |

65 |
A theory of bisimulation for the π-calculus
- Tiu, Sangiorgi, et al.
- 1996
(Show Context)
Citation Context ... . We refer the reader to [6] for background material on π-calculus. There are many bisimulation equivalences on π-processes. What is most relevant in this section is the open bisimilarity defined in =-=[8]-=-. Actually we will use a version of open bisimilarity stronger than Sangiorgi’s. Definition 6. Let R be a binary relation on the set of π-processes. The relation R is an open bisimulation if whenever ... |

44 |
The π-calculus
- Sangiori, Walker
- 2001
(Show Context)
Citation Context ...s are, well, variables that can be instantiated by any λ-terms. But variable names alone do not suffice in practice. This is clear from the mobile process interpretation of object oriented languages (=-=[10]-=-). The usual practice is to postulate that N consists of two parts: a set Nv of variable names and a set Nc of constant names. We can now define a χ-process to be a χ-term in which all variable names ... |

4 |
Plain CHOCS—A Second Generation Calculus for Higher Order Processes
- Thomsen
- 1993
(Show Context)
Citation Context ...]. ⊓⊔ In the remaining of the section, we justify our claim that the higher order calculus is a combination of χ and λ. 6.2 Recursion As a test for local bisimilarity, we examine Thomsen’s recursion (=-=[9]-=-) in this section. Suppose that E contains free variable X and a does not occur in E. Thesfollowing abbreviations will be used: W a X(E) def = a[a]|a(X)(a[a].E|a[X]), recX.E def = (a)(W a X(E)|a[W a X... |