## Parallel PCF has a Unique Extensional Model (1991)

Venue: | In Proc. 6th IEEE Annual Symp. Logic in Computer Science |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Stoughton91parallelpcf,

author = {Allen Stoughton},

title = {Parallel PCF has a Unique Extensional Model},

booktitle = {In Proc. 6th IEEE Annual Symp. Logic in Computer Science},

year = {1991},

pages = {146--151},

publisher = {IEEE Computer Society Press}

}

### OpenURL

### Abstract

We show that the continuous function model is the unique extensional (but not necessarily pointwise ordered) model of the variant of the applied typed lambda calculus PCF that includes the "parallel or" operation. 1 Introduction Several extensional models of the applied typed lambda calculus PCF are known to exist, including: (i) The continuous function model, which is order-extensional (pointwise ordered) but not equationally fully abstract [Plo]. (A model is equationally fully abstract when terms are identified in the model exactly when they are operationally equivalent.) (ii) The stable function model, which is neither order-extensional nor equationally fully abstract [Ber][BCL]. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and order-extensional [Mil][Sto2]. (A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defin...

### Citations

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LCF considered as a programming language
- Plotkin
- 1977
(Show Context)
Citation Context ...al models of the applied typed lambda calculus PCF are known to exist, including: (i) The continuous function model, which is order-extensional (pointwise ordered) but not equationally fully abstract =-=[Plo]-=-. (A model is equationally fully abstract when terms are identified in the model exactly when they are operationally equivalent.) (ii) The stable function model, which is neither order-extensional nor... |

54 |
Full abstraction for sequential languages: the state of the art
- Berry, Curien, et al.
- 1985
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Citation Context ...bstract when terms are identified in the model exactly when they are operationally equivalent.) (ii) The stable function model, which is neither order-extensional nor equationally fully abstract [Ber]=-=[BCL]-=-. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and order-extensional [Mil][Sto2]. (A model is inequationally ful... |

45 |
Fully abstract models of typed *-calculi
- Milner
- 1977
(Show Context)
Citation Context ... nor equationally fully abstract [Ber][BCL]. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and order-extensional =-=[Mil]-=-[Sto2]. (A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defined than the second.) (iv) The initial object of the a... |

41 |
Modèles complètement adéquats et stables des lambda-calculus typés. Thèse d’Etat, Université Paris VII
- BERRY
- 1979
(Show Context)
Citation Context ...lly abstract when terms are identified in the model exactly when they are operationally equivalent.) (ii) The stable function model, which is neither order-extensional nor equationally fully abstract =-=[Ber]-=-[BCL]. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and order-extensional [Mil][Sto2]. (A model is inequationall... |

29 |
Fully Abstract Models of Programming Languages
- Stoughton
- 1986
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9 |
Interdefinability of parallel operations
- Stoughton
- 1991
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Citation Context ...y)); where Not of sort ' ! ' is x: If x 0 1. For n 2 !, define operators And n of sort ' n by: And 0 = 1 and And n+1 = xy 1 \Delta \Delta \Delta yn : If x (And n y 1 \Delta \Delta \Delta yn ) 0: From =-=[Sto3]-=-, we know that we can define the parallel if operator, PIf , of sort ' 3 by PIf = Y ' 4 H 0, where H of sort ' 4 ! ' 4 is defined by H = fwxyz: If (POr (PAnd (Eq y w) (Eq z w)) (PAnd x (Eq y w)) (PAnd... |

5 |
Equationally fully abstract models of PCF
- Stoughton
- 1990
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Citation Context ...equationally fully abstract [Ber][BCL]. (iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and order-extensional [Mil]=-=[Sto2]-=-. (A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defined than the second.) (iv) The initial object of the above c... |