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Sánchez Gil, Lidia and Hidalgo Herrero, Mercedes and Ortega Mallén, Yolanda
(2001)
*Relating function spaces to resourced function spaces.*
In
Proceeding SAC '11 Proceedings of the 2011 ACM Symposium on Applied Computing.
ACM, New York, pp. 1301-1308.
ISBN 978-1-4503-0113-8

PDF
791kB |

## Abstract

In order to prove the computational adequacy of the (operational)natural semantics for lazy evaluation with respect to a standard denotational semantics, Launchbury defines a resourced denotational semantics. This should be equivalent to the standard one when given infinite resources, but this fact cannot be so directly established, because each semantics produces values in a different domain. The values obtained by the standard semantics belong to the usual lifted function space D = [D → D]⊥, while those produced by the resourced semantics belong to [C → E] where E satisfies the equation E = [[C → E] → [C → E]]⊥ and C (the domain of resources) is a countable chain domain defined as the least solution of the domain equation C = C⊥.

We propose a way to relate functional values in the standard

lifted function space to functional values in the corresponding resourced function space. We first construct the initial solution for the domain equation E = [[C → E] →

[C → E]]⊥ following Abramsky’s construction of the initial

solution of D = [D → D]⊥. Then we define a “similarity”

relation between values in the constructed domain and values

in the standard lifted function space. This relation is

inspired by Abramsky’s applicative bisimulation.

Finally we prove the desired equivalence between the standard denotational semantics and the resourced semantics for the lazy λ-calculus.

Item Type: | Book Section |
---|---|

Uncontrolled Keywords: | Domain theory; Denotational semantics; λ-calculus. |

Subjects: | Sciences > Mathematics > Logic, Symbolic and mathematical |

ID Code: | 17218 |

Deposited On: | 27 Nov 2012 09:07 |

Last Modified: | 02 Sep 2020 10:19 |

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