# Relating function spaces to resourced function spaces.

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Sánchez Gil, Lidia y Hidalgo Herrero, Mercedes y 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

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## Resumen

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.

Tipo de documento: Sección de libro Domain theory; Denotational semantics; λ-calculus. Ciencias > Matemáticas > Lógica simbólica y matemática 17218 27 Nov 2012 09:07 26 Nov 2014 09:42

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