Relating function spaces to resourced function spaces
Lidia Sánchez-Gil, Mercedes Hidalgo-Herrero, Yolanda Ortega-Mallén · 2011
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⊥.