Year: 2008
Type: preprint
Abstract: We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a restricted form, which we call prime systems. A denotational semantics is defined with this interpretation. We define the syntactical normal form approximations of a term and prove the Approximation Theorem: The semantics of a term equals the limit of the semantics of its approximations. The proof uses inclusive predicates (logical relations). The semantics is adequate with respect to the observation of Boolean values. It is also fully abstract in the presence of the parallel case-function.
Source: arXiv (Cornell University)
Author: Müller, Fritz
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1668029505