Year: 1975
Type: conference-paper
Abstract: This paper is about mathematical problems in programming language semantics and their influence on recursive function theory. We define a notion of computability on continuous higher types (for all types) and show its equivalence to effective operators. This result shows that our computable operators can model mathematically (i.e. extensionally) everything that can be done in an operational semantics. These new recursion theoretic concepts which are appropriate to semantics also allow us to construct Scott models for the λ-calculus which contain all and only computable elements. Depending on the choice of the initial cpo, our general theory yields a theory for either strictly determinate or else arbitrary non-deterministic objects (parallelism).
Authors: Herbert Egli, Robert L. Constable
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1996152169