Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Implementation and applications of Scott's logic for computable functions
Proceedings of ACM conference on Proving assertions about programs
Programming Language Semantics Using Extensional $\lambda$-Calculus Models
Programming Language Semantics Using Extensional $\'lambda$-Calculus Models
Models of LCF.
Recursive definitions of partial functions and their computations
Recursive definitions of partial functions and their computations
Semantics of the Domain of Flow Diagrams
Journal of the ACM (JACM)
Bases for chain-complete posets
IBM Journal of Research and Development
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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 &lgr;-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). The formal theory is developed in part II of this paper. Part I gives motivation and comparison with related work.