Computability concepts for programming language semantics
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Final report of the ANSI/X3/SPARC DBS-SG relational database task group
ACM SIGMOD Record
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We prove a theorem which provides an intuitive understanding of the meaning of $\lambda$-terms in Scott''s extensional $\lambda$-calculus models. This allows us to use those models for the definition of high-level programming languages. In order to illustrate this we define a programming language which includes blocks and (arbitrary recursive) procedures. Two aspects justify this approach. First of all, the logical properties of those (typeless) $\lambda$-calculus models are appealing for a formalization similar to LCF [6] which formalizes typed $\lambda$-calculus models. Secondly, not having the type restrictions that LCF imposes allows us to define the semantics of high-level programming languages in the spirit of ``mathematical semantics'''' [12] (which is usually based on recursively defined domains), thus the semantic nature of syntactic constructs can be exhibited clearly. Keywords: Mathematical semantics, Programming Languages, $\lambda$-calculus Models, typed, typeless, extensional, Logic, LCF.