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The \(\Sigma{}\lambda\)-calculus and derived program forms. (English) Zbl 0741.03005

Summary: The \(\Sigma\lambda\)-calculus is an extension of an applied \(\lambda\)- calculus designed to abstract parallel and non-deterministic function application evaluation. The abstraction is extended to include Landin’s closure, and constant terms and a special form of the conditional allows the regular logics to be developed along the lines of the Hilbert- Ackermann approach. The regular logics are used to characterize derived conditionals in extensions to Dijkstra’s weakest preconditions. It is shown that various styles of programming — top-down, bottom-up, recursive and iterative — are expressible in the \(\Sigma\lambda\)- calculus. Lists and streams are found to be useful in expressing time- dependent behaviour of computational systems. An approximate Church- Rosser Theorem is given.

MSC:

03B40 Combinatory logic and lambda calculus
68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
03B70 Logic in computer science
68N01 General topics in the theory of software
03B50 Many-valued logic
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