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The Lambda Calculus. Its Syntax and Semantics (Paperback, New)
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The Lambda Calculus. Its Syntax and Semantics (Paperback, New)
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The Lambda Calculus, treated in this book mainly in its untyped
version, consists of a collection of expressions, called lambda
terms, together with ways how to rewrite and identify these. In the
parts conversion, reduction, theories, and models the view is
respectively 'algebraic', computational, with more ('coinductive')
identifications, and finally set-theoretic. The lambda terms are
built up from variables, using application and abstraction.
Applying a term F to M has as intention that F is a function, M its
argument, and FM the result of the application. This is only the
intention: to actually obtain the result one has to rewrite the
expression FM according to the reduction rules. Abstraction
provides a way to create functions according to the effect when
applying them. The power of the theory comes from the fact that
computations, both terminating and infinite, can be expressed by
lambda terms at a 'comfortable' level of abstraction.
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