Programming Language Theory: Difference between revisions

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	The Church-Turing Thesis equates a vaguely-defined set of "computable" functions with the [http://en.wikipedia.org/wiki/Computable_function partial recursive functions]. Several systems are only as powerful as the partial recursives (''Turing-complete''): Turing machines and the λ-calculus are two. Programming languages provide further syntaxes and semantics, but all you really need in life is combinatory logic.		The Church-Turing Thesis equates a vaguely-defined set of "computable" functions with the [http://en.wikipedia.org/wiki/Computable_function partial recursive functions]. Several systems are only as powerful as the partial recursives (''Turing-complete''): Turing machines and the λ-calculus are two. Programming languages provide further syntaxes and semantics, but all you really need in life is combinatory logic. Peter J. Landin's 1965 ACM report, "A correspondence between ALGOL 60 and Church's Lambda-notation", jump-started most of this.<blockquote>''There may, indeed, be other applications of the system than its use as a logic.'' -- Alonzo Church, 1932</blockquote>

	==Applicative/Functional Programming==		==Applicative/Functional Programming==