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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 have been proven equivalent to the partial recursives in power, such as Turing machines and the λ-calculus (practical programming languages generally provide further syntaxes and semantics, but a [[Real Programmer]] is perfectly happy with combinatory logic and a beer). Peter J. Landin's 1965 ACM report, "A correspondence between ALGOL 60 and Church's Lambda-notation", is blamed by most textbooks for jump-starting the study of programming language theory, ensuring computer scientists forty years later would still be exploring "topoi", "sheaves" and "fixed-point combinators".<blockquote>''There may, indeed, be other applications of the system than its use as a logic.'' -- Alonzo Church, 1932</blockquote> | 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 have been proven equivalent to the partial recursives in power, such as Turing machines and the λ-calculus (practical programming languages generally provide further syntaxes and semantics, but a [[Real Programmer]] is perfectly happy with combinatory logic and a beer). Peter J. Landin's 1965 ACM report, "A correspondence between ALGOL 60 and Church's Lambda-notation", is blamed by most textbooks for jump-starting the study of programming language theory, ensuring computer scientists forty years later would still be exploring "topoi", "sheaves", "Curry-Howard correspondences" and "fixed-point combinators".<blockquote>''There may, indeed, be other applications of the system than its use as a logic.'' -- Alonzo Church, 1932</blockquote> | ||

==Functions and Declarative Programming== | ==Functions and Declarative Programming== |

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