Content uploaded by Adrian Rezus

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All content in this area was uploaded by Adrian Rezus on Dec 27, 2016

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Content uploaded by Adrian Rezus

Author content

All content in this area was uploaded by Adrian Rezus on Dec 27, 2016

Content may be subject to copyright.

... We mention but a few. More information about the Lambda Calculus may be obtained from [1,11,29]. ...

The Lambda Calculus is a formal system, originally intended as a tool in the foundation of mathematics, but mainly used to study the concepts of algorithm and effective computability. Recently, the Lambda Calculus and related systems acquire attention from Computer Science for another reason too: several important programming language concepts can be explained elegantly and can be studied successfully in the framework of the Lambda Calculi. We show this mainly by means of examples. We address ourselves to interested computer scientists who have no prior knowledge of the Lambda Calculus. The concepts discussed include: parameterization, definitions, recursion, elementary and composite data types, typing, abstract types, control of visibility and life-time, and modules.

... However, despite this, it seems to have been ignored by most of the later type-theory community. (Though it is listed in A. Rezus' bibliography [27].) Nor, as far as I know, did it influence those who later worked on NF. ...

This article is essentially an extended review with historical comments. It looks at an algorithm published in 1943 by M.
H. A. Newman, which decides whether a lambda-calculus term is typable without actually computing its principal type. Newman's
algorithm seems to have been completely neglected by the type-theorists who invented their own rather different typability
algorithms over 15 years later.

Under an appropriate decoration (typing), the extended lambda-calculus (also known as lambda-pi-calculus or as lambda-calculus with surjective pairing) is an equational proof system for classical logic. Exemplified here is the first order case.

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