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May 7, 2015 · The Lambda Calculus only does computation, that is, we must tell it exactly and in perfect detail how we can get from xto y. One possible way of doing that works by starting with 0, and applying the successor function xtimes: x S 0 = x (λ abc.b(abc)) (λ sz.z) The resulting expression will be the numeric value of x.
The Lambda calculus is an abstract mathematical theory of computation, involving \lambda λ functions. The lambda calculus can be thought of as the theoretical foundation of functional programming. It is a Turing complete language; that is to say, any machine which can compute the lambda calculus can compute everything a Turing machine can (and ...
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A Tutorial Introduction to the Lambda Calculus. Raul Rojas FU Berlin, WS-97/98. Abstract This paper is a short and painless introduction to the calculus. Originally developed in order to study some mathematical properties of e ectively com- putable functions, this formalism has provided a strong theoretical foundation for the family of ...
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A Tutorial Introduction to the Lambda Calculus. Raul Rojas Freie Universit at Berlin Version 2.0, 2015. Abstract This paper is a concise and painless introduction to the -calculus. This formalism was developed by Alonzo Church as a tool for study- ing the mathematical properties of e ectively computable functions.
to the Lambda Calculus Raul Rojas (Edited by Norman Ramsey) Freie Universit at Berlin Version 2.0, 2015 Edit version 2.0-1, March 2018 Editor’s note This tutorial has been lightly edited in three ways. The original uses a nonstandard abbreviation for Curried functions of multiple arguments; this abbreviation has been elimi-nated.
A Simple Example. Here's an example of a simple lambda expression that defines the "plus one" function: λx.x+1 (Note that this example does not illustrate the pure lambda calculus, because it uses the + operator, which is not part of the pure lambda calculus; however, this example is easier to understand than a pure lambda calculus example.)
We write e1fe2=xg to mean expression e1 with all free occurrences of x replaced with e2. We call ( x: e1) e2 and e1fe2=xg -equivalent. Rewriting ( x: e1) e2 into e1fe2=xg is called a -reduction. This corresponds to executing a lambda calculus expression. Di erent semantics for the lambda.
