## A Tutorial Introduction to the Lambda Calculus

a tutorial introduction to the lambda calculus. Raul Rojas . FU Berlin, WAS 97/98. Abstract. This document is a brief and painless introduction to the tutorial Î» ….

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**A Tutorial Introduction to the Lambda Calculus**, Contents:

- Definition

1.1 Free and bound variables - Arithmetic

2.1 Addition

2.2 Multiplication - Conditionals

3.1 Logical operations

3.2 A conditional test

3.3 The predecessor function

3.4 Equality and inequalities - Recursion
- Projects for the reader

Projects for the reader

- Define the functions âless thanâ and âgreater thanâ of two numerical arguments.
- Define the positive and negative integers using pairs of natural numbers.
- Define addition and subtraction of integers.
- Define the division of positive integers recursively.
- Define the function n! = n Â· (n â 1) Â·Â·Â· 1 recursively.
- Define the rational numbers as pairs of integers.
- Define functions for the addition, subtraction, multiplication and division of rationals.
- Define a data structure to represent a list of numbers.
- Define a function which extracts the first element from a list.
- Define a recursive function which counts the number of elements in a list.
- Can you simulate a Turing machine using Î» calculus?

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