# Catalogue of Artificial Intelligence Techniques

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## Lambda Calculus

**Keywords:**
alpha conversion, beta reduction, terms

### Categories: Knowledge Representation

Author(s): **Alan Smaill**

Various formal systems based on that invented by Church to formalise the properties of functions acting on arguments and being combined to form other functions. This involves `lambda-abstraction'. The function given by:

can be written using lambda-abstraction as:

so that:

Application is written as juxtaposition, e.g., for . Terms made up using application and lambda abstraction can be manipulated in various ways, e.g., rename bound variables (alpha conversion), and rewrite as

(beta reduction). Lambda calculus is the formalism that underlies Lisp.

### References:

- Barendregt, H.P.,
*The lambda calculus, its syntax and semantics*, North-Holland, Amsterdam and Oxford, 1984 (revised edition ).

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