# Catalogue of Artificial Intelligence Techniques

View Maths as: Images | MathML

## 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 $f$ given by:

can be written using lambda-abstraction as:

so that:

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

(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 ).

### Comments:

No comments.