# Lambda Calculus/Basic Definitions

From Wikibooks, open books for an open world

## Axioms[edit]

The first concept is that of abstraction. It is analogous to defining a function.

**λx.M**

This defines a function which takes an argument x and returns a term M. Functions in lambda calculus have no name.

The second concept is that of invocation. IT is essentially a function call.

**M N**

This binds the argument N to the term M

## Definitions[edit]

- Term
- A term in Lambda calculus is a defined function. A term may contain variables.
- Variable
- A variable, may represent any term. A term may contain free variables or bound variables
- Bound variables
- A bound variable is a variable which will be bound to some term passed as an argument. Eg, In
**λx.xy**, x is a bound variable. - Free variables
- A free variable is any variable in a term which is not bound to some other term. Eg, In
**λx.xy**, y is a free variable.