Lambda Calculus/Basic Definitions

Axioms
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

 * 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.