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.