Free and Bound Variables in Lambda Calculus: What are they and how can we calculate them?

Covers calculating free (unbound) and bound variables in lambda calculus, and defining an algorithm over the syntax of the lambda calculus.
This builds on our knowledge of the basic building blocks of the lambda calculus, and how that is reflected in its formal grammar. Covers a lambda calculus with variables, function application and function abstraction (or in short form: var, app, abs).
More on free and bound variables:
en.wikipedia.org/wiki/Lambda_calculus#Free_and_bound_variables
en.wikipedia.org/wiki/Free_variables_and_bound_variables#Function_expressions
00:00 Building blocks of the lambda calculus
00:32 Rules to determine free (unbound) and bound variables
00:57 Rule 1: Function abstraction binds variables
02:06 Rule 2: Variables not bound are free (unbound)
03:05 Calculating free and bound variables with mathematical rules on the grammar
05:20 Worked example: finding free variables using the mathematical rules
07:56 Exercise 1: Informally finding free variables
08:35 Exercise 2: Informally finding free variables
09:09 Summary