Before we really dive in to the specifics of λ calculus, let’s consider exactly what makes it a calculus. To most of us, the word calculus means something very specific: the differential and integral calculus invented by Isaac Newton and Gottfried Leibnitz. λ calculus has nothing to do with that kind of calculus!

In mathematical terms, a calculus is a system for symbolically manipulating expressions. Differential calculus is a calculus because it’s a way of manipulating expressions that represent mathematical functions. λ calculus is a calculus because it describes how to manipulate expressions that describe computations.

The way that we define a calculus is very much like the way that we defined ...

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