# Why is lambda calculus a "calculus"?

The only definition of "calculus" I'm aware of is the study of limits, derivatives, integrals, etc. in analysis. In what sense is lambda calculus (or things like mu calculus) a "calculus"? How does it relate to calculus in analysis?

• Is has not so much to do with Calculus or Analysis, Calculus is meant here in the sense that you have definite rules to which you manipulate symbols. In german it is called "Lambda Kalkül" where the word "Kalkül" refers to such systems of rules of manipulations, and Calculus is just termed "Analysis", so there is not this interference in naming. Nov 5, 2013 at 18:58
• My dictionary says, "calculus: a particular method or system of calculation or reasoning." Nov 5, 2013 at 19:20

## 2 Answers

A calculus is just a system of reasoning. One particular calculus (well, actually two closely related calculi: the differential calculus and the integral calculus) has become so widespread that it is just known as "calculus", as if it were the only one. But, as you have observed, there are other calculi, such as the lambda calculus, mu calculus, pi calculus, propositional calculus, predicate calculus, sequent calculus and Professor Calculus.

Calculus refers to systematic methods of treating problems by a special system of algebraic notations, generally a method of calculation.

• Are all algebras calculuses? Are all calculuses algebras? If not, what's the distinction or how is one specialised vs the other? Jan 25, 2020 at 13:50
• @codeshot I bethat only certain al Oct 10, 2021 at 0:08
• @codeshot I suspect that only certain algebras could give rise to calculi. Could there be algebras that are fundamentally incomputable, thus unable to be faithfully represented on a computer? Because you would ultimately need to embed both the algebra and the calculi onto the differentiable manifold, but some manifolds seem to be undifferentiable, so unable to be calculated on a computer to an arbitrary order of accuracy. Oct 10, 2021 at 0:25