| FWIW I think it's an insightful question. Other replies to this thread do a pretty good job at pointing out the applications of lambda calculus. I want to contribute this excerpt from one of the original papers on the topic: "In this paper we present a set of postulates for the foundation of formal logic, in which we avoid use of the free, or real, variable... Our reason for avoiding use of the free variable is that we require that every combination of symbols belonging to our system, if it represents
a proposition at all, shall represent a particular proposition, unambiguously, and without the addition of verbal explanations." The motivation was a setting for doing "precise and unambiguous" mathematics. Mathematical results are used pervasively today, so the overall vision is obviously important. Whereas The Calculus was developed in response to the difficulty of calculating physical quantities, such as those about celestial bodies, the lambda calculus had a more foundational motivation. None-the-less, lambda calculus is tremendously useful for solving "real world" problems. Most of these problems arise where doing "precise mathematics" is important but tedious, difficult and/or time-consuming; or the related task of defining computations correctly. |