[rbonvall]

The lambda calculus teaches you how to build computation from a very simple evaluation rule called "beta reduction" which is just a fancy name for "search and replace" with function parameters. If you can find a system that can rewrite terms in such a fashion, you can compute whatever you want using the tricks you learn in lambda calculus.

For example, C++ templates were not meant to be Turing-complete, but they work by rewriting terms [1], so you can encode lambda calculus in it, and run arbitrary programs at compile time.

Philip Wadler does a better job than me at getting excited by lambda calculus. He calls it "the omniversal programming language", and claims that aliens will probably have discovered it [2].

[1]: http://matt.might.net/articles/c++-template-meta-programming... [2]: https://www.youtube.com/watch?v=IOiZatlZtGU