How helpful is knowing lambda calculus?

math functional-programming computer-science lambda-calculus
TraumaPony picture TraumaPony · Sep 22, 2008 · Viewed 20.5k times · Source

To all the people who know lambda calculus: What benefit has it bought you, regarding programming? Would you recommend that people learn it?

Answer

Norman Ramsey picture Norman Ramsey · Dec 17, 2008

The benefit of lambda calculus is that it's an extremely simple model of computation that is equivalent to a Turing machine. But while a Turing machine is more like assembly language, lambda calculus is more a like a high-level language. And if you learn Church encodings that will help you learn the programming technique called continuation-passing style, which is quite useful for implementing backtracking search and other neat tricks.

The main use of lambda calculus in practice is that it is a great laboratory tool for studying new programming-language ideas. If you have an idea for a new language feature, you can add the new feature to the lambda calculus and you get something that is expressive enough to program while being simple enough to study very thoroughly. This use is really more for language designers and theorists than for programmers.

Lambda calculus is also just very cool in its own right: just like knowing assembly language, it will deepen your understanding of computation. It's especially fun to program a universal turing machine in the lambda calculus. But this is foundational mathematics, not practical programming.

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