How helpful is knowing lambda calculus?

Question

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

Answer 1

The benefits for me is a more compact synergistic programming. Stuff tends to flow horizontally more than vertically. Plus it is very useful for prototyping simple algorithms. Don't know if I am using it to its full potential but I find it very useful.

Answer 2

The lambda calculus is a computational model, just like the turing machine. Thus, it is useful if you need to implement a certain evaluator for a language based on this model, however, in practice, you just need the basic idea (uh. place argument semantically correct in the body of a function?) and that's about it.

Answer 3

If you want to program in any functional programming language, it's essential. I mean, how useful is it to know about Turing machines? Well, if you write C, the language paradigm is quite close to Turing machines -- you have an instruction pointer and a current instruction, and the machine takes some action in the current state, and then ambles along to the next instruction.

In a functional language, you simply can't think like that -- that's not the language paradigm. You have to think back to lambda calculus, and how terms are evaluated there. It will be much harder for you to be effective in a functional language if you don't know lambda calculus.

Answer 4

One posible way to learn lambda calculus is

http://en.wikipedia.org/wiki/Lambda_Calculus

Or, if you want more, here is my blog dedicated to lambda calculus and stuff like that

http://weblogs.manas.com.ar/lziliani/

As every abstraction of computations, with lambda calculus you can model stuff used in most programming languages, like subtyping. For more about this, one of the best books with practical uses of lambda calculus in this sense is

http://www.amazon.com/Types-Programming-Languages-Benjamin-Pierce/dp/0262162091/ref=sr_1_1?ie=UTF8&s=books&qid=1222088714&sr=8-1

Answer 5

I think the use of lambda calculus with respect to programming in practice is that it is a quite minimal system that captures the essence of abstraction (or "anonymous functions" or closures, if you will). Other than that I don't think it is generally essential except when you need to implement abstraction yourself (as Tetha (114646) mentioned).

I also completely disagree with Denis Bueno (114701) who says that it is essential for functional programming. It is perfectly well possible to define, use or understand a functional language without any lambda calculus at all. In order to understand the evaluation of terms in functional languages (which, in my opinion, somewhat contradicts the use of a functional language) you will most likely be better of learning about term rewrite systems.

Answer 6

I agree with those that say it is theoretically possible to learn functional programming without learning the lambda calculus-- but what's the advantage of not learning the lambda calculus? It's not as if it takes a big investment of time.

Most likely, it will help you understand functional programming better. But even if it doesn't, it's still a cool thing worth learning. The Y-combinator is a thing of beauty.

Answer 7

I'd also like to mention that if you're doing anything in the area of NLP, lambda calculus is at the foundation of a massive body of work in compositional semantics.

Answer 8

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.

Answer 9

If you only want to be a technician and write programs to do things, then you don't really need to know lambda-calculus, finite-state machines, pushdown automata, finite-state machines, regular expressions, context-free grammar, discrete mathematics, etc.

But if you have curiosity about the deeper mysteries underlying this stuff, you can start to wonder how these questions might be answered. The concepts are beautiful and will expand your imagination. I also think they, incidentally, make one a better practicioner.

What got me hooked was Minsky's book Computation: Finite and Infinite Machines.

Answer 10

To be honest, learning lambda calculus before functional programming has made me realize that the two are as unrelated as C is to any imperative programming.

Lambda calculus is a functional programming language, an esoteric one, a Turing tarpit if you like; accidentally it's also the first.

The majority of functional programming languages at all do not require you to 'learn' lambda calculus, whatever that would mean, lambda calculus is insanely minimal, you can 'learn' its axioms in an under an hour. To know the results from it, like the fixedpoint theorem, the Church-Rosser Theorem et cetera is just irrelevant to functional programming.

Also, lambda-abstractions are often held to be 'functions', I disagree with that, they are algorithms, not functions, a minor difference, most 'functional languages' treat their functions more in the way classical mathematics does.

However, to for instance effectively use Haskell you do need to understand certain type systems, that's irrespective of lambda calculus, the System F type system can be applied to all 'functions' and requires no lambda abstractions at all. Commonly in maths we say f : R^2 -> R : f (x) = x^2. We could've said: f (x) = x^2 :: R -> R -> R. In fact, Haskell comes pretty close to this notation.

Lambda calculus is a theoretical formalism, Haskell's functions are really no more 'lambda abstractions' than f : f(x) = x^2 really, what makes lambda abstractions interesting is that it enables us to define what are normally seen as 'constants' as 'functions', no functional language does that because of the huge computational overhead. Haskell and alike is just a restricted form of System F's type system applied to functions as used in everyday classical maths. Functions in Haskell are certainly not the anonymous formally symbolic reduction-applicants as they are in lambda-calculus. Most functional programming languages are not symbolic reduction-based re-writing systems. Lisps are to some degree but that's a paradigm on its own and its 'lambda keyword' really doesn't satisfy calling it lambda calculus.