Had never heard of the lambda calculus before. Very cool.
Does it have any practical applications? Or is it mostly a theoretical / conceptual tool?
Does it have any practical applications? Or is it mostly a theoretical / conceptual tool?
At the same time, practical functional languages are often surprisingly limited extensions of an underlying lambda calculus, perhaps with types. In fact, Caramel is more or less what an untyped Haskell or purely functional subset of Scheme would look like with fewer parentheses and macros.
Where can I see a demonstration of this? For example, what does it mean to evaluate something like decorators in Python and how will one go about doing that with lambda calculus?
Introductory resources on programming language theory usually have examples, after giving you a thorough grounding in the basic untyped lambda calculus. In particular, this is how they usually introduced type system features, but there are interesting things like continuations that don't necessarily involve types. Types and Programming Languages by Benjamin Pierce is a great resource, but you can probably find free lecture notes to the same effect. (I'd look them up, but I'm on my phone so it's a bit of a hassle.)
The most interesting non-introductory (but still self-contained) example I've seen was Barry Jay's Pattern Calculus book. He introduces pattern matching and first class patterns, first without types and then with, all building upon the lambda calculus. His ideas cover functional, imperative and object-oriented features, and it's fascinating to see a whole language developed piece-by-piece like that. If you're curious about PL theory and want to dive pretty deep, I think this is a book worth looking at.
Broad-coverage CCG Semantic Parsing with AMR
Yoav Artzi, Kenton Lee and Luke Zettlemoyer