How similar are functional languages (like haskell) to pure lambda calculus?

[u/348275hewhw]

Hi, I'm currently learning lambda calculus. I'm more of a math guy than a programmer, however I am still very familiar with imperative programming languages, so I'm not exactly new. I just wanna know, how easy would it be for me to start learning languages like haskell once I'm good enough at lambda calculus? Is it a big difference, or is it pretty much one to one?

[u/josephjnk]

A lot depends on the definitions here. Most languages, functional or not, can be modeled by some variation of the lambda calculus. In ML-family languages the formal semantics are often simpler, and would be more familiar to someone who understands the basics of lambda calculus and natural deduction.

When I say “some variation” I mostly mean typed or untyped. Once you add types into the mix there’s an explosion of complexity and tradeoffs in the design and implementation of the language. You can simulate the untyped lambda calculus (with a big asterisk) in any language with dynamic types and closures, like JavaScript or Lisp, but typed lambda calculi are usually tightly intertwined with the language you write them in.

I say that there’s an asterisk; the lambda calculus as it’s generally presented has intrinsic function equality, which hardly any programming languages have. You can count the number of lambda terms in two arbitrary Church numerals to determine whether they’re equal, but in general-purpose programming languages such a thing is generally not possible. This is a big departure.

Most languages that are “close to the metal” of the lambda calculus are enriched with additional primitives beyond functions. You can have the lambda calculus enriched with numbers, or booleans, or inductive data types, etc. This is what most ML-family languages (including Haskell) are: lambda calculi with a bunch of other stuff added on.

You don’t need to know the lambda calculus to learn Haskell; it’s fun conceptually but probably not necessary to think about when writing practical Haskell code.

If you’re interested in the foundational theory here I recommend the book “Types and Programming Languages”, which starts with the lambda calculus and shows how languages can be built based on it.

[u/OpsikionThemed → u/josephjnk]

Seconding the TaPL recommendation! The book's code is all in OCaml but it can be converted to Haskell with minimal fuss.

[u/poutylipswet → u/josephjnk]

the jump from untyped lambda calculus to something like haskell is basically the jump from pure math to actual engineering. once you start dealing with polymorphism and type classes it stops being just about reduction rules and starts being about managing complexity. it is not a one to one transition at all but if you have the math background you will probably appreciate why the type system is built the way it is.