blog-static/content/blog/12_compiler_let_in_lambda/index.md

title	date	tags	draft
Compiling a Functional Language Using C++, Part 12 - Let/In and Lambdas	2020-04-20T20:15:16-07:00	C and C++ Functional Languages Compilers	true

Now that our language's type system is more fleshed out and pleasant to use, it's time to shift our focus to the ergonomics of the language itself. I've been mentioning let/in expressions and lambda expressions for a while now. The former will let us create names for expressions that are limited to a certain scope (without having to create global variable bindings), while the latter will allow us to create functions without giving them any name at all.

Let's take a look at let/in expressions first, to make sure we're all on the same page about what it is we're trying to implement. Let's start with some rather basic examples, and then move on to more complex examples. The most basic use of a let/in expression is, in Haskell:

let x = 5 in x + x

In the above example, we bind the variable x to the value 5, and then refer to x twice in the expression after the in. The whole snippet is one expression, evaluating to what the in part evaluates to. Additionally, the variable x does not escape the expression - {{< sidenote "right" "used-note" "it cannot be used anywhere else." >}} Unless, of course, you bind it elsewhere; naturally, using x here does not forbid you from re-using the variable. {{< /sidenote >}}

Now, consider a slightly more complicated example:

let sum xs = foldl (+) 0 xs in sum [1,2,3]

Here, we're defining a function sum, {{< sidenote "right" "eta-note" "which takes a single argument:" >}} Those who favor the point-free programming style may be slightly twitching right now, the words eta reduction swirling in their mind. What do you know, fold-based sum is even one of the examples on the Wikipedia page! I assure you, I left the code as you see it deliberately, to demonstrate a principle. {{< /sidenote >}} the list to be summed. We will want this to be valid in our language, as well. We will soon see how this particular feature is related to lambda functions, and why I'm covering these two features in the same post.

Let's step up the difficulty a bit more, with an example that, {{< sidenote "left" "translate-note" "though it does not immediately translate to our language," >}} The part that doesn't translate well is the whole deal with patterns in function arguments, as well as the notion of having more than one equation for a single function, as is the case with safeTail.

It's not that these things are impossible to translate; it's just that translating them may be worthy of a post in and of itself, and would only serve to bloat and complicate this part. What can be implemented with pattern arguments can just as well be implemented using regular case expressions; I dare say most "big" functional languages actually just convert from the former to the latter as part of the compillation process. {{< /sidenote >}} illustrates another important principle:

let
    safeTail [] = Nothing
    safeTail [x] = Just x
    safeTail (_:xs) = safeTail xs
    myTail = safeTail [1,2,3,4]
in
    myTail

The principle here is that definitions in let/in can be recursive and polymorphic. Remember the note in [part 10]({{< relref "10_compiler_polymorphism.md" >}}) about let-polymorphism? This is it: we're allowing polymorphic variable bindings, but only when they're bound in a let/in expression (or at the top level).

The principles demonstrated by the last two snippets mean that compiling let/in expressions, at least with the power we want to give them