One of the better features from functional programming languages are variant types (a.k.a. algebraic data types). Basically they are a way of enumerating a small set of possibilities and then making sure that you handle every possible case. However, in real world use variant types tend to run into a few annoying problems. While working on the Harmonic compiler, I found that Scala’s case classes addressed some of these shortcomings.

My goal in writing Scala code was to never have an assert false to cover situations I knew could not occur. I did not quite succeed, but I got really close, much closer than I ever got in any other language. Mostly where I failed I knew that I could refactor the types but I did not want to spend the time to do it. In this post I want to explain how and why the case class approach seems to work better than traditional variant types. In later posts I’ll cover some of the other tricks that I ended up using, particularly the approach I used to having an AST whose shape changed over time.

In O’Caml, you have something like this (I forget the precise syntax):

type expr =
|    bin_op of (op, expr, expr)
|    un_op of (op, expr)
|    tuple of (expr list)
|    ...
;

This seems great at first, but you often run into two situations. The first, which is very common, is that you want to have some helper routine which handles a subset of expressions. For example:

let lower_bin_op op left right = ...
let lower_un_op op expr = ...
let lower_expr expr = 
    case expr of
    |    bin_op(x, y, z) -> lower_bin_op x y z
    |    un_op(op, x) -> lower_un_op op x
    |    tuple(exprs) -> L.map lower_expr exprs
    |    ...

But now you can see that we duplicated the contents of bin_op and un_op in the arguments to lower_bin_op and lower_un_op. This is annoying. So we end up doing this:

type bin_op = { op: op, left: expr, right: expr };
type un_op = { op: op, expr: expr };
type expr = bin_op of bin_op | un_op of un_op | tuple of expr list

OK, so far, kind of annoying, but no big problem. But what about the situation where you want a helper function that handles two or three related cases? You have no choice but to write code like:

let get_op expr = 
    case expr of 
    |    bin_op(op, _, _) -> op
    |    un_op(op, _) -> op
    |    _ -> fail "impossible: not an operator expr!"

This seems to happen a lot: sometimes the language does not allow the full set of expressions in all contexts; sometimes you have lowered your AST; sometimes you have a series of functions which handle certain cases and fall through to other functions for the remaining cases. Or sometimes you just want a nice helper that extracts some common piece of data that appears in multiple cases, like the one above.

Now what happens in Scala? In Scala, when you defined your expression type, you would write:

sealed abstract trait Expr
sealed abstract trait OpExpr extends Expr {
       def op: Op
}
case class UnOp(op: Op, expr: Expr) extends OpExpr
case class BinOp(op: Op, left: Expr, right: Expr) extends OpExpr
case class Tuple(exprs: List[Expr]) extends Expr

Now I can write our first example as:

def lowerBinOp(expr: BinOp) = {...}
def lowerUnOp(expr: UnOp) = {...}
def lowerExpr(expr: Expr) = {
    expr match {
         case expr: BinOp => lowerBinOp(expr)
         case expr: UnOp => lowerUnOp(expr)
         case Tuple(exprs) => exprs.foreach(lowerExpr)
    }
}

The key here is that BinOp and UnOp are automatically types of their own, unlike in O’Caml, where variants are not a type. What I did in the match expression is to define a second variable expr that shadows the original expr but has a more refined type. I found myself doing this a lot when I wrote Scala.

OK, so far so good. What about the second example, where we extracted the operator from any operator expression? Turns out that was already defined: note that UnOp and BinOp both extended OpExpr, which defined a virtual op property. So I can write expr.op and so long as the expression is a binary operator or a unary operator everything is good. If you wanted to write something like the O’Caml, that is of course possible too:

def getOp(expr: OpExpr) = {
    expr match {
        case BinOp(op, _, _) => op
        case UnOp(op, _) => op
    }
}

Only now there is no need for the explicit fail case. So basically using inheritance and subtyping you got a very flexible categorization scheme. Since traits support multiple inheritance you are not limited to trees, but can have arbitrary DAGs, which is very helpful.