Extensible TypeScript with Object Algebras · Programming should be enjoyable
jnkr.tech
A lightweight approach to maintainable systems

I think object algebras have huge potential to improve the way complex software is written but I’ve never seen them used in practice. I think one reason why is that the research paper which introduced them is pretty hard to read. This post is my attempt to change that.

I’ve been working on this post off and on for like two years so I’m really excited to share it with people. It is very long. There’s a lot of ground to cover.

  • expr@programming.dev
    0·
    3 months ago

    This is a very common toy example we use in Haskell, though honestly this OOP version leaves a lot to be desired, comparatively

    The issue is that it tries to shoehorn separation of data and functions on data into a paradigm that’s fundamentally about fusing those two things together.

    Here’s the Haskell version. Note how much simpler it is because data and functions are separate:

    data Expr
  = Lit Int
  | Add Expr Expr

eval :: Expr -> Int
eval expr = case expr of
  Lit n -> n
  Add a b -> eval a + eval b

print :: Expr -> String
print expr = case expr of
  Lit n -> show n
  Add a b -> "(" ++ print a ++ " + " ++ print b ++ ")"

    Typescript can do something similar:

    type Expr = {
  kind: 'Lit',
  value: number
} | {
  kind: 'Add',
  left: Expr,
  right: Expr
}

function eval(expr: Expr): number {
  switch(expr.kind){
    case 'Lit': return expr.value;
    case 'Add': return eval(expr.left) + eval(expr.right);
    default:
      const _impossible: never = expr;
      return _impossible;
}

function print(expr: Expr): string {
  switch(expr.kind){
    case 'Lit': return `${expr.value}`;
    case 'Add': return `(${print(expr.left)} + ${print(expr.right)})`;
    default:
      const _impossible: never = expr;
      return _impossible;
}

    Both the OOP approach and Typescript itself struggle with additions to the algebra composed of different types, however. For example, imagine extending it to handle booleans as well, supporting equality operations. It’s difficult to make that well-typed using the techniques discussed thus far. In Haskell, we can handle that by making Expr a GADT, or Generalized Algebraic Data Type. That article actually already provides the code for this, so you can look there if you’re curious how it works.

    • jnkrtech@programming.devOP
      0·
      3 months ago

      Yes, this pattern is covered in my post on algebraic data types (linked at the start of the object algebras post.) The problem you mention about adding new data variants is exactly what object algebras solves. With object algebras data and functions are only co-located at the smallest possible granularity, so the desired functions and the desired data types can be composed as needed.

      • expr@programming.dev
        0·
        3 months ago

        Your post only showed adding functionality over the algebra, not new types on which the algebra operates (or “sorts”, as they are otherwise known). In other words, you can’t easily extend Expr to support Boolean logic in addition to addition itself. For a concrete example, how could you represent ternary operators like in the expression 2 + 2 == 4 ? 1 : 2, such that it’s well typed and will never result in an exception? With GADTs, this is very simple to do:

        data Expr a where
  Lit :: Int -> Expr Int
  Add :: Expr Int -> Expr Int -> Expr Int
  Eq :: Expr Int -> Expr Int -> Expr Bool
  If :: Expr Bool -> Expr Int -> Expr Int ->  Expr Int

eval :: Expr a -> a
eval expr = case expr of
  Lit n -> n
  Add a b -> eval a + eval b
  Eq a b -> eval a == eval b
  If p a b -> if eval p then eval a else eval b

-- >> eval example == 1 => true
example :: Expr Int
example =
  If ((Lit 2 `Add` Lit 2)  `Eq` Lit 4) (Lit 1) (Lit 2)