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

    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)