how to parse strings to syntax tree using GADTs

Question

I was reading GADT introduction here and it I found the idea of restricting programmer to create only right type of syntax tree great, and I put this idea into my simple lambda calculus interpreter, but later I realized that I can't parse a string to this syntax tree, because one parse function needs to return different types of syntax tree, depending on input. Here's an example:

{-# LANGUAGE GADTs #-}
data Ident
data Lambda
data Application

data Expr a where
    Ident :: String -> Expr Ident
    Lambda :: Expr Ident -> Expr a -> Expr Lambda
    Application :: Expr a -> Expr a -> Expr Application

Before using GADTs, I was using this:

data Expr = Lambda Expr Expr
          | Ident String
          | Application Expr Expr

GADTs are great advantage here, bacuse now I can't create invalid syntax trees like Lambda (Application ..) ...

But with GADTs, I couldn't parse a string and create parse tree. Here are parser for Lambda, Ident, and Application expressions:

ident :: Parser (Expr Ident)
ident = ...

lambda :: Parser (Expr Lambda)
lambda = ...

application :: Parser (Expr Application)
application = ...

Now the problem is:

expr = choice [ident, application, lambda]

This obviously doesn't work, since each parser is returning different types.

So, is there a way to parse a string and create a syntax tree, with GADTs ?

score 8 · Accepted Answer · answered Jun 19 '12 at 15:45

8

You can use GADTs to make a type that contains Expr a for some unknown a.

data AnyExpr where AnyExpr :: Expr a -> AnyExpr

In situations where you don't want to restrict Expr to a specific type, use AnyExpr.

anyExpr :: Parser (Expr a) -> Parser AnyExpr
anyExpr p = fmap AnyExpr p

expr :: Parser AnyExpr
expr = choice [anyExpr ident, anyExpr application, anyExpr lambda]

answered Jun 19 '12 at 15:45

Heatsink

7,721
1
25
36

that's a great idea, thanks! but I still wonder if we have any other ways to do what I want, and whether what I'm doing is a good idea or not .. – sinan Jun 19 '12 at 15:58
2

@sinan - this is fine, but another approach would be to define two AST's, one for the parse output and one for actually working with. The parse output tree would be untyped, and the working AST would use GADTs like you've already implemented. – John L Jun 19 '12 at 17:01

how to parse strings to syntax tree using GADTs

1 Answers1