The journey to create combinators for parsing and pretty-pretting continues!

This post (along with the new syntax-optics repo) combines two previous efforts:

• "Elegant AST Parsing and Building with Prisms" declared Prisms to parse and print ASTs, but lacking descriptive errors when the parsing fails
• "Basic error reporting for optics" declared new lens-compatible optics that add error reporting to parse errors

The resulting combinators let us nicely declare syntax:

data Expr
    = Lit Int
    | Add Expr Expr
    | Mul Expr Expr
    deriving (Show, Eq)
makePrisms ''Expr

expr :: VerbosePrism' String String Expr
expr = tokens . takeExpr . endOfTokens

takeExpr :: VerbosePrism' String [String] (Expr, [String])
takeExpr =
    infixOpLeftRecursion p "+" _Add $           -- Additions of
    infixOpLeftRecursion p "*" _Mul $           -- multiplications of
    tryMatchAtom p (prismFallback _Lit) _Show $ -- literals or
    parens takeExpr                             -- expressions in parens
    where
        p = Proxy @String

expr can be used to both pretty-print and to parse:

> expr # (Lit 1 `Mul` (Lit 2 `Add` Lit 3)) `Add` Lit 4
"1 * (2 + 3) + 4"

> "1 * (2 + 3) + 4" ^? expr
Just (Add (Mul (Lit 1) (Add (Lit 2) (Lit 3))) (Lit 4))

Now, to also get the syntax errors when parsing, we can use the new ^?? operator rather than lens's ^?:

> "2 + 3 * * 5" ^?? expr
Left "Unexpected \"*\""

Still lacking in the library

• The errors from syntax-optics do not currently report source-code locations of syntax errors.
• An AVerbosePrism type synonym, similar in spirit to ALens and APrism, is currently missing. With it the library would not need RankNTypes nor Proxy parameters which it currently requires (p in the example in this post).

I've tried to define AVerbosePrism but haven't succeeded so far. Help and advice from lens wizards would be very appreciated!

Notes

• Title image by Jean François WITZ.