Dear all,

I was wondering whether it was possible to write fold expressions more elegantly. Suppose I have the following

datastructure:

data Expr = Add Expr Expr

          | Sub Expr Expr

          | Mul Expr Expr

          | Eq  Expr Expr

          | B Bool

          | I Int

          deriving Show

          

type ExprAlgebra r = (r -> r -> r, -- Add

                      r -> r -> r, -- Sub

                      r -> r -> r, -- Mul

                      r -> r -> r, -- Eq

                      Bool   -> r, -- Bool

                      Int -> r     -- Int

                      )

                      

foldAlgebra :: ExprAlgebra r -> Expr -> r

foldAlgebra alg@(a, b, c ,d, e, f) (Add x y) = a (foldAlgebra alg x) (foldAlgebra alg y)

foldAlgebra alg@(a, b, c ,d, e, f) (Sub x y) = b (foldAlgebra alg x) (foldAlgebra alg y)

foldAlgebra alg@(a, b, c ,d, e, f) (Mul x y) = c (foldAlgebra alg x) (foldAlgebra alg y)

foldAlgebra alg@(a, b, c ,d, e, f) (Eq  x y) = d (foldAlgebra alg x) (foldAlgebra alg y)

foldAlgebra alg@(a, b, c ,d, e, f) (B b')    = e b'

foldAlgebra alg@(a, b, c ,d, e, f) (I i)     = f i

If I am correct, this works, however if we for example would like to replace all Int's by booleans (note: this is to illustrate my problem):

replaceIntByBool = foldAlgebra (Add, Sub, Mul, Eq, B, \x -> if x == 0 then B False else B True)

As you can see, a lot of "useless" identity code. Can I somehow optimize this? Can someone give me some pointers how I can write this more clearly (or with less code?) So I constantly don't have to write Add, Sub, Mul, for those things that I just want an "identity function"?

Thanks in advance!

Jun Jie