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Simple arithmetic expression language

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expressions.hs
Haskell
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module Expressions where
 
import Data.Maybe
import Text.Printf
import Control.Applicative
 
data Expr = Term Int | Op Operator Expr Expr | Var String
deriving (Show, Eq)
 
data Operator = Sum | Mult | Sub | Div
deriving (Show, Eq)
data Result a = Failure [String] | Success a
deriving (Show, Eq)
foldExpr :: (Int -> a) -> (Operator -> a -> a -> a) -> (String -> a) -> Expr -> a
foldExpr ft _ _ (Term i) = ft i
foldExpr ft fo fv (Op o u v) = fo o (foldExpr ft fo fv u) (foldExpr ft fo fv v)
foldExpr ft fo fv (Var id) = fv id
 
eval :: [(String, Int)] -> Expr -> Result Int
eval env = foldExpr Success applyOp getV
where
getV x = maybe (Failure [x]) Success $ lookup x env
 
applyOp :: Operator -> Result Int -> Result Int -> Result Int
applyOp o x y = getOp o <$> x <*> y
 
getOp :: Operator -> Int -> Int -> Int
getOp o = case o of
Sum -> (+)
Mult -> (*)
Sub -> (-)
Div -> div
 
printExpr :: Expr -> String
printExpr = foldExpr show (flip (printf "(%s %s %s)") . printOp) id
 
printOp o = case o of
Sum -> "+"
Mult -> "*"
Sub -> "-"
Div -> "/"
countTerms :: Expr -> Int
countTerms = foldExpr (const 1) (const (+)) (const 1)
 
sample = Op Mult (Op Sum (Var "x") (Var "y")) (Term 4)
 
instance Functor Result where
fmap f (Success a) = Success (f a)
fmap _ (Failure es) = Failure es
 
instance Applicative Result where
pure v = Success v
(Success f) <*> (Success x) = Success (f x)
(Failure xs) <*> (Failure ys) = Failure $ xs ++ ys
(Failure xs) <*> _ = Failure xs
_ <*> (Failure ys) = Failure ys

I had to change these lines:
26: printExpr = foldExpr show (\o u v -> printf "(%s %s %s)" u (printOp o) v)
35: countTerms = foldExpr (const 1) (_ -> (+))

Oops, that was slack. It seems we didn't actually compile that version in our haste at the end of the session. I've corrected it here now.

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