Haskell - Expressions P70540


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We want to have a module to mainpulate and evaluate integer expressions with addition, substraction, multiplication and division operations. In order to do so, the following type is declared:

data Expr = Val Int | Add Expr Expr | Sub Expr Expr | Mul Expr Expr | Div Expr Expr

For instance, Add (Val 3) (Div (Val 4) (Val 2)) represents 3 + 4 / 2, which evaluates to 5.

1. Evaluation without errors (20 points)

Using the Expr type, define a function eval1 :: Expr -> Int that, given an expression, returns its evaluation. You can assume there will never be divisions by zero.

2. Evaluation with possible error (30 points)

Using the Expr type, define a function eval2 :: Expr -> Maybe Int that, given an expression, returns its evaluationn as a Just value. In the case that some division by zero occurs, the result must be Nothing. You probably want to use the do notation over the Maybe a monad.

3. Evaluation with error report (30 points)

Using the Expr type, define a function eval3 :: Expr -> Either String Int that, given an expression, returns its evaluation as Right value. In the case that some division by zero occurs, the result must be Left "div0". You probably want to use the do notation over the Either a b monad.

Public test cases

  • Input

    eval1 (Val 2)
eval1 (Add (Val 2) (Val 3))
eval1 (Sub (Val 2) (Val 3))
eval1 (Div (Val 4) (Val 2))
eval1 (Mul (Add (Val 2) (Val 3)) (Sub (Val 2) (Val 3)))

    Output

    2
5
-1
2
-5

  • Input

    eval2 (Val 2)
eval2 (Add (Val 2) (Val 3))
eval2 (Sub (Val 2) (Val 3))
eval2 (Div (Val 4) (Val 2))
eval2 (Mul (Add (Val 2) (Val 3)) (Sub (Val 2) (Val 3)))
eval2 (Div (Val 4) (Val 0))
eval2 (Add (Div (Val 4) (Val 0)) (Val 3))
eval2 (Add (Val 3) (Div (Val 4) (Val 0)))

    Output

    Just 2
Just 5
Just (-1)
Just 2
Just (-5)
Nothing
Nothing
Nothing

  • Input

    eval3 (Val 2)
eval3 (Add (Val 2) (Val 3))
eval3 (Sub (Val 2) (Val 3))
eval3 (Div (Val 4) (Val 2))
eval3 (Mul (Add (Val 2) (Val 3)) (Sub (Val 2) (Val 3)))
eval3 (Div (Val 4) (Val 0))
eval3 (Add (Div (Val 4) (Val 0)) (Val 3))
eval3 (Add (Val 3) (Div (Val 4) (Val 0)))

    Output

    Right 2
Right 5
Right (-1)
Right 2
Right (-5)
Left "div0"
Left "div0"
Left "div0"
    • Information
    Author
    Jordi Petit
    Language
    English
    Translator
    Jordi Petit
    Original language
    Catalan
    Other languages
    Catalan
    Official solutions
    Haskell
    User solutions
    Haskell