Lesson 54 of 55

15 mins read

Capstone Project: Domain Expression Evaluator & AST Engine

In Plain English

Put all your Haskell skills into practice by building a complete domain expression tree evaluator supporting numeric literals, binary operations (+, -, *, /), variable bindings, and safe error handling using Either.

Deep Dive: How It Works

System Architecture:

2. Environment: type Env = [(String, Double)] for variable lookups.

3. Pure Evaluator: eval :: Env -> Expr -> Either String Double.

4. Safe Error Propagation: Catches division by zero and unbound variables gracefully.

Core Rules to Remember

End-to-End Algebraic Design: Combines recursive ADTs, pattern matching, and error monad mechanics.

Safe Evaluation Engine: Guaranteed crash-proof expression evaluation with explicit domain errors.

Live Interactive Example

Hit Run Code to see it live

Pure Expression AST Evaluator

Python 3.12

module Main where

data Expr
    = Val Double
    | Var String
    | Add Expr Expr
    | Mul Expr Expr
    | Div Expr Expr
    deriving (Show, Eq)

type Env = [(String, Double)]

eval :: Env -> Expr -> Either String Double
eval _   (Val n)     = Right n
eval env (Var name)  = case lookup name env of
    Just v  -> Right v
    Nothing -> Left ("Unbound variable: " ++ name)
eval env (Add e1 e2) = do
    v1 <- eval env e1
    v2 <- eval env e2
    return (v1 + v2)
eval env (Mul e1 e2) = do
    v1 <- eval env e1
    v2 <- eval env e2
    return (v1 * v2)
eval env (Div e1 e2) = do
    v1 <- eval env e1
    v2 <- eval env e2
    if v2 == 0 
        then Left "Division by zero"
        else return (v1 / v2)

main :: IO ()
main = do
    let env = [("x", 10.0), ("y", 5.0)]
    -- Expression: (x + y) * 2
    let expr1 = Mul (Add (Var "x") (Var "y")) (Val 2.0)
    -- Expression: x / 0
    let expr2 = Div (Var "x") (Val 0.0)

putStrLn $ "Evaluate (x + y) * 2: " ++ show (eval env expr1)
    putStrLn $ "Evaluate x / 0: " ++ show (eval env expr2)

Output Console

Click "Run Code" to view the rendered output.

How it works: The evaluator safely computed 30.0 and cleanly returned Left "Division by zero".

Your Turn: Micro Challenge

No pressure! Edit the starter code below and test your solution with instant feedback.

Micro Exercise

Evaluate Expression Tree

Evaluate `Add (Val 15.0) (Val 27.0)` in an empty environment `[]`.
Print `"Evaluated: "` followed by `show (eval [] (Add (Val 15.0) (Val 27.0)))`.

Sandbox Output

Click "Run & Check" to test your solution.

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