# Write a Type Evaluator in Haskell

## Understanding the Basics

Before diving into the code, let's make sure we have a solid grasp of the foundational concepts:

Data Types

Our journey begins by defining two crucial data types:

• Expr: This data type represents various types of expressions, including integer and boolean literals, arithmetic operations (addition, subtraction, multiplication, division), equality comparisons, less than comparisons, and conditional expressions.
• Type: In the context of this guide, we're focusing on two possible types: IntType and BoolType.

## The Type Evaluator Code

Now, let's break down the code piece by piece:

``` ```haskell -- Define a data type to represent expressions data Expr = IntLiteral Int | BoolLiteral Bool | Add Expr Expr | Subtract Expr Expr | Multiply Expr Expr | Divide Expr Expr | Equal Expr Expr | LessThan Expr Expr | If Expr Expr Expr deriving Show -- Define a data type to represent types data Type = IntType | BoolType deriving Eq -- Define a type inference function typeInference :: Expr -> Maybe Type typeInference (IntLiteral _) = Just IntType typeInference (BoolLiteral _) = Just BoolType typeInference (Add e1 e2) = do t1 <- typeInference e1 t2 <- typeInference e2 if t1 == IntType && t2 == IntType then Just IntType else Nothing typeInference (Subtract e1 e2) = do t1 <- typeInference e1 t2 <- typeInference e2 if t1 == IntType && t2 == IntType then Just IntType else Nothing typeInference (Multiply e1 e2) = do t1 <- typeInference e1 t2 <- typeInference e2 if t1 == IntType && t2 == IntType then Just IntType else Nothing typeInference (Divide e1 e2) = do t1 <- typeInference e1 t2 <- typeInference e2 if t1 == IntType && t2 == IntType then Just IntType else Nothing typeInference (Equal e1 e2) = do t1 <- typeInference e1 t2 <- typeInference e2 if t1 == t2 then Just BoolType else Nothing typeInference (LessThan e1 e2) = do t1 <- typeInference e1 t2 <- typeInference e2 if t1 == IntType && t2 == IntType then Just BoolType else Nothing typeInference (If e1 e2 e3) = do t1 <- typeInference e1 t2 <- typeInference e2 t3 <- typeInference e3 if t1 == BoolType && t2 == t3 then Just t2 else Nothing ``` ```

## Type Inference Function

At the heart of our type evaluator lies the `typeInference` function. Here's how it operates:

• When dealing with integer and boolean literals, it swiftly returns their respective types, whether it's IntType or BoolType.
• For arithmetic operations, such as addition or subtraction, our function takes a recursive approach. It calls typeInference on subexpressions and ensures both subexpressions have the type IntType. If they do, it returns Just IntType; otherwise, it returns Nothing.
•  In the case of equality and less than comparisons, we check that the subexpressions have compatible types, either both IntType or both BoolType. If the conditions align, we return Just BoolType.
• Lastly, for conditional expressions (the If case), we first confirm that the condition is a boolean. Then, we verify that the types of the two branches are identical, returning Just that common type. If the conditions aren't met, we return Nothing.

## Conclusion

Mastering the art of creating a type evaluator in Haskell is an essential skill for comprehending Haskell's type system thoroughly. The code we've provided is a fundamental example that you can expand upon to handle more complex expressions and additional types. Understanding type inference is pivotal in writing Haskell code that is both elegant and error-free. As you continue your Haskell programming journey, you'll find that this expertise opens doors to developing more efficient and reliable software, making you a more proficient programmer in the Haskell ecosystem.