# Write a Type Evaluator in Haskell

June 19, 2024
Professor Marcus
🇦🇺 Australia
Professor Marcus Johnson is an experienced Haskell programmer with a background in Mathematics and Computer Science. With over 600 completed assignments, Professor Johnson specializes in teaching functional programming concepts, category theory, and lambda calculus in Haskell. He is known for his clear explanations and passion for sharing his knowledge with students.
Key Topics
• Building a Type Evaluator in Haskell
• Understanding the Basics
• The Type Evaluator Code
• Type Inference Function
• Conclusion
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## 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.

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