The Haskell Mindset

Introduction

We all have our deeply rooted beliefs and programming paradigms we’re passionate about both for rational reasons and pure enjoyment. Functional programming often appears intimidating shrouded deeply in academic terminology and abstract concepts.

But what if I told you that understanding functional programming doesn’t have to be a daunting journey? What if the reasoning behind it is not only accessible but might actually transform how you think about code?

Most individuals have come from the imperative mindset of programming and because of this your minds computational model needs to learn some new concepts. You will read and sometimes hear from individuals that you need to “unlearn” some things from this imperative mindset, but I say we don’t need to unlearn it but we need to expand our comprehension into new ideas and concepts.

Why Haskell?

Haskell was born in academia and it was designed for research, teaching and of course learning which explains its reputation for complex terminology and abstractions. With semantics based on the Miranda language, it offers a unique approach to programming.

At its core, Haskell is a purely functional, strongly typed language that enforces immutability. Unlike OCaml, which provides ways to escape through mutable types, Haskell embraces purity completely. This alone Is why I feel it is worth learning Haskell first. It will force the mindset and not allow you to fallback on the imperative way of thinking.

This purity means programs don’t modify state, they transform inputs to outputs without side effects. The result is referential transparency: given the same inputs, functions always produce the same outputs. This predictability becomes a powerful tool for reasoning about code and eliminating entire classes of bugs.

Why Theory matters

You’ll often hear that “you don’t need to understand category theory or advanced mathematics to program in Haskell.” This statement is technically true, you can write functional code without diving into the theoretical aspects. But it’s also somewhat misleading.

While you can certainly begin programming in Haskell without a mathematics degree, understanding even the basics of its theoretical foundations will dramatically accelerate your learning curve and deepen your appreciation of the language’s design choices.

So what theory matters and what doesn’t? I would start off first by saying take it slow and be open to learning a new way of thinking and programming. Your brains computational model may not fit the functional way of thinking at the beginning, but the benefits of sticking to it in the end pays off.

So what are the benefits? Why do we need to understand this? Let’s explain with a few examples.

• Function composition (f . g): Understanding why composition is central to functional programming helps you write more concise, pointfree style code and understand the relationship between functions.
• Morphisms: These are simply structure preserving maps a fancy way of saying “functions that maintain important properties”
• Isomorphisms: Recognizing when two different representations are essentially equivalent helps you make better data modeling decisions
• Identity functions: These seemingly trivial functions (id x = x) become powerful tools in higher-order functions and abstractions
• Monads These encapsulate computation patterns, especially side effect so you can write clean, composable code even when dealing with things like IO, state, or failure

When you encounter monads, functors, and applicatives in Haskell, they won’t seem like arbitrary language features but logical extensions of these mathematical principles.

You might be wondering: “Doesn’t this complicate programming more than necessary? Why learn these theoretical concepts just to write code?” That’s a fair question. Learning Haskell involves a different investment than picking up another imperative language. The payoff comes in the form of powerful abstractions, fewer bugs, and code that’s often more concise and maintainable.

Is Haskell for everyone? Perhaps not. But if you’re curious about a deeper approach to solving problems, one that has influenced modern features in languages from JavaScript to Rust, the journey into functional thinking offers rewards that extend beyond Haskell itself.

Connecting the dots

Let’s try to understand why a few of the examples above actually matter. When it comes to functional programming we know that our programs are made up of functions and then composed in a way to solve the problem we are writing abstractions for. The way we write our programs is a personal art form. We all attempt to write concise, clear code so that others and ourselves can understand it clearly.

Let’s talk about function composition and revisit type annotations to help clearly demonstrate my point.

Suppose we have function f and g

f :: A -> B

g :: B -> A

We can now say we have some function f that has type A to B and some function g that has type B to A. We can now see that we can compose these functions as such:

g . f

Which reads g after f because we have an arrow from A -> B and then function g takes B -> A. Which we have now created a new function that goes from A -> C

(g . f) :: A -> C

This works by applying f first then applying g to the result. This process can be shown in Haskell with the following syntax.

(g . f) x = g (f x)

From our list above we can also determine that these are isomorphic. How so? We can determine they are isomorphic since we have a function f that goes from A -> B and function g that goes from B -> A such that g . f = id_a and f . g = id_b where id is the identity function. We can convert back and forth between the types without losing any information.

So from a simple composition we have seen some concepts behind it. How is this practical? Let’s look at a trivial example that sums and squares a list and we can see how our understanding of function composition can arguably make this clearer and more concise.

sumListSq :: [Int] -> Int
sumListSq xs = (foldr (+) 0 xs) ^ 2

This works and in such a simple example this might be fine, but with our understanding of function composition we can refactor this and make it a little more concise and clear.

sumListSq :: [Int] -> Int
sumListSq = (^2) . foldr (+) 0

So what exactly did we do?

1. We recognized that sumListSq is the composition of two functions: First by summing the list (foldr (+) 0) and then squaring the result (^2)
2. Instead of explicitly naming the parameter xs and showing the transformation step by step we directly compose the function by using “.” operator.
3. The parameter is implicit in pointfree style so we are now focusing on the transformation itself rather than the data being transformed.

This becomes even more powerful as we create more complex pipelines focusing on the transformations.

calcListToDbl :: [Int] -> Double
calcListToDbl = sqrt . fromIntegral . sum . filter even . map (*2)

Here, we’re composing five different functions into a single, readable pipeline without naming a single intermediate value or parameter. This style can make code more declarative, focusing on what is happening rather than how it’s implemented.

We’ve spent considerable time exploring function composition and basic category theory not as an academic exercise, but as foundations for a fundamentally different way of approaching software development.

When we shift from merely reading a type annotation like [Int] -> Double as “a function that takes a list of integers and produces a double,” to understanding it as a morphism, a transformation that preserves structure while converting data from one form to another our entire perspective changes.

Our mindset as we begin to write these abstractions will begin to shift to understanding how our data relates and how we can better architect software to be correct, efficient and maintainable in a way that we may have not thought of or are able to with the imperative mindset.

1. We begin to see programs as pipelines of transformations rather than sequences of instructions
2. We focus on how data types relate to each other through well-defined mappings
3. We leverage the type system to make invalid states unrepresentable
4. We compose small, verifiable functions into clear and concise behaviors

The beauty of the functional approach isn’t just that it allows us to write more concise code, though that’s often a side effect. Rather, it’s that it provides a framework for thinking about software that naturally leads to solutions that are correct by construction, efficient through optimization, and maintainable through clear separation of concerns. This, I feel is the beginning of the building blocks of a Haskell mindset.

Resources

If you’re interested in furthering your knowledge in the mindset of Functional Programming I’ve included some free and paid resources.

• Why Functional Programming Matters by John Hughes (PDF)
• Category Theory For Programmers by Bartosz Milewski(Github, Blog)
• Thinking Functionally with Haskell by Richard Bird (Amazon)
• Grokking Functional Programming by Michal Plachta (Manning)