Key Principles of Functional Programming

Why This Matters

Functional programming isn't just an alternative coding style—it's a paradigm that fundamentally changes how you think about computation. In this course, you're being tested on your ability to recognize why certain design choices lead to safer, more maintainable code. The principles here—immutability, pure functions, higher-order functions, and referential transparency—form the foundation for understanding concepts like concurrency, program correctness, type systems, and algorithmic efficiency.

These principles interconnect in powerful ways: immutability enables referential transparency, which makes reasoning about code straightforward. Pure functions combined with higher-order functions allow for elegant composition. When you encounter exam questions about debugging, optimization, or code design, you'll need to identify which principle applies and why. Don't just memorize definitions—know what problem each principle solves and how they work together to create robust programs.

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Foundations of Safety and Predictability

These principles eliminate entire categories of bugs by ensuring that code behaves consistently and predictably. The core mechanism is removing hidden dependencies and side effects so that functions become reliable building blocks.

Immutability

• Data cannot be modified after creation—instead of changing values, you create new data structures with the desired changes
• Eliminates shared state bugs by ensuring concurrent threads can't accidentally corrupt each other's data
• Simplifies debugging because you can trace exactly where each value originated without tracking mutations

Pure Functions

• Same input always produces same output—no hidden dependencies on external state or time
• Zero side effects means the function doesn't modify variables, write to files, or change anything outside its scope
• Dramatically improves testability since you can verify behavior with simple input/output checks, no mocking required

Referential Transparency

• Any expression can be replaced with its value—if $$f(x) = 5$$, you can substitute 5 anywhere $$f(x)$$ appears
• Enables compiler optimizations like memoization and common subexpression elimination automatically
• Makes code self-documenting because function calls describe exactly what value they produce

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Abstraction and Composition

These principles let you build complex behavior from simple, reusable pieces. The mechanism is treating functions as data that can be combined, passed around, and transformed like any other value.

First-Class and Higher-Order Functions

• Functions are values—you can store them in variables, pass them as arguments, and return them from other functions
• Higher-order functions like map, filter, and reduce abstract common patterns, eliminating repetitive loop code
• Enables callbacks and strategies without the boilerplate of defining classes or interfaces

Function Composition

• Combines functions into pipelines—the output of one function feeds directly into the next, written as $$f \circ g$$ or f(g(x))
• Promotes single-responsibility design where each function does one thing well
• Declarative data flow makes complex transformations readable as a sequence of named operations

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Control Flow and Data Processing

These principles provide alternatives to imperative loops and conditionals. The mechanism is expressing computation as transformations and pattern-based dispatch rather than step-by-step instructions.

Recursion

• Functions call themselves to break problems into smaller, identical subproblems until reaching a base case
• Natural fit for recursive data structures—processing trees, linked lists, and nested JSON becomes intuitive
• Requires tail-call optimization in production code to prevent stack overflow; many functional languages guarantee this

Pattern Matching

• Destructures data and branches in one step—extracts values while simultaneously checking structure
• Exhaustiveness checking by the compiler ensures you handle all possible cases, catching bugs at compile time
• Replaces verbose if-else chains with concise, readable case expressions

Lazy Evaluation

• Expressions evaluate only when needed—computation is deferred until the result is actually used
• Enables infinite data structures like streams of all prime numbers; you only compute what you consume
• Potential memory pitfalls from accumulated thunks require understanding when strictness is necessary

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Type Systems and Data Modeling

These principles leverage the type system to make invalid states unrepresentable. The mechanism is encoding domain knowledge into types so the compiler catches logic errors before runtime.

Algebraic Data Types

• Sum types (OR) represent choices—an Option is either Some(value) or None, nothing else
• Product types (AND) combine fields—a Point has both an $$x$$ and a $$y$$ coordinate
• Pattern matching integration lets you safely destructure and handle each variant exhaustively

Declarative Programming Style

• Describes what, not how—filter(isEven, numbers) expresses intent without loop mechanics
• Higher abstraction level reduces cognitive load by hiding implementation details
• Often more concise because common patterns are captured in reusable higher-order functions

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Quick Reference Table

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Self-Check Questions

1. Which two principles work together to guarantee that a function can be safely called from multiple threads without locks?

2. A compiler replaces all calls to $$square(4)$$ with the literal 16. Which principle makes this optimization valid, and what property must the square function have?

3. Compare and contrast recursion and lazy evaluation as strategies for processing a potentially infinite stream of data. What are the trade-offs?

4. You're debugging code where a function returns different results on successive calls with identical arguments. Which principle has been violated, and what's the likely cause?

5. An FRQ asks you to refactor imperative loop code into functional style. Which three principles would guide your approach, and how would each contribute to the solution?