Functional Programming Cheat Sheet

1. Foundations of Functional Programming

Functional programming is a declarative paradigm that treats computation as the evaluation of mathematical functions. Rather than describing step-by-step procedures that mutate sta...

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2. Functions and Higher-Order Programming

Functional programming treats functions as first-class values: they can be assigned to variables, passed as arguments, returned from other functions, and stored in data structures....

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3. Data Structures and Types

Functional programming favors immutable data structures that, when modified, produce new versions while preserving the old. Persistent data structures achieve this efficiently thro...

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4. Recursion, Folds, and Evaluation

Since loops rely on mutable state, functional programming replaces them with recursion, in which a function calls itself on smaller subproblems until it reaches a base case. Deep r...

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5. Functors, Applicatives, and Monads

The functor–applicative–monad hierarchy is a layered abstraction for sequencing computations on wrapped values. A functor is any type that implements a map operation, letting you a...

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6. Type System Concepts

Haskell's type classes provide a mechanism for ad-hoc polymorphism, defining behavior that works across many types. Common examples include \( \text{Eq} \) for equality comparison,...

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7. Lambda Calculus and Category Theory

Lambda calculus, invented by Alonzo Church in the 1930s, is the theoretical foundation of functional programming. It has only three constructs: variables, abstraction \( \lambda x....

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8. Real-World Functional Programming and Concurrency

Different functional languages emphasize different aspects of the paradigm. Haskell is pure and lazy by default, with monadic IO and a powerful type system. OCaml is strict by defa...

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