Haskell is a purely functional programming language that features strong static typing, lazy evaluation, and immutability by default.
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Functions in Haskell are defined using equations, e.g., 'add x y = x + y'. The type signature is optional but recommended: 'add :: Int -> Int -> Int'.
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Pattern matching is a way of deconstructing values to use their components, allowing functions to behave differently based on the input patterns.
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Lazy evaluation means expressions are only evaluated when their results are needed, allowing for efficient handling of infinite data structures and improved performance.
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Types are labels for values, while typeclasses are interfaces defining behavior. For example, Int is a type, and Num is a typeclass for numeric operations.
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Lists in Haskell are created using square brackets, e.g., [1,2,3]. They can also be created using range notation like [1..10] or list comprehensions.
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'=' is used for definition/assignment, while '==' is used for equality comparison. For example, 'x = 5' defines x, while 'x == 5' checks if x equals 5.
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IO in Haskell is handled through monads, specifically the IO monad, which safely separates pure functions from operations with side effects.
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Guards are boolean expressions used to test properties of values and control program flow, similar to if-then-else but more readable.
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Maybe is a type for values that might not exist, with constructors Just a (for present values) and Nothing (for absent values), helping handle potential failures safely.
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Recursion is a fundamental concept where functions call themselves to solve problems. It's especially important in Haskell as there are no traditional loops.
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Single-line comments start with -- and multi-line comments are enclosed between {- and -}.
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The $ operator is used for function application without parentheses, with lower precedence than normal application. It helps reduce code clutter.
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Lists are concatenated using the ++ operator, e.g., [1,2] ++ [3,4] results in [1,2,3,4].
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A higher-order function is one that takes functions as arguments or returns functions as results. Common examples include map, filter, and fold.
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The State monad represents computations that carry state through a sequence of operations. It's useful for maintaining mutable state in a pure functional way, with get and put operations for state manipulation.
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To implement a custom typeclass, use the 'class' keyword to define the typeclass and 'instance' to provide implementations. Example: 'class MyShow a where myShow :: a -> String'.
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Functors are types that implement fmap, allowing function application over wrapped values. They must satisfy identity and composition laws: fmap id = id and fmap (f . g) = fmap f . fmap g.
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Applicative functors extend functors with pure and <*> operations, allowing application of wrapped functions to wrapped values and sequential composition of effects.
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Monad transformers combine multiple monads into a single monad, allowing composition of different effects. Common examples include StateT, ReaderT, and ExceptT.
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Lenses are composable abstractions for accessing and modifying parts of immutable data structures, making it easier to work with nested records and complex data types.
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foldl performs left-associated reduction (from left to right), while foldr performs right-associated reduction. They differ in evaluation order and stack usage.
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Type inference uses the Hindley-Milner algorithm to automatically determine types of expressions without explicit annotations, while maintaining type safety.
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Generalized Algebraic Data Types allow for more precise type constraints on constructors, enabling type-safe operations that would be impossible with regular ADTs.
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Type families are functions on types, allowing type-level programming and associated type relationships. They're useful for type-safe computations and generic programming.
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Exceptions in Haskell are handled using Either, Maybe, or ExceptT for pure code, and catch/throw in IO monad for impure operations.
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The Reader monad represents computations that need access to a shared environment, avoiding explicit parameter passing through deep call chains.
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Lazy I/O allows reading files lazily but can lead to resource management issues. Better alternatives include strict I/O or streaming libraries like conduit.
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Phantom types are type parameters that don't appear in the data constructor, used for adding compile-time constraints and improving type safety.
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Concurrent Haskell uses lightweight threads (forkIO), STM for atomic operations, and MVars/TVars for communication between threads, all with functional guarantees.
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Free monads provide a way to separate program description from interpretation, enabling flexible composition of domain-specific languages and better separation of concerns in large applications.
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Rank-n types allow for polymorphic functions to be passed as arguments where the caller can't specify the types. They're useful for encoding higher-rank polymorphism and creating more flexible abstractions.
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The GHC runtime uses thunks to implement lazy evaluation, with sophisticated mechanisms for sharing, blackholing to prevent infinite loops, and garbage collection of evaluated thunks.
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Type-level computations use type families, data kinds, and promoted datatypes to perform calculations at compile time, enabling static guarantees and complex generic programming.
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Category theory provides the mathematical foundation for Haskell's abstractions like functors, monads, and arrows, helping define lawful and composable interfaces.
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Optimization involves understanding strictness annotations, RULES pragmas, fusion, worker/wrapper transformation, and GHC's rewrite rules for performance tuning.
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Arrows generalize functions and monads, providing a unified interface for computation. They're useful for stream processing, circuit description, and parser combinators.
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Dependent types allow types to depend on values. While Haskell doesn't directly support them, they can be emulated using singletons, GADTs, and type families.
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STM provides atomic, composable transactions for concurrent programming, using TVars for shared state and ensuring consistency through optimistic execution and rollback.
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Type roles (nominal, representational, phantom) control how type parameters behave with respect to coercion, ensuring type safety with newtypes and generic programming.
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Type families provide functions on types with explicit equations, while functional dependencies specify relationships between type variables in multi-parameter type classes.
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GHC's typechecker uses constraint solving, unification, and sophisticated inference algorithms to verify program correctness and resolve complex type-level computations.
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Bidirectional pattern synonyms provide custom patterns with both pattern matching and construction capabilities, allowing abstraction over data representation.
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Impredicative polymorphism allows instantiating quantified types with polymorphic types, which is challenging for type inference and requires special compiler support.
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Effect systems can be implemented using free monads, extensible effects, or capability-based approaches to track and compose computational effects statically.
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Relation algebras provide mathematical foundations for database queries, graph algorithms, and program verification through categorical abstractions.
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Linear types ensure resources are used exactly once, enabling safe resource management, optimization opportunities, and better reasoning about memory usage.
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Lazy pattern matching involves creating thunks for unevaluated patterns and managing evaluation order to maintain lazy semantics while ensuring pattern match completeness.
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Type-level proofs use GADTs, type families, and constraint kinds to encode and verify program properties at compile time through the type system.
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Purely functional data structures use techniques like path copying, structural sharing, and amortization to achieve efficiency while maintaining immutability.
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