Haskell evaluates expressions using a process called lazy evaluation, also known as non-strict evaluation. In Haskell, expressions are not immediately evaluated when they are bound to variables or used in function calls. Instead, they are only evaluated when their values are actually needed.

Lazy evaluation allows Haskell to avoid unnecessary computations and enables the use of potentially infinite data structures. When an expression is evaluated, Haskell uses a strategy called memoization, which means that the result is stored and reused for subsequent evaluations, avoiding redundant computations.

Another key aspect of Haskell's evaluation is that it follows a call-by-need evaluation strategy. This means that the arguments of a function are not evaluated until they are required to compute the function's result. This strategy allows functions to be defined more generally, without worrying about the order of evaluation.

Moreover, Haskell provides constructs like guards and pattern matching that allow for more efficient evaluation by selectively evaluating only the necessary parts of an expression. Pattern matching enables the matching of expressions to predefined patterns, allowing specific branches to be evaluated based on the given input.

Overall, Haskell's evaluation strategy of lazy and call-by-need evaluation, along with features like memoization and pattern matching, provides a powerful and efficient way of evaluating expressions while minimizing unnecessary computations.

## What is the role of partial application in Haskell expression evaluation?

Partial application plays a crucial role in Haskell expression evaluation. In Haskell, functions are automatically curried by default, which means that a function that takes multiple arguments can be invoked with fewer arguments than expected. When a function is partially applied, it returns a new function that takes the remaining arguments.

During expression evaluation, partial application allows for creating new functions by applying only a subset of the arguments to an existing function. This helps in creating more expressive and reusable code by promoting function composition and abstraction.

Partial application also enables lazy evaluation in Haskell. By partially applying a function and returning a new function, Haskell can defer the evaluation of the remaining arguments until they are actually needed. This lazy evaluation strategy improves efficiency as it avoids unnecessary computations.

In summary, partial application in Haskell expression evaluation allows for function composition, code reusability, and lazy evaluation, contributing to the expressive power and efficiency of the language.

## What is the role of currying in Haskell expression evaluation?

Currying is a technique used in Haskell to evaluate expressions by transforming functions that take multiple arguments into a sequence of functions, each with a single argument.

In Haskell, a function is curried by default. This means that a function that conceptually takes multiple arguments actually takes one argument and returns another function that takes the next argument. This process can be repeated until all arguments are consumed and the final result is produced.

Currying plays a role in Haskell expression evaluation by allowing functions to be partially applied. Partial application means that a function can be called with fewer arguments than expected, resulting in a new function with the remaining arguments waiting to be supplied. This provides great flexibility and composability in defining and using functions.

The evaluation of curried functions follows a process called lazy evaluation, where expressions are only evaluated when needed. This allows for efficient computation by avoiding unnecessary evaluations and allows for the expression of infinite data structures.

Overall, currying in Haskell expression evaluation enables functional programming paradigms such as higher-order functions, function composition, and programming with partially applied functions.

## How does Haskell evaluate expressions?

Haskell uses lazy evaluation to evaluate expressions. This means that expressions are not evaluated until their values are actually needed.

When a Haskell program is executed, it builds up a lazy computation graph of expressions. When a value is needed, the computation graph is traversed, and only the necessary expressions to compute the desired value are evaluated. This allows Haskell to avoid unnecessary computations and potentially infinite loops, as expressions are only evaluated when their results are actually needed.

Lazy evaluation also allows for more efficient computation, as it avoids unnecessary work. For example, in cases where an expression only needs a part of a data structure, Haskell can avoid evaluating the entire structure and only compute the necessary parts.

However, lazy evaluation can sometimes lead to unexpected behavior, as it may cause expressions to be evaluated in a different order than expected. This is known as non-strict semantics, as the order of evaluation is determined by the need for values rather than by the order of expressions in the code.

In some cases, Haskell also supports strict evaluation, where expressions are evaluated immediately. This can be useful for cases where the laziness of Haskell's default evaluation strategy is not desired.

## How does Haskell handle function application?

Haskell handles function application in a consistent manner, adhering to the expression syntax and type system rules. Here are a few key points about how Haskell handles function application:

- Function application is denoted by a space character between the function name and its argument(s). For example, calling a function f with arguments x and y is written as f x y.
- In Haskell, function application has the highest precedence and is left associative. This means that if a function is applied to multiple arguments, the application is performed from left to right. For example, f x y z is equivalent to ((f x) y) z.
- Function application is considered a type of operator that takes a function as its left operand and its argument(s) as its right operand(s). This can be seen as a form of syntactic sugar where infix operators are treated as normal functions. For instance, the operator + is actually a function (+) that takes two arguments.
- Currying is a fundamental aspect of Haskell's function application. Currying allows a multi-argument function to be transformed into a chain of single-argument functions. This means that when a function is applied to less than its total number of arguments, a new function is returned that takes the remaining arguments. For example, if f is a function of two arguments, f x returns another function that takes the second argument.
- The type system in Haskell also takes function application into account. Function types are expressed as a series of arrows, where the type of a multi-argument function is represented as a sequence of arrow types. For instance, a function that takes arguments of types a, b, and c and returns a result of type d is represented as (a -> b -> c -> d).

Overall, Haskell's approach to function application allows for flexible and concise expression of computations while maintaining a strong type system.