# Solved: boolean

Sure, here goes.

The power of boolean in Haskell has the ability to create logic that can define so many possibilities and outcomes. They form the foundation of control structures and decision making in Haskell.

Understanding how to effectively use Boolean values can enhance the logic of your code and the power of your Haskell programs.

## The Beauty of Boolean in Haskell

Boolean in Haskell is a data type. It has two value constructors, True and False, which are the logical constants representing the two truth values. Haskell uses the Bool type for Boolean algebra. Boolean logic forms the basis of mathematical logic and is used in electrical engineering and computer science. Besides, they’re used to compare variables and expressions.

In Haskell, Boolean logic is centered around the 3 core operations: AND, OR, and NOT. In Haskell, these are denoted as &&, ||, and not respectively. Just like mathematical operations, boolean operations follow specific precedence and associativity rules.

```-- The 'AND' operation
True && True   -- evaluates to True
True && False  -- evaluates to False
False && True  -- evaluates to False
False && False -- evaluates to False

-- The 'OR' operation
True || True   -- evaluates to True
True || False  -- evaluates to True
False || True  -- evaluates to True
False || False -- evaluates to False

-- The 'NOT' operation
not True  -- evaluates to False
not False -- evaluates to True
```

Boolean functions are the functions that take Boolean inputs and return Boolean outputs. These functions implement complex logical operations based on our needs and are an integral part of programming in Haskell.

Lets dive deeper into Haskell’s Boolean Functions:

The powerful programming language Haskell has in-built functions that take in boolean values as parameters and output boolean values as per the logic they are defined with. These functions include “and”, “or”, and “not”.

Using these functions we can perform logical operations on boolean lists.

```and [True, True, False] -- evaluates to False
or [True, False, False] -- evaluates to True
not True -- evaluates to False
```

The “and” function returns True if and only if all elements in the list are True. The “or” function returns True if at least one element in the list is True. The “not” function flips the input boolean value, if it is True it becomes False and vice versa.

## Conditional Structures Using Boolean Logic

Believe it or not, Boolean plays a crucial role in conditional structuring in coding with Haskell. In Haskell, the if-then-else expression is used to introduce decision-making abilities in our programs. Here’s an example of a Haskell program using Boolean logic to decide which string to print based on an integer’s value:

checkNumber :: Int -> String
checkNumber n =
if n > 10 then “More than ten”
else if n < 10 then "Less than ten" else "It’s ten" main = putStrLn(checkNumber 10) -- It’s ten [/code] In the above program, checkNumber takes an integer as input and depending on the value of the integer, returns a corresponding string. To make this decision, it uses an if-then-else clause in which the initial condition (n > 10 or n < 10) will be a boolean expression that the Haskell program evaluates to either the True or the False. The expression right after "then" is executed if the condition is True; otherwise, if the condition is False, the expression right after "else" is executed. This is a basic example of decision-making in Haskell programming using Boolean logic.

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