In Haskell, both **operators** and **functions** are used to perform operations on values, but they differ in their syntax and sometimes in how they are used. Here’s a breakdown of the differences:

### 1. Syntax and Notation

**Operators**: Typically use symbols (! # $ % * + . / < = > ? \ ^ | : – ~) rather than letters (e.g.,`+`

,`*`

,`&&`

,`++`

) and are used in**infix notation**. This means they are placed between the operands (e.g.,`3 + 4`

).**Functions**: Typically use alphabetic names (e.g.,`add`

,`sum`

,`map`

) and are used in**prefix notation**, where the function name comes before its arguments (e.g.,`add 3 4`

).

**Example**:

```
-- Using an operator (infix notation)
3 + 4 -- Result: 7
-- Using a function (prefix notation)
add 3 4 -- Result: 7
```

### 2. Infix vs. Prefix Application

**Operators**are generally used infix by default, which makes them look more like mathematical expressions. You can use operators as**prefix functions**by enclosing them in parentheses (e.g.,`(+) 3 4`

).**Functions**are typically used in prefix notation but can be used in**infix**notation if enclosed in backticks (e.g.,`3 `add` 4`

).

**Example**:

```
-- Using the `+` operator as a prefix function
(+) 3 4 -- Result: 7
-- Using a function in infix notation
let add x y = x + y
3 `add` 4 -- Result: 7
```

### 3. Custom Operators vs. Regular Functions

- You can create
**custom operators**in Haskell by using symbolic names (e.g.,`!+!`

,`++=`

). Custom operators have to be symbols rather than letters. **Functions**can be named with alphabetic identifiers, allowing more descriptive naming (e.g.,`multiply`

,`concatLists`

).

**Example of a Custom Operator**:

```
-- Defining a custom operator that mimics add (+)
(!+!) :: Int -> Int -> Int
x !+! y = x + y
3 !+! 4 -- Result: 7
```

### 4. Readability and Intent

**Operators**are often used when an operation is simple, frequently used, or mathematically intuitive (e.g.,`+`

for addition,`*`

for multiplication). They can make code involving calculations or data manipulation concise and closer to mathematical notation.**Functions**are generally used when an operation is more complex or needs a descriptive name for clarity (e.g.,`filter`

,`map`

,`sumList`

). This improves readability, especially in larger programs.

### 5. Precedence and Associativity

**Operators**have defined**precedence**and**associativity**, which control the order of evaluation in expressions. For example,`*`

has higher precedence than`+`

, so`3 + 4 * 2`

is evaluated as`3 + (4 * 2)`

.**Functions**don’t have precedence rules like operators. They are evaluated in the order they are applied, from left to right, unless parentheses are used to change the order.

### Summary Table

Aspect | Operators | Functions |
---|---|---|

Syntax | Symbols (e.g., `+` , `*` , `&&` ) | Alphabetic names (e.g., `add` , `map` ) |

Default Notation | Infix | Prefix |

Infix Usage | By default, e.g., `3 + 4` | Use backticks, e.g., `3 `add` 4` |

Custom Naming | Symbols only | Alphabetic names |

Precedence/Associativity | Yes | No |

Readability Intent | For concise, common operations | For descriptive, complex operations |

In essence, operators are specialized, symbolic functions that allow for infix notation and precedence handling, while functions are more general-purpose and are often used to improve readability with descriptive names.

Conceptually, there is no difference between an operator and a function, and you can use backticks or parens to make one work like the other.

`💡 `**Helpful References**
**StackOverflow - Difference between an operator and a function in Haskell**
https://stackoverflow.com/questions/2480974/what-is-the-difference-between-an-operator-and-a-function-in-haskell

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