# # Infix operators

## # Prelude

### # Logical

`&&`

(opens new window) is logical AND, `||`

(opens new window) is logical OR.

`==`

(opens new window) is equality, `/=`

(opens new window) non-equality, `<`

(opens new window) / `<=`

lesser and `>`

/ `>=`

greater operators.

### # Arithmetic operators

The numerical operators `+`

(opens new window), `-`

(opens new window) and `/`

(opens new window) behave largely as you'd expect. (Division works only on fractional numbers to avoid rounding issues – integer division must be done with `quot`

(opens new window) or `div`

(opens new window)). More unusual are Haskell's three exponentiation operators:

```
4^5 ≡ (4*4)*(4*4)*4
```

```
3^^(-2) ≡ 1 / (2*2)
```

Unlike `^`

, this requires a fractional base type (i.e. `4^^5 :: Int`

will not work, only `4^5 :: Int`

or `4^^5 :: Rational`

).

`**`

(opens new window) implements real-number exponentiation. This works for very general arguments, but is more computionally expensive than `^`

or `^^`

, and generally incurs small floating-point errors. ```
2**pi ≡ exp (pi * log 2)
```

### # Lists

There are two concatenation operators:

```
[1,2] ++ [3,4] ≡ 1 : 2 : [3,4] ≡ 1 : [2,3,4] ≡ [1,2,3,4]
```

`!!`

(opens new window) is an indexing operator.

```
[0, 10, 20, 30, 40] !! 3 ≡ 30
```

Note that indexing lists is inefficient (complexity **O**(**n**) instead of **O**(1) for arrays (opens new window) or **O**(log **n**) for maps (opens new window)); it's generally preferred in Haskell to deconstruct lists by folding ot pattern matching instead of indexing.

### # Control flow

```
f $ x ≡ f x
≡ f(x) -- disapproved style
```

This operator is mostly used to avoid parentheses. It also has a strict version `$!`

(opens new window), which forces the argument to be evaluated before applying the function.

`.`

(opens new window) composes functions. ```
(f . g) x ≡ f (g x) ≡ f $ g x
```

## # Finding information about infix operators

Because infixes are so common in Haskell, you will regularly need to look up their signature etc.. Fortunately, this is just as easy as for any other function:

```
Prelude> :i +
class Num a where
(+) :: a -> a -> a
...
-- Defined in ‘GHC.Num’
infixl 6 +
Prelude> :i ^^
(^^) :: (Fractional a, Integral b) => a -> b -> a
-- Defined in ‘GHC.Real’
infixr 8 ^^
```

This tells me that `^^`

binds more tightly than `+`

, both take numerical types as their elements, but `^^`

requires the exponent to be integral and the base to be fractional.

The less verbose `:t`

requires the operator in parentheses, like

```
Prelude> :t (==)
(==) :: Eq a => a -> a -> Bool
```

## # Custom operators

In Haskell, you can define any infix operator you like. For example, I could define the list-enveloping operator as

```
(>+<) :: [a] -> [a] -> [a]
env >+< l = env ++ l ++ env
GHCi> "**">+<"emphasis"
"**emphasis**"
```

You should always give such operators a fixity declaration (opens new window), like

```
infixr 5 >+<
```

(which would mean `>+<`

binds as tightly as `++`

and `:`

do).

#### # Remarks

Most Haskell functions are called with the function name followed by arguments (prefix notation). For functions that accept two arguments like (+), it sometimes makes sense to provide an argument before and after the function (infix).

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