After evaluating *attrset* and *attrpath*, the computational complexity is O(log(*n*)) for *n* attributes in the *attrset*

## Arithmetic

Numbers will retain their type unless mixed with other numeric types:
Pure integer operations will always return integers, whereas any operation involving at least one floating point number returns a floating point number.

Evaluation of the following numeric operations throws an evaluation error:
- Division by zero
- Integer overflow, that is, any operation yielding a result outside of the representable range of [Nix language integers](./syntax.md#number-literal)

See also [Comparison] and [Equality].

The `+` operator is overloaded to also work on strings and paths.


## String concatenation

> **Syntax**
>
> *string* `+` *string*

Concatenate two [strings][string] and merge their [string contexts](./string-context.md).


## Path concatenation

> **Syntax**
>
> *path* `+` *path*

Concatenate two [paths][path].
The result is a path.


## Path and string concatenation

> **Syntax**
>
> *path* + *string*

Concatenate *[path]* with *[string]*.
The result is a path.

> **Note**
>
> The string must not have a [string context](./string-context.md) that refers to a [store path].


## String and path concatenation

> **Syntax**
>
> *string* + *path*

Concatenate *[string]* with *[path]*.
The result is a string.

> **Important**
>
> The file or directory at *path* must exist and is copied to the [store].
> The path appears in the result as the corresponding [store path].



## Update

> **Syntax**
>
> *attrset1* // *attrset2*

Update [attribute set] *attrset1* with names and values from *attrset2*.

The returned attribute set will have all of the attributes in *attrset1* and *attrset2*.
If an attribute name is present in both, the attribute value from the latter is taken.


## Comparison

Comparison is

- [arithmetic] for [numbers][number]
- lexicographic for [strings][string] and [paths][path]
- item-wise lexicographic for [lists][list]:
  elements at the same index in both lists are compared according to their type and skipped if they are equal.

All comparison operators are implemented in terms of `<`, and the following equivalencies hold:

| comparison   | implementation        |
|--------------|-----------------------|
| *a* `<=` *b* | `! (` *b* `<` *a* `)` |
| *a* `>`  *b* |       *b* `<` *a*     |
| *a* `>=` *b* | `! (` *a* `<` *b* `)` |


## Equality

- [Attribute sets][attribute set] and [lists][list] are compared recursively, and therefore are fully evaluated.
- Comparison of [functions][function] always returns `false`.
- Numbers are type-compatible, see [arithmetic] operators.
- Floating point numbers only differ up to a limited precision.



## Logical implication

Equivalent to `!`*b1* `||` *b2*  (or `if` *b1* `then` *b2* `else true`)


## Pipe operators

- *a* `|>` *b* is equivalent to *b* *a*
- *a* `<|` *b* is equivalent to *a* *b*

> **Example**
>
> ```
> nix-repl> 1 |> builtins.add 2 |> builtins.mul 3
> 9
>
> nix-repl> builtins.add 1 <| builtins.mul 2 <| 3
> 7
> ```

> **Warning**
>
> This syntax is part of an
> [experimental feature](@docroot@/development/experimental-features.md)
> and may change in future releases.
>
> To use this syntax, make sure the
> [`pipe-operators` experimental feature](@docroot@/development/experimental-features.md#xp-feature-pipe-operators)
> is enabled.
> For example, include the following in [`nix.conf`](@docroot@/command-ref/conf-file.md):
>
> ```
> extra-experimental-features = pipe-operators
> ```