Merge pull request #7498 from fricklerhandwerk/path+string

refactor documentation of operators, document `+` for strings and paths

2 files changed, 169 insertions, 29 deletions

diff --git a/doc/manual/src/language/operators.md b/doc/manual/src/language/operators.md
index 32398189d..797f13bd3 100644
--- a/doc/manual/src/language/operators.md
+++ b/doc/manual/src/language/operators.md
@@ -1,28 +1,167 @@
 # Operators
 
-The table below lists the operators in the Nix language, in
-order of precedence (from strongest to weakest binding).
-
-| Name                     | Syntax                              | Associativity | Description                                                                                                                                                                                                                   | Precedence |
-| ------------------------ | ----------------------------------- | ------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------- |
-| Select                   | *e* `.` *attrpath* \[ `or` *def* \] | none          | Select attribute denoted by the attribute path *attrpath* from set *e*. (An attribute path is a dot-separated list of attribute names.) If the attribute doesn’t exist, return *def* if provided, otherwise abort evaluation. | 1          |
-| Application              | *e1* *e2*                           | left          | Call function *e1* with argument *e2*.                                                                                                                                                                                        | 2          |
-| Arithmetic Negation      | `-` *e*                             | none          | Arithmetic negation.                                                                                                                                                                                                          | 3          |
-| Has Attribute            | *e* `?` *attrpath*                  | none          | Test whether set *e* contains the attribute denoted by *attrpath*; return `true` or `false`.                                                                                                                                  | 4          |
-| List Concatenation       | *e1* `++` *e2*                      | right         | List concatenation.                                                                                                                                                                                                           | 5          |
-| Multiplication           | *e1* `*` *e2*,                      | left          | Arithmetic multiplication.                                                                                                                                                                                                    | 6          |
-| Division                 | *e1* `/` *e2*                       | left          | Arithmetic division.                                                                                                                                                                                                          | 6          |
-| Addition                 | *e1* `+` *e2*                       | left          | Arithmetic addition.                                                                                                                                                                                                          | 7          |
-| Subtraction              | *e1* `-` *e2*                       | left          | Arithmetic subtraction.                                                                                                                                                                                                       | 7          |
-| String Concatenation     | *string1* `+` *string2*             | left          | String concatenation.                                                                                                                                                                                                         | 7          |
-| Not                      | `!` *e*                             | none          | Boolean negation.                                                                                                                                                                                                             | 8          |
-| Update                   | *e1* `//` *e2*                      | right         | Return a set consisting of the attributes in *e1* and *e2* (with the latter taking precedence over the former in case of equally named attributes).                                                                           | 9          |
-| Less Than                | *e1* `<` *e2*,                      | none          | Arithmetic/lexicographic comparison.                                                                                                                                                                                                        | 10         |
-| Less Than or Equal To    | *e1* `<=` *e2*                      | none          | Arithmetic/lexicographic comparison.                                                                                                                                                                                                        | 10         |
-| Greater Than             | *e1* `>` *e2*                       | none          | Arithmetic/lexicographic comparison.                                                                                                                                                                                                        | 10         |
-| Greater Than or Equal To | *e1* `>=` *e2*                      | none          | Arithmetic/lexicographic comparison.                                                                                                                                                                                                        | 10         |
-| Equality                 | *e1* `==` *e2*                      | none          | Equality.                                                                                                                                                                                                                     | 11         |
-| Inequality               | *e1* `!=` *e2*                      | none          | Inequality.                                                                                                                                                                                                                   | 11         |
-| Logical AND              | *e1* `&&` *e2*                      | left          | Logical AND.                                                                                                                                                                                                                  | 12         |
-| Logical OR               | *e1* <code>&#124;&#124;</code> *e2* | left          | Logical OR.                                                                                                                                                                                                                   | 13         |
-| Logical Implication      | *e1* `->` *e2*                      | none          | Logical implication (equivalent to <code>!e1 &#124;&#124; e2</code>).                                                                                                                                                                            | 14         |
+| Name                                   | Syntax                                     | Associativity | Precedence |
+|----------------------------------------|--------------------------------------------|---------------|------------|
+| [Attribute selection]                  | *attrset* `.` *attrpath* \[ `or` *expr* \] | none          | 1          |
+| Function application                   | *func* *expr*                              | left          | 2          |
+| [Arithmetic negation][arithmetic]      | `-` *number*                               | none          | 3          |
+| [Has attribute]                        | *attrset* `?` *attrpath*                   | none          | 4          |
+| List concatenation                     | *list* `++` *list*                         | right         | 5          |
+| [Multiplication][arithmetic]           | *number* `*` *number*                      | left          | 6          |
+| [Division][arithmetic]                 | *number* `/` *number*                      | left          | 6          |
+| [Subtraction][arithmetic]              | *number* `-` *number*                      | left          | 7          |
+| [Addition][arithmetic]                 | *number* `+` *number*                      | left          | 7          |
+| [String concatenation]                 | *string* `+` *string*                      | left          | 7          |
+| [Path concatenation]                   | *path* `+` *path*                          | left          | 7          |
+| [Path and string concatenation]        | *path* `+` *string*                        | left          | 7          |
+| [String and path concatenation]        | *string* `+` *path*                        | left          | 7          |
+| Logical negation (`NOT`)               | `!` *bool*                                 | none          | 8          |
+| [Update]                               | *attrset* `//` *attrset*                   | right         | 9          |
+| [Less than][Comparison]                | *expr* `<` *expr*                          | none          | 10         |
+| [Less than or equal to][Comparison]    | *expr* `<=` *expr*                         | none          | 10         |
+| [Greater than][Comparison]             | *expr* `>` *expr*                          | none          | 10         |
+| [Greater than or equal to][Comparison] | *expr* `>=` *expr*                         | none          | 10         |
+| [Equality]                             | *expr* `==` *expr*                         | none          | 11         |
+| Inequality                             | *expr* `!=` *expr*                         | none          | 11         |
+| Logical conjunction (`AND`)            | *bool* `&&` *bool*                         | left          | 12         |
+| Logical disjunction (`OR`)             | *bool* `||` *bool*                         | left          | 13         |
+| [Logical implication]                  | *bool* `->` *bool*                         | none          | 14         |
+
+[string]: ./values.md#type-string
+[path]: ./values.md#type-path
+[number]: ./values.md#type-number
+[list]: ./values.md#list
+[attribute set]: ./values.md#attribute-set
+
+## Attribute selection
+
+Select the attribute denoted by attribute path *attrpath* from [attribute set] *attrset*.
+If the attribute doesn’t exist, return *value* if provided, otherwise abort evaluation.
+
+<!-- FIXME: the following should to into its own language syntax section, but that needs more work to fit in well -->
+
+An attribute path is a dot-separated list of attribute names.
+An attribute name can be an identifier or a string.
+
+> *attrpath* = *name* [ `.` *name* ]...
+> *name* = *identifier* | *string*
+> *identifier* ~ `[a-zA-Z_][a-zA-Z0-9_'-]*`
+
+[Attribute selection]: #attribute-selection
+
+## Has attribute
+
+> *attrset* `?` *attrpath*
+
+Test whether [attribute set] *attrset* contains the attribute denoted by *attrpath*.
+The result is a [Boolean] value.
+
+[Boolean]: ./values.md#type-boolean
+
+[Has attribute]: #has-attribute
+
+## Arithmetic
+
+Numbers are type-compatible:
+Pure integer operations will always return integers, whereas any operation involving at least one floating point number return a floating point number.
+
+See also [Comparison] and [Equality].
+
+The `+` operator is overloaded to also work on strings and paths.
+
+[arithmetic]: #arithmetic
+
+## String concatenation
+
+> *string* `+` *string*
+
+Concatenate two [string]s and merge their string contexts.
+
+[String concatenation]: #string-concatenation
+
+## Path concatenation
+
+> *path* `+` *path*
+
+Concatenate two [path]s.
+The result is a path.
+
+[Path concatenation]: #path-concatenation
+
+## Path and string concatenation
+
+> *path* + *string*
+
+Concatenate *[path]* with *[string]*.
+The result is a path.
+
+> **Note**
+>
+> The string must not have a string context that refers to a [store path].
+
+[Path and string concatenation]: #path-and-string-concatenation
+
+## String and path concatenation
+
+> *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].
+
+[store path]: ../glossary.md#gloss-store-path
+[store]: ../glossary.md#gloss-store
+
+[Path and string concatenation]: #path-and-string-concatenation
+
+## Update
+
+> *attrset1* + *attrset2*
+
+Update [attribute set] *attrset1* with names and values from *attrset2*.
+
+The returned attribute set will have of all the attributes in *e1* and *e2*.
+If an attribute name is present in both, the attribute value from the former is taken.
+
+[Update]: #update
+
+## Comparison
+
+Comparison is
+
+- [arithmetic] for [number]s 
+- lexicographic for [string]s and [path]s
+- item-wise lexicographic for [list]s:
+  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* `)` |
+
+[Comparison]: #comparison-operators
+
+## Equality
+
+- [Attribute sets][attribute set] and [list]s are compared recursively, and therefore are fully evaluated.
+- Comparison of [function]s always returns `false`.
+- Numbers are type-compatible, see [arithmetic] operators.
+- Floating point numbers only differ up to a limited precision.
+
+[function]: ./constructs.md#functions
+
+[Equality]: #equality
+
+## Logical implication
+
+Equivalent to `!`*b1* `||` *b2*.
+
+[Logical implication]: #logical-implication
+
diff --git a/doc/manual/src/language/values.md b/doc/manual/src/language/values.md
index 08baa8f95..3973518ca 100644
--- a/doc/manual/src/language/values.md
+++ b/doc/manual/src/language/values.md
@@ -85,9 +85,10 @@
   Numbers, which can be *integers* (like `123`) or *floating point*
   (like `123.43` or `.27e13`).
 
-  Numbers are type-compatible: pure integer operations will always
-  return integers, whereas any operation involving at least one
-  floating point number will have a floating point number as a result.
+  See [arithmetic] and [comparison] operators for semantics.
+
+  [arithmetic]: ./operators.md#arithmetic
+  [comparison]: ./operators.md#comparison
 
 - <a id="type-path" href="#type-path">Path</a>