# Value-types

A runtime value in Cozo can be of the following _value-types_:
* `Null`
* `Bool`
* `Number`
* `String`
* `Bytes`
* `List`

`Number` can be `Float` (double precision) or `Int` (signed, 64 bits). Cozo will auto-promote `Int` to `Float` when necessary.

`List` can contain any number of mixed-type values, including other lists.

Cozo sorts values according to the above order, e.g. `null` is smaller than `true`, which is in turn smaller than the list `[]`.

Within each type values are _compared_ according to logic custom to each type: 

* `false < true`;
* `-1 == -1.0 < 0 == 0.0 < 0.5 == 0.5 < 1 == 1.0` (however, see the caveat below); 
* Lists are ordered lexicographically by their elements;
* Bytes are compared lexicographically;
* Strings are ordered lexicographically by their UTF-8 byte representations.

!> Because there are two internal number types `Int` and `Float` under the umbrella type `Number`, sorting numbers can be more complex than anticipated: when sorting, the integer always comes before the equivalent float. For example, `1.0 == 1`, `1.0 >= 1` and `1.0 <= 1` all evaluate to true, but when sorting `1` and `1.0` are two _different_ values and `1` is placed before `1.0`. This may create problems when applying aggregations since if a grouping key contains both `1.0` and `1`, they are treated as separate group headings. In such cases, it may help to use explicit coercion `to_float` or `round` to coerce all sorted values to the same type.


# Value literals

`null` for the type `Null`, `false` and `true` for the type `Bool` are standard.

Numbers ...

Strings ...

There is no literal representation for `Bytes` due to restrictions placed by JSON. But ...

Lists ...

# Schema-types

In schema definition, the required type for a value can be specified by any of the following _schema-types_

* `Ref`
* `Component`
* `Int`
* `Float`
* `Bool`
* `String`
* `Bytes`
* `List`

When retrieving triples' values, the schema-types `Ref`, `Component`, and `Int` are all represented by the value-type `Number` (actually `Int`). The entity (the subject of the triple) is always a `Ref`, always represented by a `Number` (`Int`).

Note the absence of the `Null` type in schema-types.

When asserting (inserting or updating) triples, if a value given is not of the correct schema-type, Cozo will first try to coerce the value and will only error out if no known coercion methods exist.