diff --git a/docs/_openvox_8x/lang_data_abstract.md b/docs/_openvox_8x/lang_data_abstract.md
index 17a307a97..5b14df643 100644
--- a/docs/_openvox_8x/lang_data_abstract.md
+++ b/docs/_openvox_8x/lang_data_abstract.md
@@ -12,6 +12,13 @@ title: "Language: Data types: Abstract data types"
 [hashes]: ./lang_data_hash.html
 [hash_missing_key_access]: ./lang_data_hash.html#accessing-values
 [numbers]: ./lang_data_number.html
+[semver]: ./lang_data_semver.html
+[uri]: ./lang_data_uri.html
+[time]: ./lang_data_time.html
+[binary]: ./lang_data_binary.html
+[error]: ./lang_data_error.html
+[sensitive]: ./lang_data_sensitive.html
+[typecasting]: ./lang_typecasting.html
 
 As described in [the Data Type Syntax][types] page, each of Puppet's main [data types][] has a corresponding value that _represents_ that data type, which can be used to match values of that type in several contexts. (For example, `String` or `Array`.)
 
@@ -257,27 +264,67 @@ The `Scalar` data type matches _all_ values of the following concrete data types
 * [Strings][]
 * [Booleans][]
 * [Regular expressions][]
+* [`SemVer` and `SemVerRange`][semver]
+* [`Timestamp` and `Timespan`][time]
 
 Note that it doesn't match `undef`, `default`, resource references, arrays, or hashes.
 
 It takes no parameters.
 
-`Scalar` is equivalent to `Variant[Integer, Float, String, Boolean, Regexp]`.
+### `ScalarData`
+
+The `ScalarData` data type matches the subset of `Scalar` that can be represented directly in JSON:
+
+* [Numbers][] (both integers and floats)
+* [Strings][]
+* [Booleans][]
+
+It doesn't match regular expressions, `SemVer`, `SemVerRange`, `Timestamp`, or `Timespan`, all of which
+`Scalar` does match. Like `Scalar`, it doesn't match `undef` or `default`.
+
+It takes no parameters.
+
+`ScalarData` is to `Scalar` what `Data` is to `RichData`: the JSON-compatible subset.
 
 ### `Data`
 
-The `Data` data type matches any value that would match `Scalar`, but it also matches:
+The `Data` data type matches any value that would match `ScalarData`, but it also matches:
 
 * `undef`
 * [Arrays][] that only contain values that would also match `Data`
-* [Hashes][] whose keys would match `Scalar` and whose values would also match `Data`
+* [Hashes][] whose keys are [strings][] and whose values would also match `Data`
 
-Note that it doesn't match `default` or resource references.
+Note that it is built on `ScalarData` rather than `Scalar`, so the members of `Scalar` that have no JSON
+equivalent are excluded: a regular expression matches `Scalar` but not `Data`. It also doesn't match
+`default` or resource references.
 
 It takes no parameters.
 
 `Data` is especially useful because it represents the subset of types that can be directly represented in almost all serialization formats (e.g. JSON).
 
+### `RichData`
+
+The `RichData` data type matches any value that would match `Data`, and also matches the types that have no
+direct JSON equivalent:
+
+* [Regular expressions][]
+* [`URI`][uri]
+* [`Binary`][binary]
+* [`Timestamp` and `Timespan`][time]
+* [`SemVer` and `SemVerRange`][semver]
+* [`Error`][error]
+* [`Sensitive`][sensitive]
+* Data types themselves, such as `Integer`
+* Resource and class references
+* `default`
+* [Arrays][] and [hashes][] containing any of the above
+
+It takes no parameters.
+
+`RichData` is what a parameter or function should accept when it needs to handle any ordinary Puppet value.
+Use `Data` instead when the value has to survive being serialized to JSON, and note that this is the
+distinction that makes `Error('boom') =~ Data` false while `Error('boom') =~ RichData` is true.
+
 ### `Collection`
 
 The `Collection` type matches _any_ array or hash, regardless of what kinds of values (and/or keys) it contains.
@@ -286,6 +333,40 @@ Note that this means it only partially overlaps with `Data` --- there are values
 
 `Collection` is equivalent to `Variant[Array[Any], Hash[Any, Any]]`.
 
+### `Iterable`
+
+The `Iterable` data type matches any value that an iterative function such as `each` or `map` can walk over.
+That includes arrays, hashes, strings, integers, and the `Iterator` values described below:
+
+```puppet
+notice([1, 2] =~ Iterable)  # true
+notice({'a' => 1} =~ Iterable) # true
+notice('abc' =~ Iterable)   # true
+notice(5 =~ Iterable)       # true
+notice(undef =~ Iterable)   # false
+```
+
+An optional parameter constrains what the value iterates over, so `Iterable[Integer]` matches only things
+that yield integers:
+
+```puppet
+notice(5 =~ Iterable[Integer]) # true
+```
+
+### `Iterator`
+
+The `Iterator` data type matches the lazy sequences produced by the chained forms of some iterative
+functions, such as `reverse_each` and `step` called without a block. Every `Iterator` is also `Iterable`,
+but ordinary arrays and hashes are not `Iterator`:
+
+```puppet
+notice([1, 2].reverse_each =~ Iterator) # true
+notice([1, 2] =~ Iterator)              # false
+```
+
+Like `Iterable`, it accepts an optional parameter for the type it yields. You rarely write `Iterator`
+yourself; it matters mainly when a function returns one and you want to constrain what it produces.
+
 ### `Catalogentry`
 
 The `Catalogentry` data type is the parent type of `Resource` and `Class`. This means that, like those types, the Puppet language contains no values that it will ever match. However, the type `Type[Catalogentry]` will match any class reference or resource reference.
@@ -358,3 +439,46 @@ function example(Variant[Integer, Init[Integer]] $x) {
    $int_value = Integer($x)  # Safe conversion
 }
 ```
+
+See [typecasting][] for the conversions `Init` tests against.
+
+### `Runtime`
+
+The `Runtime` data type matches values that belong to the implementation language underneath Puppet rather
+than to the Puppet language itself. It takes the runtime name and the type name within it:
+
+```puppet
+Runtime['ruby', 'Symbol']
+```
+
+You cannot create such a value in a manifest. The type exists so that Ruby functions and types can describe
+arguments that are Ruby objects with no Puppet equivalent, and so those arguments can be type-checked.
+
+### `Object`
+
+The `Object` data type is the parent of types created with the Pcore object model, which is how modules
+define types that have named attributes and their own methods. An object type is declared by passing a hash
+that names it and lists its attributes:
+
+```puppet
+$greeter = Object[{name => 'Greeter', attributes => {greeting => String}}]
+$g = $greeter.new('hello')
+
+notice($g.greeting)    # hello
+notice($g =~ $greeter) # true
+```
+
+In practice you rarely write this form inline. Modules declare object types in their `types` directory, one
+type per file.
+
+### `TypeSet`
+
+The `TypeSet` data type groups several object types together under one name and version, so a module can
+publish a related family of types rather than a loose collection. A type set records a name, a version, and
+the types it contains.
+
+A module publishes one by declaring it in `types/init_typeset.pp`, which OpenVox loads as the type set named
+after the module. Type sets are not written inline in a manifest.
+
+The type parser accepts any capitalization, so `Typeset` also works, but `TypeSet` is the spelling OpenVox
+itself uses when it renders the type.
diff --git a/docs/_openvox_8x/lang_data_boolean.md b/docs/_openvox_8x/lang_data_boolean.md
index a429e83b8..c7a101ff7 100644
--- a/docs/_openvox_8x/lang_data_boolean.md
+++ b/docs/_openvox_8x/lang_data_boolean.md
@@ -33,8 +33,26 @@ If you want to convert other values to booleans with more permissive rules (`0`
 
 The [data type][] of boolean values is `Boolean`.
 
-It matches only the values `true` or `false`, and accepts no parameters.
+On its own it matches only the values `true` or `false`.
 
+### Parameters
+
+`Boolean` takes an optional parameter that narrows it to one of the two values:
+
+```puppet
+notice(true =~ Boolean[true])   # true
+notice(false =~ Boolean[true])  # false
+notice(false =~ Boolean[false]) # true
+```
+
+This is useful when a parameter must be one specific value rather than either, such as a flag that may only
+ever be switched on:
+
+```puppet
+class example (
+  Boolean[true] $must_be_enabled = true,
+) { }
+```
 
 ### Related data types
 
diff --git a/docs/_openvox_8x/lang_data_type.md b/docs/_openvox_8x/lang_data_type.md
index 2205dc4c6..819104b4d 100644
--- a/docs/_openvox_8x/lang_data_type.md
+++ b/docs/_openvox_8x/lang_data_type.md
@@ -36,6 +36,16 @@ title: "Language: Data types: Data type syntax"
 [catalogentry]: ./lang_data_abstract.html#catalogentry
 [any]: ./lang_data_abstract.html#any
 [callable]: ./lang_data_abstract.html#callable
+[sensitive]: ./lang_data_sensitive.html
+[notundef]: ./lang_data_abstract.html#notundef
+[init]: ./lang_data_abstract.html#init
+[scalardata]: ./lang_data_abstract.html#scalardata
+[richdata]: ./lang_data_abstract.html#richdata
+[iterable]: ./lang_data_abstract.html#iterable
+[iterator]: ./lang_data_abstract.html#iterator
+[runtime]: ./lang_data_abstract.html#runtime
+[object]: ./lang_data_abstract.html#object
+[typeset]: ./lang_data_abstract.html#typeset
 
 Each value in the Puppet language has a data type, like "string." There is also a set of values _whose data type is "data type."_
 
@@ -158,6 +168,7 @@ These are the "real" data types, which make up the most common values you'll int
 * [`Timestamp` and `Timespan`][time]
 * [`SemVer` and `SemVerRange`][semver]
 * [`Error`][error]
+* [`Sensitive`][sensitive]
 * [`Undef`][undef]
 * [`Default`][default]
 
@@ -173,18 +184,27 @@ Resource references and class references are implemented as data types, although
 Abstract data types let you do more sophisticated or permissive type checking.
 
 * [`Scalar`][Scalar]
+* [`ScalarData`][ScalarData]
 * [`Collection`][Collection]
 * [`Variant`][Variant]
 * [`Data`][Data]
+* [`RichData`][RichData]
 * [`Pattern`][Pattern]
 * [`Enum`][Enum]
 * [`Tuple`][Tuple]
 * [`Struct`][Struct]
 * [`Optional`][Optional]
+* [`NotUndef`][NotUndef]
 * [`Catalogentry`][Catalogentry]
 * [`Type`][inpage_type]
 * [`Any`][Any]
 * [`Callable`][Callable]
+* [`Init`][Init]
+* [`Iterable`][Iterable]
+* [`Iterator`][Iterator]
+* [`Runtime`][Runtime]
+* [`Object`][Object]
+* [`TypeSet`][TypeSet]
 
 ## The `Type` data type