This document is licensed under a Creative Commons Attribution 3.0 License.
JSON [RFC4627] has proven to be a highly useful object serialization and messaging format. JSON-LD [JSON-LD] harmonizes the representation of Linked Data in JSON by outlining a common JSON representation format for expressing directed graphs; mixing both Linked Data and non-Linked Data in a single document. This document outlines an Application Programming Interface and a set of algorithms for programmatically transforming JSON-LD documents.
This document is merely a public working draft of a potential specification. It has no official standing of any kind and does not represent the support or consensus of any standards organisation.
This document is an experimental work in progress.
JSON, as specified in [RFC4627], is a simple language for representing data on the Web. Linked Data is a technique for creating a graph of interlinked data across different documents or Web sites. Data entities are described using IRIs, which are typically dereferencable and thus may be used to find more information about an entity, creating a "Web of Knowledge". JSON-LD is intended to be a simple publishing method for expressing not only Linked Data in JSON, but also for adding semantics to existing JSON.
JSON-LD is designed as a light-weight syntax that can be used to express Linked Data. It is primarily intended to be a way to use Linked Data in Javascript and other Web-based programming environments. It is also useful when building interoperable Web services and when storing Linked Data in JSON-based document storage engines. It is practical and designed to be as simple as possible, utilizing the large number of JSON parsers and libraries available today. It is designed to be able to express key-value pairs, RDF data, RDFa [RDFA-CORE] data, Microformats [MICROFORMATS] data, and Microdata [MICRODATA]. That is, it supports every major Web-based structured data model in use today.
The syntax does not necessarily require applications to change their JSON, but allows to easily add meaning by adding context in a way that is either in-band or out-of-band. The syntax is designed to not disturb already deployed systems running on JSON, but provide a smooth upgrade path from JSON to JSON with added semantics. Finally, the format is intended to be easy to parse, efficient to generate, convertible to RDF in one pass, and require a very small memory footprint in order to operate.
This document is a detailed specification for a serialization of Linked Data in JSON. The document is primarily intended for the following audiences:
To understand the basics in this specification you must first be familiar with JSON, which is detailed in [RFC4627]. You must also understand the JSON-LD Syntax [JSON-LD], which is the base syntax used by all of the algorithms in this document. To understand the API and how it is intended to operate in a programming environment, it is useful to have working knowledge of the JavaScript programming language [ECMA-262] and WebIDL [WEBIDL]. To understand how JSON-LD maps to RDF, it is helpful to be familiar with the basic RDF concepts [RDF-CONCEPTS].
Examples may contain references to existing vocabularies and use prefixes to refer to Web Vocabularies. The following is a list of all vocabularies and their prefix abbreviations, as used in this document:
dc
, e.g., dc:title
)foaf
, e.g., foaf:knows
)rdf
, e.g., rdf:type
)xsd
, e.g., xsd:integer
)JSON [RFC4627] defines several terms which are used throughout this document:
There are a number of ways that one may participate in the development of this specification:
This API provides a clean mechanism that enables developers to convert JSON-LD data into a a variety of output formats that are easier to work with in various programming languages. If a JSON-LD API is provided in a programming environment, the entirety of the following API must be implemented.
[NoInterfaceObject]
interface JsonLdProcessor {
object expand (object input, optional object? context) raises (InvalidContext);
object compact (object input, optional object? context) raises (InvalidContext, ProcessingError);
object frame (object input, object frame, object options) raises (InvalidFrame);
object normalize (object input, optional object? context) raises (InvalidContext);
object triples (object input, JsonLdTripleCallback
tripleCallback, optional object? context) raises (InvalidContext);
};
compact
input
according to the steps in the
Compaction Algorithm. The
input
must be copied, compacted and returned if there are
no errors. If the compaction fails, an appropirate exception must be
thrown.
Parameter | Type | Nullable | Optional | Description |
---|---|---|---|---|
input | object | ✘ | ✘ | The JSON-LD object to perform compaction on. |
context | object | ✔ | ✔ | The base context to use when compacting the input . |
Exception | Description | ||||
---|---|---|---|---|---|
InvalidContext |
| ||||
ProcessingError |
|
object
expand
input
according to the steps in the
Expansion Algorithm. The
input
must be copied, expanded and returned if there are
no errors. If the expansion fails, an appropriate exception must be thrown.
Parameter | Type | Nullable | Optional | Description |
---|---|---|---|---|
input | object | ✘ | ✘ | The JSON-LD object to copy and perform the expansion upon. |
context | object | ✔ | ✔ | An external context to use additionally to the context embedded in input when expanding the input . |
Exception | Description | ||||
---|---|---|---|---|---|
InvalidContext |
|
object
frame
input
using the frame
according to the steps in the
Framing Algorithm. The
input
is used to build the framed output and is returned if
there are no errors. If there are no matches for the frame,
null
must be returned. Exceptions must be thrown if there are
errors.
Parameter | Type | Nullable | Optional | Description |
---|---|---|---|---|
input | object | ✘ | ✘ | The JSON-LD object to perform framing on. |
frame | object | ✘ | ✘ | The frame to use when re-arranging the data. |
options | object | ✘ | ✘ | A set of options that will affect the framing algorithm. |
Exception | Description | ||||
---|---|---|---|---|---|
InvalidFrame |
|
object
normalize
input
according to the steps in the
Normalization Algorithm. The
input
must be copied, normalized and returned if there are
no errors. If the compaction fails, null
must be returned.
Parameter | Type | Nullable | Optional | Description |
---|---|---|---|---|
input | object | ✘ | ✘ | The JSON-LD object to perform normalization upon. |
context | object | ✔ | ✔ | An external context to use additionally to the context embedded in input when expanding the input . |
Exception | Description | ||||
---|---|---|---|---|---|
InvalidContext |
|
object
triples
input
according to the
RDF Conversion Algorithm, calling
the provided tripleCallback
for each triple generated.
Parameter | Type | Nullable | Optional | Description |
---|---|---|---|---|
input | object | ✘ | ✘ | The JSON-LD object to process when outputting triples. |
tripleCallback |
| ✘ | ✘ | A callback that is called whenever a processing error occurs on
the given input .
This callback should be aligned with the
RDF API. |
context | object | ✔ | ✔ | An external context to use additionally to the context embedded in input when expanding the input . |
Exception | Description | ||||
---|---|---|---|---|---|
InvalidContext |
|
object
The JsonLdTripleCallback is called whenever the processor generates a
triple during the triple()
call.
[NoInterfaceObject Callback]
interface JsonLdTripleCallback {
void triple (DOMString subject, DOMString property, DOMString objectType, DOMString object, DOMString? datatype, DOMString? language);
};
triple
Parameter | Type | Nullable | Optional | Description |
---|---|---|---|---|
subject | DOMString | ✘ | ✘ | The subject IRI that is associated with the triple. |
property | DOMString | ✘ | ✘ | The property IRI that is associated with the triple. |
objectType | DOMString | ✘ | ✘ | The type of object that is associated with the triple. Valid values
are IRI and literal . |
object | DOMString | ✘ | ✘ | The object value associated with the subject and the property. |
datatype | DOMString | ✔ | ✘ | The datatype associated with the object. |
language | DOMString | ✔ | ✘ | The language associated with the object in BCP47 format. |
void
All algorithms described in this section are intended to operate on language-native data structures. That is, the serialization to a text-based JSON document isn't required as input or output to any of these algorithms and language-native data structures must be used where applicable.
JSON-LD specifies a number of syntax tokens and keywords that are using in all algorithms described in this section:
@context
@base
@vocab
@coerce
@literal
@iri
@language
@datatype
:
@subject
@type
@context
keyword.
Processing of JSON-LD data structure is managed recursively. During processing, each rule is applied using information provided by the active context. Processing begins by pushing a new processor state onto the processor state stack and initializing the active context with the initial context. If a local context is encountered, information from the local context is merged into the active context.
The active context is used for expanding keys and values of a JSON object (or elements of a list (see List Processing)).
A local context is identified within a JSON object having a key of
@context
with string or a JSON object value. When processing a local
context, special processing rules apply:
@base
key, it must have a value of a simple
string with the lexical form of an absolute IRI. Add the base mapping to the local
context. Turtle allows @base to be relative. If we did this, we would have to add IRI Expansion.
@vocab
key, it must have a value of a simple
string with the lexical form of an absolute IRI. Add the vocabulary mapping to the
local context after performing IRI Expansion on
the associated value.
@coerce
key, it must have a value of a
JSON object. Add the @coerce
mapping to the local context
performing IRI Expansion on the associated value(s).
@coerce
mapping into the
active context's @coerce
mapping as described below.
@coerce
mapping from the local context to the
active context overwriting any duplicate values.
Map each key-value pair in the local context's
@coerce
mapping into the active context's
@coerce
mapping, overwriting any duplicate values in
the active context's @coerce
mapping.
The @coerce
mapping has either a single
prefix:term
value, a single term value or an
array of prefix:term
or term values.
When merging with an existing mapping in the active context,
map all prefix and term values to
array form and replace with the union of the value from
the local context and the value of the
active context. If the result is an array
with a single value, the processor may represent this as a string value.
The initial context is initialized as follows:
@base
is set using @coerce
is set with a single mapping from @iri
to @type
.{
"@base": document-location,
"@coerce": {
"@iri": "@type"
}
}
Keys and some values are evaluated to produce an IRI. This section defines an algorithm for transforming a value representing an IRI into an actual IRI.
IRIs may be represented as an absolute IRI, a term, a prefix:term construct, or as a value relative to @base
or @vocab
.
The algorithm for generating an IRI is:
@coerce
mapping) and the active context has a @vocab
mapping,
join the mapped value to the suffix using textual concatenation.@base
mapping,
join the mapped value to the suffix using the method described in [RFC3986].Some keys and values are expressed using IRIs. This section defines an algorithm for transforming an IRI to a compact IRI using the terms and prefixes specified in the local context.
The algorithm for generating a compacted IRI is:
Some values in JSON-LD can be expressed in a compact form. These values are required to be expanded at times when processing JSON-LD documents.
The algorithm for expanding a value is:
@iri
, expand the value
by adding a new key-value pair where the key is @iri
and the value is the expanded IRI according to the
IRI Expansion rules.@literal
and the unexpanded value. The second
key-value pair will be @datatype
and the associated
coercion datatype expanded according to the
IRI Expansion rules.Some values, such as IRIs and typed literals, may be expressed in an expanded form in JSON-LD. These values are required to be compacted at times when processing JSON-LD documents.
The algorithm for compacting a value is:
@iri
, the compacted
value is the value associated with the @iri
key,
processed according to the
IRI Compaction steps.@literal
key.
This algorithm is a work in progress, do not implement it.
As stated previously, expansion is the process of taking a JSON-LD input and expanding all IRIs and typed literals to their fully-expanded form. The output will not contain a single context declaration and will have all IRIs and typed literals fully expanded.
This algorithm is a work in progress, do not implement it.
As stated previously, compaction is the process of taking a JSON-LD input and compacting all IRIs using a given context. The output will contain a single top-level context declaration and will only use terms and prefixes and will ensure that all typed literals are fully compacted.
This algorithm is a work in progress, do not implement it.
A JSON-LD document is a representation of a directed graph. A single directed graph can have many different serializations, each expressing exactly the same information. Developers typically don't work directly with graphs, but rather, prefer trees when dealing with JSON. While mapping a graph to a tree can be done, the layout of the end result must be specified in advance. This section defines an algorithm for mapping a graph to a tree given a frame.
The framing algorithm takes JSON-LD input that has been normalized according to the Normalization Algorithm (normalized input), an input frame that has been expanded according to the Expansion Algorithm (expanded frame), and a number of options and produces JSON-LD output. The following series of steps is the recursive portion of the framing algorithm:
null
.Invalid Frame Format
exception. Add each matching item from the normalized input
to the matches array and decrement the
match limit by 1 if:
rdf:type
that exists in the item's list of rdf:type
s. Note:
the rdf:type
can be an array, but only one value needs
to be in common between the item and the
expanded frame for a match.rdf:type
property, but every property in the
expanded frame exists in the item.@embed
keyword, set the object embed flag to its value.
If the match frame contains an @explicit
keyword, set the explicit inclusion flag to its value.
Note: if the keyword exists, but the value is neither
true
or false
, set the associated flag to
true
.@subject
property, replace the item with the value
of the @subject
property.@subject
property, and its IRI is in the
map of embedded subjects, throw a
Duplicate Embed
exception.@subject
property and its IRI is not in the
map of embedded subjects:
@subject
.rdf:type
:
@iri
value that exists in the
normalized input, replace the object in the
recusion input list with a new object containing
the @subject
key where the value is the value of
the @iri
, and all of the other key-value pairs for
that subject. Set the recursion match frame to the
value associated with the match frame's key. Replace
the value associated with the key by recursively calling this
algorithm using recursion input list,
recursion match frame as input.null
otherwise.null
,
process the omit missing properties flag:
@omitDefault
keyword, set the
omit missing properties flag to its value.
Note: if the keyword exists, but the value is neither
true
or false
, set the associated
flag to true
.@default
keyword is set in the
property frame set the item's value to the value
of @default
.null
set it to
the item, otherwise, append the item to the
JSON-LD output.
This algorithm is a work in progress, do not implement it.
Normalization is the process of taking JSON-LD input and performing a deterministic transformation on that input that results in all aspects of the graph being fully expanded and named in the JSON-LD output. The normalized output is generated in such a way that any conforming JSON-LD processor will generate identical output given the same input. The problem is a fairly difficult technical problem to solve because it requires a directed graph to be ordered into a set of nodes and edges in a deterministic way. This is easy to do when all of the nodes have unique names, but very difficult to do when some of the nodes are not labeled.
In time, there may be more than one normalization algorithm that will need to be identified. For identification purposes, this algorithm is named "Universal Graph Normalization Algorithm 2011" (UGNA2011).
@subject
and the value is a string that is an IRI or
a JSON object containing the key @iri
and
a value that is a string that is an IRI.
s<NUMBER>
or
c<NUMBER>
.
When performing the steps required by the normalization algorithm, it is helpful to track the many pieces of information in a data structure called the normalization state. Many of these pieces simply provide indexes into the graph. The information contained in the normalization state is described below.
_:
and that has a
path, via properties, that starts with the
node reference.
_:
and that has a path, via properties, that ends with
the node reference.
_:
, is not used by any other
node's label in the JSON-LD input, and does not
start with the characters _:c14n
. The prefix has two uses.
First it is used to temporarily name nodes during the normalization
algorithm in a way that doesn't collide with the names that already
exist as well as the names that will be generated by the normalization
algorithm. Second, it will eventually be set to _:c14n
to
generate the final, deterministic labels for nodes in the graph. This
prefix will be concatenated with the labeling counter to
produce a node label. For example, _:j8r3k
is
a proper initial value for the labeling prefix.
1
.
The normalization algorithm expands the JSON-LD input, flattens the data structure, and creates an initial set of names for all nodes in the graph. The flattened data structure is then processed by a node labeling algorithm in order to get a fully expanded and named list of nodes which is then sorted. The result is a deterministically named and ordered list of graph nodes.
@subject
and the value is the
concatenation of the labeling prefix
and the string value of the labeling counter.
Increment the labeling counter.@iri
and the value is
the value of the @subject
key in the node._:c14n
, relabel the node
using the Node Relabeling Algorithm.
@subject
key associated
with a value starting with _:
according to the steps in the
Deterministic Labeling Algorithm.
This algorithm renames a node by generating a unique new label and updating all references to that label in the node state map. The old label and the normalization state must be given as an input to the algorithm. The old label is the current label of the node that is to be relabeled.
The node relabeling algorithm is as follows:
_:c14n
and the
old label begins with _:c14n
then return as
the node has already been renamed.
The deterministic labeling algorithm takes the normalization state and produces a list of finished nodes that is sorted and contains deterministically named and expanded nodes from the graph.
_:c14n
, the
labeling counter to 1
,
the list of finished nodes to an empty array, and create
an empty array, the list of unfinished nodes._:
then put the node reference in the
list of finished nodes.
_:
then put the node reference in the
list of unfinished nodes.
_:c14n
from the list of unfinished nodes and
add it to the list of finished nodes.
The shallow comparison algorithm takes two unlabeled nodes, alpha and beta, as input and determines which one should come first in a sorted list. The following algorithm determines the steps that are executed in order to determine the node that should come first in a list:
_:
is first.
_:
, then the node associated with the
lexicographically lesser label is first._:c14n
is first.
The object comparison algorithm is designed to compare two graph node property values, alpha and beta, against the other. The algorithm is useful when sorting two lists of graph node properties.
@literal
is first.
@datatype
is first.
@language
is first.
@iri
is first.The deep comparison algorithm is used to compare the difference between two nodes, alpha and beta. A deep comparison takes the incoming and outgoing node edges in a graph into account if the number of properties and value of those properties are identical. The algorithm is helpful when sorting a list of nodes and will return whichever node should be placed first in a list if the two nodes are not truly equivalent.
When performing the steps required by the deep comparison algorithm, it is helpful to track state information about mappings. The information contained in a mapping state is described below.
1
.
s1
and its
index is set to 0
.
The deep comparison algorithm is as follows:
outgoing direction
to the algorithm as inputs.
outgoing direction
to the algorithm as inputs.
incoming direction
to the algorithm as inputs.
incoming direction
to the algorithm as inputs.
The node serialization algorithm takes a node state, a
mapping state, and a direction (either
outgoing direction
or incoming direction
) as
inputs and generates a deterministic serialization for the
node reference.
true
.
outgoing direction
and the
incoming list otherwise, if the label starts with
_:
, it is the target node label:
1
or the length of the
adjacent unserialized labels list, whichever is greater.0
, perform the
Combinatorial Serialization Algorithm
passing the node state, the mapping state for the
first iteration and a copy of it for each subsequent iteration, the
generated serialization label, the direction,
the adjacent serialized labels map, and the
adjacent unserialized labels list.
Decrement the maximum serialization combinations by
1
for each iteration.
The algorithm generates a serialization label given a label and a mapping state and returns the serialization label.
_:c14n
,
the serialization label is the letter c
followed by the number that follows _:c14n
in the
label.
s
followed by the string value of
mapping count. Increment the mapping count by
1
.
The combinatorial serialization algorithm takes a node state, a mapping state, a serialization label, a direction, a adjacent serialized labels map, and a adjacent unserialized labels list as inputs and generates the lexicographically least serialization of nodes relating to the node reference.
1
or the length of the
adjacent unserialized labels list, whichever is greater.
0
:
1
for each iteration.
outgoing direction
then directed serialization refers to the
outgoing serialization and the
directed serialization map refers to the
outgoing serialization map, otherwise it refers to the
incoming serialization and the
directed serialization map refers to the
incoming serialization map. Compare the
serialization string to the
directed serialization according to the
Serialization Comparison Algorithm.
If the serialization string is less than or equal to
the directed serialization:
The serialization comparison algorithm takes two serializations, alpha and beta and returns either which of the two is less than the other or that they are equal.
The mapping serialization algorithm incrementally updates the serialization string in a mapping state.
_
character and the
serialization key to the
serialization string.
true
.
0
onto the key stack.
The label serialization algorithm serializes information about a node that has been assigned a particular serialization label.
[
character to the
label serialization.@subject
property. The keys should be processed in
lexicographical order and their associated values should be processed
in the order produced by the
Object Comparison Algorithm:
<
KEY>
where KEY is the current key. Append string to the
label serialization.@iri
key with a
value that starts
with _:
, set the object string to
the value _:
. If the value does not
start with _:
, build the object string
using the pattern
<
IRI>
where IRI is the value associated with the
@iri
key.@literal
key and a
@datatype
key, build the object string
using the pattern
"
LITERAL"^^<
DATATYPE>
where LITERAL is the value associated with the
@literal
key and DATATYPE is the
value associated with the @datatype
key.@literal
key and a
@language
key, build the object string
using the pattern
"
LITERAL"@
LANGUAGE
where LITERAL is the value associated with the
@literal
key and LANGUAGE is the
value associated with the @language
key."
LITERAL"
where LITERAL is the value associated with the
current key.|
separator character to the
label serialization.]
character to the
label serialization.[
character to the
label serialization.<
PROPERTY>
<
REFERER>
where PROPERTY is the property associated with the
incoming reference and REFERER is either the subject of
the node referring to the label in the incoming reference
or _:
if REFERER begins with
_:
.
|
separator character to the
label serialization.]
character to the
label serialization.When normalizing xsd:double values, implementers must
ensure that the normalized value is a string. In order to generate the
string from a double value, output equivalent to the
printf("%1.6e", value)
function in C must be used where
"%1.6e" is the string formatter and value
is the value to be converted.
To convert the a double value in JavaScript, implementers can use the following snippet of code:
// the variable 'value' below is the JavaScript native double value that is to be converted (value).toExponential(6).replace(/(e(?:\+|-))([0-9])$/, '$10$2')
When data needs to be normalized, JSON-LD authors should not use values that are going to undergo automatic conversion. This is due to the lossy nature of xsd:double values.
Some JSON serializers, such as PHP's native implementation,
backslash-escapes the forward slash character. For example, the value
http://example.com/
would be serialized as
http:\/\/example.com\/
in some
versions of PHP. This is problematic when generating a byte
stream for processes such as normalization. There is no need to
backslash-escape forward-slashes in JSON-LD. To aid interoperability between
JSON-LD processors, a JSON-LD serializer must not backslash-escape
forward slashes.
Round-tripping data can be problematic if we mix and match @coerce rules with JSON-native datatypes, like integers. Consider the following code example:
var myObj = { "@context" : { "number" : "http://example.com/vocab#number", "@coerce": { "xsd:nonNegativeInteger": "number" } }, "number" : 42 }; // Map the language-native object to JSON-LD var jsonldText = jsonld.normalize(myObj); // Convert the normalized object back to a JavaScript object var myObj2 = jsonld.parse(jsonldText);
At this point, myObj2 and myObj will have different values for the "number" value. myObj will be the number 42, while myObj2 will be the string "42". This type of data round-tripping error can bite developers. We are currently wondering if having a "coerce validation" phase in the parsing/normalization phases would be a good idea. It would prevent data round-tripping issues like the one mentioned above.
A JSON-LD document may be converted to any other RDF-compatible document format using the algorithm specified in this section.
The JSON-LD Processing Model describes processing rules for extracting RDF from a JSON-LD document. Note that many uses of JSON-LD may not require generation of RDF.
The processing algorithm described in this section is provided in order to demonstrate how one might implement a JSON-LD to RDF processor. Conformant implementations are only required to produce the same type and number of triples during the output process and are not required to implement the algorithm exactly as described.
The RDF Conversion Algorithm is a work in progress.
This section is non-normative.
JSON-LD is intended to have an easy to parse grammar that closely models existing practice in using JSON for describing object representations. This allows the use of existing libraries for parsing JSON.
As with other grammars used for describing Linked Data, a key concept is that of a resource. Resources may be of three basic types: IRIs, for describing externally named entities, BNodes, resources for which an external name does not exist, or is not known, and Literals, which describe terminal entities such as strings, dates and other representations having a lexical representation possibly including an explicit language or datatype.
Data described with JSON-LD may be considered to be the representation of a graph made up of subject and object resources related via a property resource. However, specific implementations may choose to operate on the document as a normal JSON description of objects having attributes.
The algorithm below is designed for in-memory implementations with random access to JSON object elements.
A conforming JSON-LD processor implementing RDF conversion must implement a processing algorithm that results in the same default graph that the following algorithm generates:
@context
key, process the local context as
described in Context.
@iri
key, set the active object by
performing IRI Expansion on the associated value. Generate a
triple representing the active subject, the active property and the
active object. Return the active object to the calling location.
@iri
really just behaves the same as @subject
, consider consolidating them.
@literal
key, set the active object
to a literal value as follows:
@datatype
key
after performing IRI Expansion on the specified@datatype
.
@language
key, use it's value to set the language of the plain literal.
@subject
key:
@subject
key, set the active
object to newly generated blank node identifier. Generate a triple
representing the active subject, the active property and the
active object. Set the active subject to the active
object.
@type
, set the active property
to rdf:type
.
@iri
coercion,
set the active object by
performing IRI Expansion on the string.
xsd:integer
or
xsd:double
, depending on if the value contains a
fractional and/or an exponential component. Generate a triple using the active
subject, active property and the generated typed literal.
xsd:boolean
.
The editors would like to thank Mark Birbeck, who provided a great deal of the initial push behind the JSON-LD work via his work on RDFj, Dave Longley, Dave Lehn and Mike Johnson who reviewed, provided feedback, and performed several implementations of the specification, and Ian Davis, who created RDF/JSON. Thanks also to Nathan Rixham, Bradley P. Allen, Kingsley Idehen, Glenn McDonald, Alexandre Passant, Danny Ayers, Ted Thibodeau Jr., Olivier Grisel, Niklas Lindström, Markus Lanthaler, and Richard Cyganiak for their input on the specification. Another huge thank you goes out to Dave Longley who designed many of the algorithms used in this specification, including the normalization algorithm which was a monumentally difficult design challenge.