Keys for XML Peter Buneman, Susan Davidson, Wenfei Fan Carmem Hara , Wang-Chiew Tan University of Pennsylvania Temple University Universidade Federal do Parana, Brazil Jonathan Mamou 1 Keys in DB design Essential part of DB design Invariant connection between the tuple and the real-world entity Important in update – Guarantee that an update will affect precisely one tuple … Keys for XML 2 Keys in XML XML documents are to do – at least - double duty as databases Examination of existing DTDs reveals a number of cases in which some element or attribute is specified as a “unique identifier” in comments Various key specifications in XML Standard, XML Data, XML Schema Keys for XML 3 Components: XML vs. relational DB Name course grade Smith Math B Jones Math A+ Smith CS A- <db> <student> <name> Smith </name> <course> Math </course> <grade> B </grade> </student> <student> <name> Jones </name> <course> Math </course> <grade> A+ </grade> </student> <student> <name> Smith </name> <course> CS </course> <grade> A- </grade> </student> </db> Keys for XML 4 Components: XML vs. relational DB (cont’d) DB If 2 tuples agree on their name and course attributes they agree everywhere XML If 2 elements agree on the name and course subelements then they are the same element Node identification? Equality? Keys for XML 5 Nodes - Value Equality name key for person nodes name may have a complex structure: first- name, last-name db company dept employee employee name government company name firstName “Bill” university employee employee employee ... lastName @id @id @id name “Bill Clinton” “Clinton” Keys for XML 6 Hierarchical structure Hierarchically structured databases, e.g. scientific data formats Top-level key to identify components of a document Secondary key to identify sub-components – Book/chapter/section – Bible/book/chapter/verse Keys for XML 7 Absolute and relative keys In an XML document, how to identify A book? a chapter? db a section? book title “XML” “1” chapter chapter number section section number section section number text “1” “...” number “6” “10” book book book number number “1” Keys for XML “5” title chapter chapter “SGML” number number text “1” “10” “…” 8 XML standard - ID attribute <!ATTLIST book <!ATTLIST chapter <!ATTLIST section title number number ID ID ID #required> #required> #required> Internal “pointers” rather than keys Scoping: ID attribute unique within the entire document rather than among a designated set of elements – can’t express relative keys, e.g., for chapters/sections. Limit to using attributes rather than elements unary: at most one ‘key’ can be defined, in terms of a single attribute value equality: on text (string) defined in a attribute type : keys must come with a DTD Keys for XML 9 XML Data Introduces a notion of keys explicitly <elementType id="booktable"> <element id="titleID" type="#title"> <element type="#author"> <element type="#pages"> <key id="bookkey"> <keyPart href="#titleID"/> </key> </elementType> BUT – Can only be defined for element types rather than for certain collections of elements e.g. book, articles, … Keys for XML 10 XPath Possible to specify interesting fragments of a document Syntax similar to navigating directories in a file system //arbitrary path . empty path / document root - path concatenator * any single node name Keys for XML XPath example Select BBB elements which have any attribute <AAA> <BBB id = "b1"/> <BBB id = "b2"/> <BBB name = "bbb"/> <BBB/> </AAA> //BBB[@*] Keys for XML 12 Xpath example (cont’d) <AAA> <BBB> </BBB> <XXX> <DDD> //GGG/ancestor::* <FFF> <GGG> </GGG> </FFF> </DDD> </XXX> <CCC> </CCC> </AAA> Keys for XML 13 XML-Schema <element name = “book”> <complexType> <sequence> <element name=“title” type=“string”/> <element name=“chapters” max0occurs=“unbounded”> <complexType> ... </complexType> </element> </sequence> </complexType> <key name=“k” > <selector xpath=“.”/> <field xpath=“title”/> </key> </element> Keys for XML 14 XML Schema (cont’d) Allow to specify keys in term of XPath expressions BUT – XPath is a relatively complex language (move down, sideways, upwards, predicates and functions can be embedded) – Equivalence/containment of XPath expressions is unresolved No efficient way to tell whether two keys are equivalent. – Value equality: restricted to text – Relative key not addressed – Structural requirement: key paths must exist and be unique. Keys for XML 15 A new key constraint language for XML Powerful enough to express absolute and relative keys Simple enough to be reasoned about efficiently – Equivalence/containment – consistency (satisfiability) – implication (keys derived from others) Capturing the semistructured nature of XML data: – independent of any types/schema – no structural requirements: tolerating missing/multiple key paths Keys for XML 16 Outline Node addresses – testing whether 2 nodes are the same node Value equality – testing whether 2 nodes have the same value Path expression language Absolute key Key Inference Relative key Strong key Some issues Keys for XML 17 Tree representation DOM (Document Object Model) Document is a hierarchical structure of nodes – Element nodes – Attribute nodes – Text nodes Keys for XML 18 Tree representation (cont’d) <db> <composer> <name> J.S. Bach </name> <born> 1685 &</born> <work num="BWV82“> <title> Ich habe genug </title> </work> <work num="BWV552“> </work> </composer> <composer period="baroque“> <name> G.F. Handel </name> <work num="HWV19“> <title> Art Thou Troubled? </title> </work> </composer> </db< Keys for XML 19 Tree representation (cont’d) db 1 2 composer 1 name 1 “J.S. Bach” 2 born 1 3 work 4 1 work work 1 @periode 1 @num 1 2 name @num 1 title “1685” composer @num num title num “BWV82” num “G.F. Handel” “HWV19” 1 “BWV552” periode “Iche abe genug” “Baroque” Keys for XML “Art Thou Troubled” 20 Tree representation (cont’d) Attribute node: name+text, terminal Text node: text, terminal Element node: – name, may have children – Text and element children held in an array • Index in the array determined by the order of the subelement in the document – Attribute children held in a dictionary • Name of the attribute used as the index Edge label uniquely identify children Keys for XML 21 Node Address A path of edge labels from the root uniquely identifies a node <l1#…#ln> – <1#2#1>, <1#3#@num> An attribute node can only occur at the end of a node address Order of attributes is unimportant Order of subelements specified by their indexes Address of a subnode relative to a node – Any subnode of a node with address <a> will have a node address of the form <a#b> where <b> is the address of the subnode relative to <a>. Keys for XML 22 Value Equality Value of a node 1.A set S of relative addresses of its subnodes 2.A partial function from S to names 3.A partial function from S to texts 2 nodes are value-equal if they agree on 1, 2, 3 Notation: a =v b Keys for XML 23 Value Equality (example) S = {., <1>, <2>, <1,1>, <2,1>} db person person ... person person name @phone 1 “123-4567” firstName 1 “George” name 2 1 lastName 1 “Bush” Keys for XML firstName 1 “George” @pnone 2 “234-5678” lastName 1 “Bush” 24 Path expressions How to identify nodes in a tree? Expression involving node names (tags + attributes) that describes a set of paths in the document tree – XPath (XML-Schema) – Regular expressions (semistructured data) Keys for XML 25 Regular Path Expressions In the normal syntax of regular expressions: db depts dept emps db.emps.emp emp emp db.(depts.dept.mgr |emps.emp) name name name db._*.name “Mary” “John” “Bill” mgr Keys for XML 26 Language for path expression 2 necessary properties – Concatenation operation, not uniform presentation in XPath • Concatenate a/b with /c/d : a/b//c/d – A path should only move down the tree • Navigation axis in XPath Keys for XML 27 Language for path expression Empty path “ε” (“.”) Node name (tag/attribute name) Wild card “_”, single node name Arbitrary path “_*” Concatenation of paths P, Q is P.Q (“*”) (“//”) (“/”) Notation – n[P]: set of nodes (node addresses) reached by starting at node n and following a path that conforms to P – [P] := root[P] Keys for XML 28 Examples Simple path – <2#2>[title] = {<2#2#1>} – [composer.work] = {<1#3>, <1#4>, <2#2>} Complex path – <2#2>[_*] – [composer._] – [_*.num] = {<2#2>, <2#2#1>, <2#2#1#1>, <2#2#@num>} = {<1#1>, <1#2>, <1#3>, <1#4>, <2#1>, <2#2>} = {<1#3#@num>, <1#4#@num>, <2#2#@num>} Keys for XML 29 Absolute key 30 Key specification Necessary to specify – Set on which we are defining the key (relation) – “Attributes” (set of column names) Pair (Q, {P1, …, Pn}) – Target path Q path expression: target set on which the key constraint is to hold – Key path {P1, …, Pn} set of simple path expressions Keys for XML 31 Key specification (cont’d) – Target path Q – Key path {P1, …, Pn} For any node n in [Q], there is a set of nodes n[Pi] found by following Pi from n (may be empty) Examples 1. (person.employees, {name.firstname, name.lastname}) 2. 3. (composer, {name}) (composer, {born}) Keys for XML 32 Formal Definition A node n satisfies a key specification (Q,{P1,... , Pk}) iff for any n1, n2 in n[Q], if for all i, 1<= i <= k , there exist z1 in n1[Pi] and z2 in n2[Pi] such that z1 =v z2 then n1 = n2. Value equality z1 =v z2 Node equality : 2 nodes are equal if they have the same node address n1 = n2 The values associated with key paths uniquely identify a node in the target set Not part of the schema, data Keys for XML 33 Remarks For any n1, n2 in [Q], if Pi is missing at either n1 or n2 then n1[Pi] and n2[Pi] are by definition disjoint Multiple nodes <db> <A> <B> 1 </B> </A> <A> <B> 1 </B> <B> 2 </B> </A> </db> Key (A, {B}) with respect to the root. The document does not satisfy the key. Keys for XML 34 Example of keys (_*.person, {id}) – 2 persons elements are disjoint on their id fields (person, {ε}) – Any 2 person nodes immediately under the root have different values (employee, {}) – Empty key. There is at most one employee under the root (_*, {id}) – Any 2 nodes are disjoint on their id fields up to value-equality – Semantics of ID attribute in the XML standard Keys for XML 35 XML vs. relational XML, paths that define keys Relational DB – Need not exist (nullvalued keys) – Do not have to be unique – Key paths specify a set of addresses within a document Keys for XML – Key values cannot be null, must exist – Have to be unique – 1NF requires each component of every tuple to be atomic value, not set 36 Remarks Equivalence of 2 path expressions is decidable Given a definition of equality on tree, do we need to have more than one key path in a key specification? – All key attributes must be represented as subnodes of some node – Constrain this node to contain only those subnodes – Too restrictive, unnecessary interference between key specifications and data models Allow a (possible empty) set of nodes at the end of each key path – How to require each of the key paths to exist and to be unique? Keys for XML 37 Remarks (cont’d) Language of path expression – Need something more powerful to express Q (person.(mother | father)*, {id}) A person element followed by zero or more father or mother elements Provisional language of path expressions Does not change in the way of the theory Keys for XML 38 Key inference In relational DB – Infer some keys from the presence of others If (Q, S) is a key and S S’, then so is (Q, S’) – Counterpart of relational inference rule If (Q.Q’, {P}) is a key, then so is (Q, {Q’.P}) – tree-like structure : if a node is identified in a tree then its ancestor are also determined I.e. if a key path P uniquely identifies a node n in [Q.Q’] then Q’.P is a key path for the ancestor of n in [Q]. Keys for XML 39 Key Inference (cont’d) If (Q,S) is a key and Q’ Q, then (Q’, S) is also a key – Any key of the set [Q] is also a key for any subset of [Q] For any finite set Σ of keys, there exists an (finite) XML document satisfying Σ – Key paths may be missing, e.g. (_*,{id}) • If key path was required to exist at all nodes specified by the target path, the XML document would have to be infinite to satisfy the key – Only holds in the absence of DTDs Keys for XML 40 Key Inference Key K = (X, {}) DTD D: <!ELEMENT foo (X, X)> foo X foo X X No XML document that both conforms to D and satisfies K DTDs interact with XML key constraint Keys for XML 41 Relative Key 42 Relative key - Motivation Motivated by scientific data format, hierarchical structure, large set of entries at the top-level Protein sequence database Swiss-prot – Accession number (key) for each entry – Within each entry, sequence of citations each identified by a number 1, 2, 3, … Linguistic database – recording of speech – Data sets held in files – Metadata provided by directory structure – /timit/train/dr1/fcjjf0/sa1.wav – TIMIT corpus, training set, dialect region 1, female speaker, speaker-ID "cjf0", sentence text "sa1", speech waveform file Keys for XML 43 An absolute key for books An absolute key to identify a book: (book, {title} ) target path: book, starting from the root and identifying a collection of books key path: title; its value uniquely identifies a book absolute: defined on the entire document db book title “XML” “1” chapter chapter number section section number section section number text “1” “...” number “6” “10” book book book number number “1” Keys for XML “5” title chapter chapter “SGML” number number text “1” “10” “…” 44 Relative key - definition Like the key of a weak entity set in DB Studios(name, address) Crews(number) A document satisfies a relative key specification (Q, (Q’,S)) iff for all nodes n in [Q], n satisfies the key (Q’,S). Absolute keys are a special case of relative keys – (Q’,S) equivalent to (ε, (Q’,S)) Keys for XML 45 A relative key for chapters A relative key: (book, (chapter, {number} ) ) A chapter number uniquely identifies a chapter within a book! Context path: book target path: chapter, starting at a book key path: number relative: defined on sub-documents, relative to the context db book title “XML” “1” chapter chapter number section section number section section number text “1” “...” number “6” “10” book book book number number “1” Keys for XML “5” title chapter chapter “SGML” number number text “1” “10” “…” 46 Absolute/Relative Key What is the difference between – Absolute key (book.chapter, {number}) – Relative key (book, (chapter, {number} ) ) db book title “XML” “1” chapter chapter number section section number section section number text “1” “...” number “6” “10” book book book number number “1” Keys for XML “5” title chapter chapter “SGML” number number text “1” “10” “…” 47 A relative key for sections Key: (book.chapter, (section, {number} ) ) A section number uniquely identifies a section within a particular chapter of a particular book! relative to the chapter containing the section, and to the book containing the chapter db book title “XML” “1” chapter chapter number section number text “1” “...” section number section section number “6” “10” book book book number number “1” Keys for XML “5” title chapter chapter “SGML” number number “1” “10” text “…” 48 Transitivity of relative keys A relative key such as (bible.book.chapter,(verse, {number})) does not uniquely identify a particular verse in the bible Book name, chapter number, verse number verse Keys for XML 49 “immediately precedes” relation (Q1, (Q’1,S1)) immediately precedes (Q2, (Q’2,S2)) if Q2 = Q1.Q’1 – (bible, (book,{name})) immediately precedes (bible.book, (chapter,{number})) – Any absolute key immediately precedes itself Keys for XML 50 “precede” relation Precede is the transitive closure of the immediately precedes relation – Qn = Q1.Q’1…Q’n-1 (bible, (book, {name})), (bible.book,(chapter, {number})), (bible.book.chapter,(verse, {number})) Keys for XML 51 Transitivity of relative keys A set Σ of relative keys is transitive if for any relative key K1 = (Q1,(Q’1,S1)) in Σ there is a key K2 = (ε,(Q’2,S2)) in Σ which precedes K1 Any transitive set of relative key must contain some absolute key Keys for XML 52 Transitivity of relative keys - example TRANSITIVE SET (ε,(bible.book, {name})) (bible.book,(chapter, {number})) (bible.book.chapter,(verse, {number})) Keys for XML 53 Insertion-friendly relative keys Transitive key specification (ε, (university, {name})) (university, (dept.employee, {emp-id})) Identify an employee: university name + emp-id Add an employee: specify a dept for the employee No way to identify a dept – Many ways to add an employee!!! Keys for XML 54 Insertion-friendly relative keys (cont’d) Insert an element in the “keyed” part of the document unambiguously by specifying where to insert the element using keys. A set Σ of relative keys is insertion-friendly if it is transitive and whenever (Q1,(Q’1.n,S1)) Σ, there is a relative key (Q2,(Q’2,S2)) Σ where |Q’2| > 0 and Q1. Q’1 = Q2.Q’2. – n is a node name Every element with a prefix along the path Q1.Q’1 can be identified through some keys Keys for XML 55 Insertion-friendly relative keys (cont’d) (ε, (university, {name})) (university, (dept, {dept-name})) (university, (dept.employee, {emp-id})) n = employee Keys for XML 56 Insertion-friendly relative keys (cont’d) (ε, (university, {name})) (university, (dept, {dept-name})) (university, (dept.employee, {emp-id})) Nothing about the dept is necessary to identify employees!!! Anomaly that occurs in non-second NF of relational databases Employees should not be children of department nodes, but only of university nodes Linkage between employees and department should be expressed through a foreign key Keys for XML 57 Notation for relative key If system of relative keys is transitive, it forms a hierarchical structure create a compressed syntax for such systems Basic syntactic form Q1{P1 ,...,Pk1}.Q2{P1,...,Pk2}. ...Qn{P1 ,...,Pkn} Keys for XML 58 Notation for relative key (cont’d) bible{}.book{name}.chapter{number}.verse{ number} (ε, (bible, {})) (bible, (book, {name}) (bible.book, (chapter,{number})) (bible.book.chapter, (verse,{number})) company{name}[.employee{id}, .department{name}] company{name}.employee{id} company{name}.department{name} Keys for XML 59 Notation for relative key Compact and understandable Ensure the internal consistency of the document To tell other how to cite a component of our document Our document have a structured “core” Keys for XML 60 Strong keys 61 Stronger definitions of keys Requirements imposed by a key in relational DB: – Uniqueness of a key – Existence of key Key paths exist and are unique (for 1 i n, n[Pi] contains exactly one node) – name is unique at <1> – work and num are not unique at this node Keys for XML 62 Stronger definitions of keys (cont’d) A node n satisfies a strong key specification (Q, {P1, …, Pk}) if – For all n’ in n[Q] and for all Pi, Pi exists and is unique at n’. – For any n1, n2 in n[Q], if for all I, n1[Pi] =v n2[Pi] then n1=n2 Keys for XML 63 Stronger definitions of keys (cont’d) (_*.person, {id}) – Any 2 person elements, have unique id and differ on those elements (person, {ε}) – Unchanged (employees, {}) – Unchanged Keys for XML 64 Stronger definitions of keys (cont’d) (_*, {k}) – Every element has a key k, including element whose name is k Finite satisfiability? Impose an infinite chain of k nodes – No finite document satisfies it Because of the requirement of existence of key paths – Structural constraint Keys for XML 65 Relative Strong Key A document satisfies a strong relative key specification (Q, (Q’,S)) iff for all nodes n in [Q], n satisfies the strong key (Q’,S) Keys for XML 66 “Unconstrained” XML : Node names as key values 67 Node names as key values Key specification must cover the practical cases without using definitions that are too complex to allow any kind of reasoning about keys Issue in “unconstrained” XML: interchanging structure (the names) with data (their values) Keys for XML 68 “unconstrained” XML <db> <parts> <widget> <id> 123 </id> <w> 1.5 </w> </widget> <widget> <id> 234 </id> <w> 2.5 </w> </widget> <gadget> <id> 123 </id> <w> 3.2 </w> </gadget> </parts> </db> <db> <parts> <part> <type> widget </type> <id> 123 </id> <w> 1.5 </w> </part> <part> <type> widget </type> <id> 234 </id> <w> 2.5 </w> </part> <part> <type> gadget </type> <id> 123 </id> <w> 3.2 </w> </part> </parts> </db> Keys for XML 69 Node names as key values (cont’d) “Unconstrained” XML – Type of a part is expressed in the tag – Key constraint: parts{}[.widget{id},.gadget{id}] Alternative XML representation – type expressed as an attribute or subelement of a part element – Key constraint: parts{}[.part{type,id}] Keys for XML 70 Introducing a new part type Introduce a thingy “unconstrained” – Change key specification – parts{}[.widget{id},.gadget{id},.thingy{id}] Alternative – No change parts{}[.part{type,id}] Ability to interchange structure and data is supposed to be one of the strong points of semistructured data and XML Keys for XML 71 Solution Adding a “virtual” subelement node-name to each named node, whose value consists of the node name Key: parts{}._{node-name, id} Does not alter any of the properties expected to hold for keys Account for any practical use of tag names in keys Keys for XML 72 Conclusion A new key constraint language for XML: – independent of any schema specifications for XML – powerful enough to express absolute and relative keys – simple enough to be reasoned about efficiently In contrast to their relational counterparts: – XML keys are more complex – the analyses of XML keys are far more intricate Keys for XML 73 References Peter Buneman, Susan Davidson, Wenfei Fan, Carmem Hara, and Wang-Chiew Tan. Keys for XML. WWW10 (2001) http://db.cis.upenn.edu/DL/xmlkeys.ps Peter Buneman, Susan Davidson, Wenfei Fan, Carmem Hara, and Wang-Chiew Tan. Reasoning about keys for XML. University of Pennsylvania. Technical Report MS-CIS-00-26, 2000 http://db.cis.upenn.edu/DL/absolute-full.ps Keys for XML 74