XML Integrity Constraints

Transcription

1 XML Integrity Constraints Mirian Halfeld Ferrari European Master s Program - Information Technologies for Business Intelligence Mirian Halfeld Ferrari (IT4BI) XML-IC 1 / 23

2 References and general information Bibliographic notes Béatrice Bouchou, Mírian Halfeld Ferrari Alves, Maria Adriana Vidigal de Lima. Attribute Grammar for XML Integrity Constraint Validation. DEXA (1) 2011 : Ullman and Widom, A first course in base systems, Prentice-Hall International, For some notions on relational bases. Béatrice Bouchou, Mírian Halfeld Ferrari, Maria Adriana Lima. Contraintes d intégrité pour XML. Visite guidée par une syntaxe homogène. Technique et Science Informatiques 28(3) : (2009) Béatrice Bouchou, Ahmed Cheriat, Mírian Halfeld Ferrari, Dominique Laurent, Maria Adriana Lima, Martin A. Musicante. Efficient Constraint Validation for Updated XML Database. Informatica (Slovenia) 31(3) : (2007) Mirian Halfeld Ferrari (IT4BI) XML-IC 2 / 23

3 Introduction Importance of integrity constraints Integrity constraints are traditionally part of a schema specification. Integrity constraints are important in order to define some semantics and to assure consistence. Several constraint languages for XML have been proposed. Different kinds of integrity constraints : keys (XKeys), foreign keys (XFK), functional dependencies (XFD), inclusion dependencies (XID) Mirian Halfeld Ferrari (IT4BI) XML-IC 3 / 23

4 To Express Integrity Constraints Path, Patterns and Instances Paths A path for an XML tree t is defined by a sequence of tags or labels. Our path languages : used to define integrity constraints over XML trees : Path language PL s (defined by ρ ::= l ρ/ρ _). Path language PL (defined by υ ::= [ ] ρ υ//ρ). The language PL s describes a path in t, while PL is a generalization of PL s including "//". A path P is valid if it conforms to the syntax of PL s or PL and for all tag l P, if l = or l Σ att, then l is the last symbol in P. Examples : /// or fac//student/coursetaken/coursecode Mirian Halfeld Ferrari (IT4BI) XML-IC 4 / 23

5 To Express Integrity Constraints Path, Patterns and Instances Path Instances Let I = v 1 /.../v n be a sequence of positions such that each v i is a direct descendant of v i 1 in t. I is an instance of P over t if and only if the sequence t(v 1 )/.../t(v n) L(A P ). A P the finite-state automaton defined according to P. fac // student / coursetaken / coursecode / fac... 0 students 0.0 student id name coursetaken coursetaken coursetaken marriedto coursecode deptname deptname coursecode deptname Peter Smith St001 Maria Caldas C BD 07S2 Computing Math C Theory 07S1 Computing Mirian Halfeld Ferrari (IT4BI) XML-IC 5 / 23

6 To Express Integrity Constraints Path, Patterns and Instances Patterns and pattern instances A pattern is a finite set of prefix-closed paths in a tree t. An instance of a pattern is defined by considering the longest common prefix and an unique instance for it. A set of paths : {fac//student/coursetaken/coursecode, fac//student/coursetaken/deptname})) Common prefix : fac//student/coursetaken fac fac This is not a pattern instance!!... 0 // students student / coursetaken / / 0.0 student... coursecode deptname / / id name coursetaken coursetaken coursetaken marriedto τ C/P,C/Q = [C BD 07S2, Computing] τ C/P,C/Q = [M 1, Math] deptname coursecode deptname coursecode coursecode deptname St001 Maria Caldas C Theory 07S1 Computing M-1 Math C BD 07S2 Computing Peter Smith Mirian Halfeld Ferrari (IT4BI) XML-IC 6 / 23

7 To Express Integrity Constraints Equalities Two types of equality Value equality : two nodes are value equal when they are roots of isomorphic sub-trees. Node equality : two nodes are node equal when they are the same position. ε 0 1 Nodes 0.1 and 1.1 are value equal pname pname Proj1 MSI Proj2 MSI price price 955X Neo 955X Neo ,00 185,00 Mirian Halfeld Ferrari (IT4BI) XML-IC 7 / 23

8 Different Integrity Constraints Functional Dependencies Functional Dependencies in Relational Databases The relational case In a relational base a functional dependency is defined as follows : Let U be the set of attributes of a relation schema R. We usually write R[U]. Let X U and A U. An instance I of R satisfies the functional dependency X A when for all two tuples u and v if u[x] = v[x] then u[a] = v[a] Given X A, we say that X functionally determines A. Consider the functional dependency Name, Year Activity Name Year Activity Mario 2010 theatre Diana 2010 theatre Peter 2010 volleyball Barbara 2011 volleyball Mario 2011 football Mirian Halfeld Ferrari (IT4BI) XML-IC 8 / 23

9 Different Integrity Constraints Functional Dependencies XFD Syntax An XML functional dependency (XFD) is an expression of the form : Notation γ = (C,({P 1 [E 1 ],...,P k [E k ]} Q [E])) C, P 1...P k and Q are path expressions. Path C represents the context for the dependency verification. {P 1,...,P k } are the determinant paths of the XFD. Q is the dependent path. Symbols E 1,...,E k represent the associated equality type. Mirian Halfeld Ferrari (IT4BI) XML-IC 9 / 23

10 Different Integrity Constraints Functional Dependencies XFD Semantics Let XML document T XFD γ = (C, ({P 1 [E 1 ],..., P k [E k ]} Q [E])) Pattern P : {C/P 1,...,C/P k, C/Q} XFD satisfaction T = γ if and only if for all two instances (I 1, I 2 ) of pattern P in T that coincide at least on their prefix C, we have : τ 1 [C/P 1,...,C/P k ] = Ei,i [1...k] τ 2 [C/P 1,...,C/P k ] τ 1 [C/Q] = E τ 2 [C/Q] where τ 1 (resp. τ 2 ) is the tuple obtained from I 1 (resp. I 2 ). Mirian Halfeld Ferrari (IT4BI) XML-IC 10 / 23

11 Different Integrity Constraints Functional Dependencies XFD Example γ 1 : (,( {///@sname[v], ////[V]} ////price[v]) )) ε pname Proj1 MSI [MSI, 955X Neo,185,00] [MSI, K8N,182,90] price quantity price quantity 955X Neo K8N , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 11 / 23

12 General ideas A general integrity constraint validation method Our goal : integrity constraint validation on XML documents. Our validation method : a grammarware (based on a grammar) describing an XML document to which we associate attributes and semantic rules. Attribute grammar : the grammar is augmented by semantic rules that define, for each integrity constraint, the verification process. Mirian Halfeld Ferrari (IT4BI) XML-IC 12 / 23

13 General ideas Building an attribute grammar Attribute grammar : attach a set of semantic rules to each production of a context-free grammar. General CFG (context free grammar) to describe an XML tree. Rule for the root element : ROOT α 1...α m. Rule for an internal element node : A α 1...α m. Rule for an element containing and for an attribute : A. Mirian Halfeld Ferrari (IT4BI) XML-IC 13 / 23

14 FSA and TSAs for XFD To model the paths of an XFD, we use finite-state automata (FSA) or transducers (FST). γ : (/,( {//@sname[v],///[v]} ///quantity[v]) )) M : e 0 e 1 e 2 T : e 3 e e (V,1) e 6 5 e (V,2) 7 T" : e 8 e 9 e 10 quantity e V 11 Mirian Halfeld Ferrari (IT4BI) XML-IC 14 / 23

15 Attribute Grammar for XFD Validation Descending Direction : Inherited Attribute conf conf is used at each node to indicate its role concerning an XFD its value is a set of FSA configurations all nodes are bound to a conf attribute, except nodes conf is an empty set when the node is not in any XFD path Mirian Halfeld Ferrari (IT4BI) XML-IC 15 / 23

16 Example : Descending direction M : e0 e1 e2 T e3 e4 e6 (V,1) e5 e7 (V,2) quantity T" : e8 e9 e10 e11 V conf = {M.e1} ǫ 0 conf = {M.e2} conf = {} conf = {T.e4, T.e9} pname conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} conf = {T.e7} price quantity price quantity 955X Neo conf = {} conf = {T.e11} K8N conf = {} conf = {T.e11} , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

17 Example : Descending direction M : e0 e1 e2 T e3 e4 e5 (V,1) e6 e7 (V,2) quantity T" : e8 e9 e10 e11 V ǫ conf = {M.e1} 0 conf = {M.e2} conf = {} pname conf = {T.e4, T.e9} conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} 955X Neo price quantity 185,00 conf = {} conf = {T.e11} conf = {T.e7} price quantity K8N conf = {} conf = {T.e11} ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

18 Example : Descending direction M : e0 e1 e2 T e3 e4 e5 (V,1) e6 e7 (V,2) quantity T" : e8 e9 e10 e11 V conf = {M.e1} ǫ 0 conf = {M.e2} conf = {} conf = {T.e4, T.e9} pname conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} 955X Neo price quantity 185,00 conf = {} conf = {T.e11} conf = {T.e7} price quantity K8N conf = {} conf = {T.e11} ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

19 Example : Descending direction M : e0 e1 e2 T e3 e4 e5 (V,1) e6 e7 (V,2) quantity T" : e8 e9 e10 e11 V ǫ conf = {M.e1} 0 conf = {M.e2} conf = {} conf = {T.e4, T.e9} pname conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} 955X Neo price quantity 185,00 conf = {} conf = {T.e11} conf = {T.e7} price quantity K8N conf = {} conf = {T.e11} ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

20 Example : Descending direction M : e0 e1 e2 T e3 e4 e5 (V,1) e6 e7 (V,2) quantity T" : e8 e9 e10 e11 V conf = {M.e1} ǫ 0 conf = {M.e2} conf = {} conf = {T.e4, T.e9} pname conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} 955X Neo price quantity 185,00 conf = {} conf = {T.e11} conf = {T.e7} price quantity K8N conf = {} conf = {T.e11} ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

21 Example : Descending direction M : e0 e1 e2 T e3 e4 e5 (V,1) e6 e7 (V,2) quantity T" : e8 e9 e10 e11 V ǫ conf = {M.e1} 0 conf = {M.e2} conf = {} conf = {T.e4, T.e9} pname conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} 955X Neo price quantity 185,00 conf = {} conf = {T.e11} conf = {T.e7} price quantity K8N conf = {} conf = {T.e11} ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

22 Example : Descending direction M : e0 e1 e2 T e3 e4 e5 (V,1) e6 e7 (V,2) quantity T" : e8 e9 e10 e11 V conf = {M.e1} ǫ 0 conf = {M.e2} conf = {} conf = {T.e4, T.e9} pname conf = {T.e5} conf = {T.e6, T.e10} conf = {T.e6, Proj1 MSI conf = {T.e7} 955X Neo conf = {T.e7} price quantity price quantity conf = {} conf = {T.e11} K8N conf = {} conf = {T.e11} , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 16 / 23

23 Just an example of a rule in the attribute grammar Production Attributes ROOT α 1... α m ROOT.conf := { M.q 1 δ M (q 0, ROOT) = q 1 } /* Inherited Attributes */ for each α i (1 i m) do α i.conf := { M.q δ M (q 1,α i ) = q } if (q 1 F M ) then α i.conf := α i.conf { T.q 1 δ T (q 0,α i ) = q 1 } { T.q 1 δ T (q 0,α i ) = q 1 } Mirian Halfeld Ferrari (IT4BI) XML-IC 17 / 23

24 Attribute Grammar for XFD Validation Ascending Direction : Synthesized Attributes c, inters, dc, ds j. c carries the dependency validity (true or false) from context level to the root. inters gathers the values from the nodes that are in determinant and dependent path intersections. ds j and dc store the values needed to verify the dependency. Mirian Halfeld Ferrari (IT4BI) XML-IC 18 / 23

25 Example : Ascending direction Computing synthesized attributes : ǫ c =< true > 0 c =< true > inters = {<< MSI, 955XNeo >, 5 >,<< MSI, K 8N >, 7 >} pname ds1 =< MSI > Proj ds1 =< MSI MSI inters = {<< ǫ, 955XNeo >, 5 >} ds2 =< 955XNeo > dc =< 5 > inters = {<< ǫ, K 8N >, 7 >} ds2 =< K 8N > dc =< 7 > ds2 =< 955XNeo > dc =< 5 > ds2 =< K 8N > dc =< 7 > price quantity price quantity 955X Neo K8N , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 19 / 23

26 Example : Ascending direction Computing synthesized attributes : c =< true > ǫ 0 c =< true > inters = {<< MSI, 955XNeo >, 5 >,<< MSI, K 8N >, 7 >} pname ds1 =< MSI > Proj ds1 =< MSI MSI inters = {<< ǫ, 955XNeo >, 5 >} ds2 =< 955XNeo > dc =< 5 > inters = {<< ǫ, K 8N >, 7 >} ds2 =< K 8N > dc =< 7 > ds2 =< 955XNeo > dc =< 5 > ds2 =< K 8N > dc =< 7 > price quantity price quantity 955X Neo K8N , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 19 / 23

27 Example : Ascending direction Computing synthesized attributes : ǫ c =< true > 0 c =< true > inters = {<< MSI, 955XNeo >, 5 >,<< MSI, K 8N >, 7 >} pname ds1 =< MSI > Proj inters = {<< ǫ, 955XNeo >, 5 >} ds1 =< MSI > ds2 =< 955XNeo dc =< 5 > MSI inters = {<< ǫ, K 8N >, 7 >} ds2 =< K 8N > dc =< 7 > ds2 =< 955XNeo > dc =< 5 > ds2 =< K 8N > dc =< 7 > price quantity price quantity 955X Neo K8N , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 19 / 23

28 Example : Ascending direction Computing synthesized attributes : ǫ c =< true > 0 c =< true > inters = {<< MSI, 955XNeo >, 5 >,<< MSI, K 8N >, 7 >} pname ds1 =< MSI > Proj inters = {<< ǫ, 955XNeo >, 5 >} ds1 =< MSI > ds2 =< 955XNeo dc =< 5 > MSI inters = {<< ǫ, K 8N >, 7 >} ds2 =< K 8N > dc =< 7 > ds2 =< 955XNeo > dc =< 5 > ds2 =< K 8N > dc =< 7 > price quantity price quantity 955X Neo K8N , ,90 7 Mirian Halfeld Ferrari (IT4BI) XML-IC 19 / 23

29 Just an example of a rule in the attribute grammar Production Attributes A /* Synthesized Attributes */ for each configuration M.q in A.conf do if (M = T ) (q F T ) y := λ T (q) j := y.rank if (y.equality = V ) then A.ds j := < value(t, ) > else A.ds j := < value(t, A) > if (M = T ) (q F T ) if (λ T (q) = V ) then A.dc := < value(t, ) > else A.dc := < pos(t, A) > Mirian Halfeld Ferrari (IT4BI) XML-IC 20 / 23

30 XFD Validation Overview xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx xxxxxx XML Document Validation using Attribute Grammar TRUE / FALSE (for each constraint) XFDs InhAtt_Stack SyntAtt_Stack Validation_HTables Auxiliary Data Structures Mirian Halfeld Ferrari (IT4BI) XML-IC 21 / 23

31 XFD Validation Overview : Auxiliary Structures Mirian Halfeld Ferrari (IT4BI) XML-IC 22 / 23

32 Overview of other Integrity constraints Constr. Path expression FSA Attributes XFD (C, ({P 1 [E 1 ],..., P k [E k ]} Q [E])) M, T and T Inherit. : : conf Synth. : c, inters, ds j, dc XID (C,({P 1,...,P k } {Q 1...Q k })) M, T and T Inherit. : : conf Synth. : c, inters, ds j, dc j XKeys (C,(Tg,{P 1,...,P k })) A C, A Tg et A P Inherit. : conf Synth. : c, tg et f XFK (C,(Tg R, {P R 1,...,P R k }) (Tg, {P 1,...,P k })) A C, A R Tg, A R P Inherit : conf Synth. : c, tg et f Mirian Halfeld Ferrari (IT4BI) XML-IC 23 / 23