## Exact XML type checking in polynomial time (2007)

### Cached

### Download Links

- [www2.in.tum.de]
- [wwwbib.informatik.tu-muenchen.de]
- [www.cse.unsw.edu.au]
- DBLP

### Other Repositories/Bibliography

Venue: | In ICDT |

Citations: | 32 - 3 self |

### BibTeX

@INPROCEEDINGS{Maneth07exactxml,

author = {Sebastian Maneth and Thomas Perst and Helmut Seidl},

title = {Exact XML type checking in polynomial time},

booktitle = {In ICDT},

year = {2007},

pages = {254--268}

}

### OpenURL

### Abstract

f on valid inputs conform to theoutput type? Since XML types are intrinsically more complex than the types found in

### Citations

255 | XMark: A Benchmark for XML Data Management
- Schmidt, Waas, et al.
- 2002
(Show Context)
Citation Context ...bitrary number of function calls may be applied to the same subdocument of the input. Quite a few useful transformations on the other hand consult every part of the input only a small number of times =-=[25]-=-. In our running example with mail and spam, every subtree of the input is processed at most twice. Therefore, we consider the subclass of smtts processing every subtree of the input at most b times. ... |

191 | Taxonomy of XML schema languages using formal language theory
- Murata, Lee, et al.
- 2005
(Show Context)
Citation Context ...act XML type checking. For the exact setting, types can be considered as regular or recognizable tree languages — thus capturing the expressive strength of virtually all known type formalisms for XML =-=[21]-=-. ⋆ National ICT Australia is funded through the Australian Governments Backing Australias Ability initiative, in part through the Australian Research CouncilsEven though the class of translations for... |

157 | Typechecking for XML Transformers
- Milo, Suciu, et al.
(Show Context)
Citation Context ...overnments Backing Australias Ability initiative, in part through the Australian Research CouncilsEven though the class of translations for which exact type checking is possible is surprisingly large =-=[6, 18, 15]-=-, the price to be paid for exactness is also extremely high. The design space for exact type checking comes as a huge “exponential wasteland”: even for simple top-down transformations, exact type chec... |

147 | XDuce: A statically typed XML processing language
- Hosoya, Pierce
(Show Context)
Citation Context ...rying XML documents. It is strongly-typed and type checking is performed via type inference rules computing approximative types for each expression. Approximative type inference is also used in XDuce =-=[13]-=- and its follow-up version CDuce [10]; navigation and deconstruction are based on an extension of the pattern matching mechanism of functional languages with regular expression constructs. Recently, ... |

119 |
Mappings and grammars on trees
- Rounds
- 1970
(Show Context)
Citation Context ... ) | q 1 | e where q 1 , cp are nonterminals. Note that selection of rules depending on input symbols now is replaced with nondeterministic choice. Context-free tree grammars were invented in the 70s =-=[24]-=-. See [7] for a comprehensive study of their basic properties. Formally, a cftg G can be represented by a tuple (E, Σ, P, E0) where E is a finite ranked set of function symbols or nonterminals, E0 ⊆ E... |

110 | Regular expression pattern matching for XML
- Hosoya, Pierce
- 2001
(Show Context)
Citation Context ...sion of the pattern matching mechanism of functional languages with regular expression constructs. Recently, Hosoya et al. proposed a type checking system based on the approximative type inference of =-=[12]-=- for parametric polymorphism for XML [11]. Type variables are interpreted as markings indicating the parameterized subparts. In [19] a sound type checking algorithm is proposed (originally developed f... |

107 |
Macro tree transducers
- Engelfriet, Vogler
- 1985
(Show Context)
Citation Context ...ll-by-name evaluation order, outermost calls are evaluated first. The parameters of a function call may themselves contain function calls which then are transferred to the body in an unevaluated form =-=[8]-=-. In this paper, however, we consider the inside-out (IO) evaluation order. This 3 Note that in [15], smtts are defined in a slightly different way. The rules there are of the form q(x0 as a(x1, . . .... |

88 | Automata theory for XML researchers
- Neven
(Show Context)
Citation Context ...e given by a document type definition (DTD) [28] or by a schema (using, e.g., RELAX NG [3]). A convenient abstraction of the existing XML type formalisms are recognizable (or: regular) tree languages =-=[21, 22]-=-. In the context of this work we use bottom-up tree automata to define recognizable tree languages. As usual, a bottom-up finite state tree automaton (fta) is a tuple A = (P, Σ, δ, F ) where P is a fi... |

52 | Static analysis of xml transformations in java
- Kirkegaard, Møller, et al.
(Show Context)
Citation Context ... XML [11]. Type variables are interpreted as markings indicating the parameterized subparts. In [19] a sound type checking algorithm is proposed (originally developed for the Java-based language XACT =-=[14]-=-) based on an XSLT flow analysis that determines the possible outcomes of pattern matching operations; for the benefit of better performance the algorithm deals with regular approximations of possible... |

50 |
XML type checking with macro tree transducers
- Maneth, Berlea, et al.
- 2005
(Show Context)
Citation Context ...overnments Backing Australias Ability initiative, in part through the Australian Research CouncilsEven though the class of translations for which exact type checking is possible is surprisingly large =-=[6, 18, 15]-=-, the price to be paid for exactness is also extremely high. The design space for exact type checking comes as a huge “exponential wasteland”: even for simple top-down transformations, exact type chec... |

46 | Macro tree transducers, attribute grammars, and MSO definable tree translations
- Engelfriet, Maneth
- 1999
(Show Context)
Citation Context ... input is processed at most twice. Therefore, we consider the subclass of smtts processing every subtree of the input at most b times. Thus in principle, b-bounded copying is a semantic property (cf. =-=[5]-=-). Instead of dealing with a semantic definition, we find it more convenient to consider syntactic b-bounded copying only. For all states q of M, we define the maximal copysnumbers b[q] as the least f... |

43 |
Grammars with Macro-like Productions
- Fischer
- 1968
(Show Context)
Citation Context ...of practically interesting transformations obtained by putting only mild restrictions on the transducers. Stay macro tree transducers are a combination of top-down tree transducers and macro grammars =-=[9]-=-. An smtt is a recursive first-order functional program that generates output trees by top-down pattern matching its first (tree) argument while possibly accumulating intermediate results in additiona... |

37 |
Context-free graph grammars
- Engelfriet
- 1997
(Show Context)
Citation Context ...e characterization of smtt output languages by cftgs is useful because emptiness for (IO-)cftgs is decidable using a similar algorithm as the one for ordinary context-free (word) grammars (see, e.g., =-=[4]-=-). Thus we have: Theorem 4. It can be decided in linear time for a cftg G whether or not L(G) = ∅. Here, we are interested in type checking transformations implemented through smtts, i.e., we want to ... |

37 | A comparison of pebble tree transducers with macro tree transducers
- Engelfriet, Maneth
(Show Context)
Citation Context ...overnments Backing Australias Ability initiative, in part through the Australian Research CouncilsEven though the class of translations for which exact type checking is possible is surprisingly large =-=[6, 18, 15]-=-, the price to be paid for exactness is also extremely high. The design space for exact type checking comes as a huge “exponential wasteland”: even for simple top-down transformations, exact type chec... |

34 | The design space of type checkers for XML transformation languages
- Møller, Schwartzbach
- 2005
(Show Context)
Citation Context ...sically more complex than the types found in conventional programming languages, the type checking problem for XML poses new challenges on the design of type checking algorithms. The excellent survey =-=[20]-=- gives an overview of the different approaches to XML type checking. In its most general setting, the type checking problem for XML transformations is undecidable. Hence, general solutions are bound t... |

32 | Frontiers of tractability for typechecking simple XML transformations
- Martens, Neven
- 2004
(Show Context)
Citation Context ...e inference can be done for a transformation language providing all standard features of most XML transformation languages using a simulation by at most three smtts. Inverse type inference is used in =-=[16, 17]-=- to identify subclasses of top-down XML transformation which have tractable exact type checking. We note that the classes considered there are incomparable to the ones considered in this paper. 2 Stay... |

32 |
Macro forest transducers
- Perst, Seidl
(Show Context)
Citation Context ...ed by mainstream programming languages like C or OCaml. The inside-out strategy evaluates innermost calls first, meaning that fully evaluated output trees are passed in accumulating parameters. As in =-=[23]-=-, we will not use an operational semantics of smtts based on rewriting, but prefer a denotational formulation which greatly simplifies proof arguments. Thus, the meaning [q ] of state q of M with k ac... |

26 |
Extensible Markup Language (XML) 1.0 (Second Edition)”, W3C Recommendation, 6 October 2000. See http://www.w3.org/TR/REC-xml (Current May 2002
- W3C
- 2003
(Show Context)
Citation Context ...rned with techniques for type checking, we need to define the type of the input and output language of a transformation. Usually, types for XML documents are given by a document type definition (DTD) =-=[28]-=- or by a schema (using, e.g., RELAX NG [3]). A convenient abstraction of the existing XML type formalisms are recognizable (or: regular) tree languages [21, 22]. In the context of this work we use bot... |

25 | Parametric polymorphism for XML
- Hosoya, Frisch, et al.
- 2005
(Show Context)
Citation Context ... functional languages with regular expression constructs. Recently, Hosoya et al. proposed a type checking system based on the approximative type inference of [12] for parametric polymorphism for XML =-=[11]-=-. Type variables are interpreted as markings indicating the parameterized subparts. In [19] a sound type checking algorithm is proposed (originally developed for the Java-based language XACT [14]) bas... |

22 |
On the complexity of typechecking top-down XML transformations
- Martens, Neven
- 2005
(Show Context)
Citation Context ...ss is also extremely high. The design space for exact type checking comes as a huge “exponential wasteland”: even for simple top-down transformations, exact type checking is exponential-time complete =-=[17]-=-. For practical considerations, however, one is interested in useful subclasses of transformations for which exact type checking is tractable. The fundamental work connecting pebble tree transducers w... |

20 | Regular tree language recognition with static information
- Frisch
- 2004
(Show Context)
Citation Context ...yped and type checking is performed via type inference rules computing approximative types for each expression. Approximative type inference is also used in XDuce [13] and its follow-up version CDuce =-=[10]-=-; navigation and deconstruction are based on an extension of the pattern matching mechanism of functional languages with regular expression constructs. Recently, Hosoya et al. proposed a type checkin... |

16 | Static validation of XSL Transformations
- Møller, Olesen, et al.
- 2005
(Show Context)
Citation Context ...ost general setting, the type checking problem for XML transformations is undecidable. Hence, general solutions are bound to be approximative, but seem to work well for practical XSLT transformations =-=[19]-=-. Another approach is to restrict the types and transformations in such a way that type checking becomes decidable; we then refer to the problem as exact XML type checking. For the exact setting, type... |

15 | XML path language (XPath) 1.0. W3C recommendation - Clark, DeRose - 1999 |

6 |
Least Solution of Equations over N
- Seidl
- 1994
(Show Context)
Citation Context ...ome i, q1, . . . , qm is the sequence of occurrences of calls qj(xi, . . .) for the same variable xi in the right-hand side t. The constraints for stay-rules are constructed analogously. According to =-=[27]-=-, the least solution of this constraint system can be constructed in linear time. Let [q], q state of M, denote this least solution. Then the smtt M is syntactically b-bounded (copying) (or, a b-smtt ... |

4 |
et.al., editors. XQuery 1.0: An XML Query Language
- Boag, Chamberlin
- 2005
(Show Context)
Citation Context ...r concatenation of forests. Related Work Approximative type checking for XML transformations is typically based on (subclasses of) recognizable tree languages. Using XPath as pattern language, XQuery =-=[1]-=- is a functional language for querying XML documents. It is strongly-typed and type checking is performed via type inference rules computing approximative types for each expression. Approximative type... |

3 |
et al. RelaxNG Specification. OASIS. Available online http://www.oasis-open.org/committees/relax-ng
- Clark, Murata
- 1980
(Show Context)
Citation Context ...need to define the type of the input and output language of a transformation. Usually, types for XML documents are given by a document type definition (DTD) [28] or by a schema (using, e.g., RELAX NG =-=[3]-=-). A convenient abstraction of the existing XML type formalisms are recognizable (or: regular) tree languages [21, 22]. In the context of this work we use bottom-up tree automata to define recognizabl... |

2 | Unranked Tree Algebra
- Bojańczyk, Walukiewicz
- 2005
(Show Context)
Citation Context ...refore, we replace the concept of a dfta by a finite forest monoid (ffm) which is a finite monoid S extended with an operation up : S × Σ → S that is used to handle upward movement in the forest (cf. =-=[2]-=-). Since the notion of linearity for smfts is completely analogous to linearity for smtts, the type checking algorithm for a linear smft T is almost the same as for linear smtts. As in the ranked tree... |

2 |
and 16:67–99
- Sci
- 1977
(Show Context)
Citation Context ... e where q 1 , cp are nonterminals. Note that selection of rules depending on input symbols now is replaced with nondeterministic choice. Context-free tree grammars were invented in the 70s [24]. See =-=[7]-=- for a comprehensive study of their basic properties. Formally, a cftg G can be represented by a tuple (E, Σ, P, E0) where E is a finite ranked set of function symbols or nonterminals, E0 ⊆ E is a set... |

1 |
Overloading is DEXPTIME
- Haskell
- 1994
(Show Context)
Citation Context ... for an smtt M is DEXPTIME-complete. Proof. The lower bound follows since translation non-emptiness is DEXPTIME-hard already in absence of accumulating parameters, i.e., for top-down tree transducers =-=[26]-=-. Since we will heavily rely on this algorithm, we briefly sketch the construction for the upper bound. Assume that M = (Q, Σ, R, Q0) and, w.l.o.g., that for every function q ∈ Q with k accumulating p... |

1 |
et.al., editors. XQuery 1.0: An XML
- Boag, Chamberlin
- 2005
(Show Context)
Citation Context ...for concatenation of forests. Related Work Approximative type checking for XML transformations is typicallybased on (subclasses of) recognizable tree languages. Using XPathas pattern language, XQuery =-=[1]-=- is a functional language for querying XML documents. It is strongly-typedand type checking is performed via forward type inference rules computing approximative types for each expression. Approximat... |

1 |
Context-Free Graph Grammars
- Clark, Murata
- 1997
(Show Context)
Citation Context ...iques for type checking we need to define the type ofthe input and output language of a transformation. Usually, types for XML documents are given by a document type definition (DTD) [28] or a schema =-=[9, 3]-=-.A convenient abstraction of the existing XML type formalisms, in particular DTDs, are recognizable (or: regular) tree languages [21, 22]. In the context of this work weuse bottom-tree automata to def... |

1 | R-Unification thanks to Synchronized-ContextfreeLanguages - R'ety, Chabin, et al. - 2005 |