Brokering Mathematical Services in the Global Network

Transcription

1 Brokering Mathematical Services in the Global Network Wolfgang Schreiner Department of Engineering for Computer-based Learning (CBL) Upper Austrian University of Applied Sciences, Hagenberg, Austria Work done at: Research Institute for Symbolic Computation (RISC-Linz) Johannes Kepler University, Linz, Austria Wolfgang Schreiner RISC-Linz/FH Hagenberg

2 Contents MathBroker Project at RISC-Linz (FWF grant P15183) Implementing services for computer mathematics using state-of-the-art Web technologies. Providing an infrastructure for brokering such services in the global network. Olga Caprotti, Rebhi Baraka. This talk: Web Services. Web Services for Computer Mathematics. Brokering Mathematical Web Services. Wolfgang Schreiner 1

3 Web Services Wolfgang Schreiner 2

4 Web Services What are web services anyway? Web Services Architecture Working Group: A Web service is a software system designed to support interoperable machine-to-machine interaction over a network. It has an interface described in a machine-processable format (specifically WSDL). Other systems interact with the Web service in a manner prescribed by its description using SOAP-messages, typically conveyed using HTTP with an XML serialization in conjunction with other Web-related standards. Services whose interfaces are based on Web-standards. Wolfgang Schreiner 3

5 Web Services Actually two levels are intermingled. Concept: interoperable machine-to-machine interaction. A Web service is a software system designed to support interoperable machine-to-machine interaction over a network. Expression: XML and Web protocols.... specifically WSDL... HTTP... XML serialization... other Web-related standards. Let us separate concepts from expression. Wolfgang Schreiner 4

6 Web Services: Concepts Vision of a global network of processes that... provide functionality on behalf of their respective owners and are described by meta-data such that a client in need of a specific functionality may identify those services that provide this functionality, invoke the services as required, and interpret the results returned by the services correctly, where the client may be a process/service itself. Humans are not necessarily part of the service request/answer loop. Wolfgang Schreiner 5

7 Web Technologies: Service Interface Generic syntax: XML (XML-Schema, XML-Namespaces). Object-level: XML-wrappers for message contents. Meta-level: XML-formatted service descriptions. Unified syntax simplifies data processing. Message formats: SOAP. Generic XML-based messaging framework. Various concrete protocol bindings (HTTP,... ). May encode message data or remote procedure calls (RPC). Service interface descriptions: WSDL. XML document-format for describing Web service interfaces as sets of endpoints. Services operate either on document-messages or on RPC-messages. WSCI (Web Services Choreography Interface) for describing message flow. Describe syntactic service interfaces. Wolfgang Schreiner 6

8 Web Technologies: Service Lookup Register entities for look-up by interested parties: By positioning them in hierarchical directories/catalogs/taxonomies. By creating an association between one entity and another. Two major registry/repository specifications: Universal Discovery Description and Integration (UDDI) standard. Business-oriented registry structure. ebxml (Electronic Business using XML) registry specification by OASIS. Low-level generic information model ( registry object ). High-level business-oriented model ( organization, user,... ) Generic APIs for accessing registries. Java API for XML registries (JAXR). Look up services in registries. Wolfgang Schreiner 7

9 Web Technologies: Service Behavior RDF: resource description framework. Describe binary relations between (collections) of resources. Directed graph of resource relations. Web Ontology Language (OWL) Formalize a domain by defining classes and properties of these classes. Define individuals and properties about them. Formal semantics based on description logic. DARPA Agent Modeling Language (DAML-S) Model agent behavior in terms of input, output, preconditions, post-conditions. Describe semantic service behaviors. Wolfgang Schreiner 8

10 Web Services: The Role of the Problem Domain How realistic is this vision? The real world s complexity prohibits this scenario in its generality. Have to focus on specific application domains. For many domains, formal descriptions may be infeasible. How to formalize a dating service? However, some domains are very well suitable. Those that deal with well-defined objects and relations between them. Our focus is on the domain of computer mathematics/logic. Wolfgang Schreiner 9

11 Web Services for Computer Mathematics Wolfgang Schreiner 10

12 Computer Mathematics/Logic The solution of mathematical problems by computer programs. Computing, simplifying, solving, proving. Computer algebra, automated theorem proving, symbolic computation, numerical computing. Maple, Mathematica, MuPad, Reduce, GAP,... ; Coq, Isabelle, PVS,... ; LAPACK,... Mostly stand-alone systems that require human interpretation and control. Work on turning stand-alone systems into web-based services: Internet Accessible Mathematical Computation (IAMC) workshop series, Mathematical Knowledge Management (MKM) workshop series, MathWeb, ActiveMath, OpenMath, MathML,... Mathematics on the Net (MONET) EU project. Problem solutions for science and engineering purposes. Wolfgang Schreiner 11

13 Examples Symbolic Integrator. Input: an algebraic expression involving elementary functions (exp, log, sin, cos,... ) Output: the symbolic integral (if it exists) or the information that is does not exist. Real Root Isolator. Input: a univariate polynomial with rational coefficients and an interval width. Output: a sequence of isolating intervals of the given width for the real solutions of the polynomial. Quantifier Eliminator. Input: a logic formula in the theory of real numbers involving universal and existential quantifiers. Output: an equivalent formula without quantifiers. Wolfgang Schreiner 12

14 Symbolic Integrator Wolfgang Schreiner 13

15 Quantifier Eliminator ======================================================= Quantifier Elimination in Elementary Algebra and Geometry by Partial Cylindrical Algebraic Decomposition Hoon Hong ======================================================= Enter a prenex formula: (A x)(a y)[ a > 0 /\ b > 0 /\ [ [ b^2 (x - c)^2 + a^2 y^2 - a^2 b^2 = 0] ==> x^2 + y^2-1 <= 0 ] ]. ======================================================= An equivalent quantifier-free formula: a > 0 /\ b > 0 /\ c - a + 1 >= 0 /\ c + a - 1 <= 0 /\ [ b^2 - a <= 0 \/ b^2 c^2 + b^4 - a^2 b^2 - b^2 + a^2 <= 0 ] ======================================================= Wolfgang Schreiner 14

16 Mathematical Services Vision of a global network of processes that... solve mathematical/logical problems and are described by meta-data such that a client in need of a mathematical/logic problem solution may identify those services that provide this solution, invoke the services as required, and interpret the results returned by the services correctly, where the client may be a process/mathematical service itself. Client need not know the specific software that provides the solution. Wolfgang Schreiner 15

17 Mathematical Web Services In terms of Web technologies... MONET consortium: A mathematical web service is a software application identified by a URI, whose interfaces and bindings are capable of being defined, described, and discovered as XML artifacts and whose data and results are encoded using markup for mathematical content. A mathematical web service supports direct interactions with other software agents using XML based messages exchanged via Internet-based protocols. But what about the characteristics of the domain? Wolfgang Schreiner 16

18 Domain Characteristics Rich variety of objects. Numbers, symbolic constants, polynomials over various coefficient domains, matrices, finite and infinite sequences, sums, matrices, functions, algebraic expressions, logic formulas,... Complicated relationships among objects and problems. Different representations of the same mathematical object in different domains. One problem may be a special case of another problem,... Symbolic computation versus scientific computing. Exact closed-form solution versus numerical approximation. In principle: complete formalization possible. Axiomatized theories with proofable properties. Problems with formal input/output specifications. In practice, no or sloppy specifications are frequent. Wolfgang Schreiner 17

19 Mathematical Object Representation: MathML W3C MathML: Mathematical Markup Language (a + b) 2 : presentation markup versus content markup. <msup> <mfenced> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> </mfenced> <mn>2</mn> </msup> <apply> <power/> <apply> <plus/> <ci>a</ci> <ci>b</ci> </apply> <cn>2</cn> </apply> Presentation markup only good for display; content markup does not specify symbol semantics (+ over which field)? Only limited applicability to web service communication. Wolfgang Schreiner 18

20 Mathematical Object Representation: OpenMath OpenMath Society: OpenMath specification 1.1 Emerging standard for representing mathematical objects. Semantics preserved when exchanged between computer programs. XML encoding and binary encoding specified. Content dictionaries (CDs) collect symbol definitions. Plain text description, informal/formal symbol properties, examples. <OMOBJ> <OMA> <OMS cd="arith1" name="power"/> <OMA> <OMS cd="arith1" name="plus"/> <OMV name="a"/> <OMV name="b"/> </OMA> <OMI>2</OMI> </OMOBJ> Wolfgang Schreiner 19

21 OpenMath Content Dictionaries <CDDefinition> <Name> log </Name> <Description> This symbol represents a binary log function... </Description> <CMP> a^b = c implies log_a c = b </CMP> <FMP> <OMOBJ> <OMA> <OMS cd="logic1" name="implies"/>... </FMP> <Example> log 100 to base 10 (which is 2). </Example> </CDDefinition> Wolfgang Schreiner 20

22 Mathematical Web Service Communication Wolfgang Schreiner 21

23 Mathematical Web Service Communication Web browser Integrator client Text/ MathML TOMCAT Java servlet container AXIS engine for SOAP SOAP Integrator service OM OpenMath Phrasebook Mathematica WSDL2Java SymbolicIntegration.wsdl deploy.wsdd Mathematica Text/MathML OpenMath object SOAP message OpenMath object Mathematica. Wolfgang Schreiner 22

24 Mathematical Web Service Communication CA system Mathematica performs the actual computation. Input and output in the Mathematica native syntax. OpenMath phrasebook performs OpenMath conversion. RIACA OpenMath library. Java class implements service. Takes OpenMath input, invokes phrasebook, returns result. AXIS engine implements SOAP service as a Java servlet. Deployment descriptor file (.wsdd) lists name of service and methods, name of Java implementation class, serializer/deserializer classes for I/O parameters. WSDL description is automatically generated by AXIS. WSDL2Java creates the communication classes needed by the client. Wolfgang Schreiner 23

25 Mathematical Web Service Communication Thus we can create mathematical web services. Use Web protocols and technologies. XML, Java servlets, SOAP, WSDL. Apache Tomcat, Apache AXIS, Sun JWSDP. Preserve semantics when communicating mathematical objects. OpenMath. RIACA OpenMath library. But how can a client locate the wanted services? Wolfgang Schreiner 24

26 Brokering Mathematical Web Services Wolfgang Schreiner 25

27 Brokering Mathematical Web Services Wolfgang Schreiner 26

28 Brokering Mathematical Web Services MSDL: Mathematical Service Description Language. Expressive enough to describe problem solved by service. Service lookup by formal specification of problem to be solved. Potential for automatic reasoning on services, e.g., if a service solves a given problem provided that an additional constraint is satisfied. Structured enough to allow registry lookup. Service lookup by name of problem to be solved. Potential to use existing registry technologies to query mathematical services. Goal is a MSDL-based service for brokering mathematical services. Wolfgang Schreiner 27

29 The Mathematical Service Description Language MSDL MathBroker (RISC-Linz) initiated the idea of a MSDL. Proposal in 2001, draft of XML schema in 2002 by Schreiner and Caprotti. MONET (EU consortium) took over the general idea. Common co-worker Olga Caprotti. MONET developed in 2003 its own schema based on a subset of MSDL. MathBroker revised MSDL. MSDL becomes an extension of the MONET schema. Common subset of both schemas preserves compatibility. MSDL is now a generalization of the MONET schema. Wolfgang Schreiner 28

30 The MSDL Layers Layer 1: Problem Description. Kind of problem: computing, simplifying, solving, proving. Input/output parameters, preconditions, postconditions. Layer 2: Algorithm Description. Refers to the problem solved by the algorithm. Adds time and space complexity, termination condition. Layer 3: Implementation Description. Refers to the algorithm used by the implementation. Adds time and space efficiency, information about software system. Layer 4: Service Description. Refers to the implementation on which the service is based. Refers to a WSDL description of the service endpoints. Refers to a description of the machine on which the service is running. Wolfgang Schreiner 29

31 The MSDL Information Model input params output params precondition postcondition Problem is special version of Problem Computing Problems, Solving Problems, Proving Problems,... solves All nodes may contain bibliographical information. time complexity space complexity Algorithm termination condition implements Issues covered Problems may be special versions of other problems Different algorithms may solve the same problem Different programs may implement the same algorithm Different realizations may use the same program Different services may provide the same realization Different services may run on same machine type time efficiency space efficiency software system Implementation optional is based on Service is bound to service port(s) WSDL service port is located on Machine Type is located on messages port types operations port processor type processor speed (SPEC) memory size Wolfgang Schreiner 30

32 A MSDL Problem Description <monet:problem name="indefinite-integration"> <monet:input name="f"> <monet:signature><om:omobj> <om:oma> <om:oms cd="sts" name="mapsto"/> <om:oms cd="setname1" name="r"/><om:oms cd="setname1" name="r"/> </om:oma> </om:omobj></monet:signature> </monet:input> <monet:output name="i">... </monet:output> <monet:post-condition> <om:omobj> <om:oma> <om:oms cd="relation1" name="eq"/> <om:omv name="i"/> <om:oma><om:oms cd="calculus1" name="indefint"/><om:omv name="f"/></om:oma> </om:oma> </om:omobj> </monet:post-condition> </monet:problem> Wolfgang Schreiner 31

33 Registering MSDL Description Libraries Development of an ebxml-based MSDL registry service. Implementation based on JAXR. Sun s Java API for XML registries. Mathematical catalogs. e.g. NIST s GAMS. Guide to Available Mathematical Software. Linking points for MSDL descriptions. MSDL information model. MSDL descriptions and their relations. ebxml for persistent storage. Java API for service access. Inherit description classes from the generic JAXR class RegistryObject. Wolfgang Schreiner 32

34 The GAMS Catalog in ebxml Wolfgang Schreiner 33

35 Registry Brokering How does a client profit from such a MSDL registry? Lookup of a service by problem name. Client provides the name of his (already registered) problem. Registry returns all services referring to that problem. Restriction to specific algorithms or implementations possible. Lookup of a service by problem classification. Client provides classification in a particular taxonomy (e.g. GAMS). Registry returns all services registered in that classification. Likewise registration of algorithms, implementations, or services possible. What else can we do? Wolfgang Schreiner 34

36 Semantic Brokering Lookup of a service by problem description. Client provides semantic description of its problem. Problem kind; input/output parameters, pre/postconditions. Broker cooperates with an automated reasoning service. Deduces from the registered problem descriptions those that semantically match the given one and returns the corresponding services. May also return services that solve a more general problem (less constrained input, more constrained output) or a more special problem (together with additional conditions). Search space may be restricted by the other means. Client specifies problem categorization or the name of a more special problem. MSDL provides the necessary information for such a scenario. Wolfgang Schreiner 35

37 Conclusions Web-based infrastructure for mathematical services. XML/OpenMath, Java servlets, SOAP, WSDL. RIACA OpenMath library, Apache Tomcat, Apache AXIS, Sun JWSDP, OASIS ebxml. Mathematical Service Description Language MSDL. Crucial influence on MONET schema. Revised as a MONET schema extension. MSDL registration service. Mathematical catalogs. Current work: MSDL information model. Future work: semantic brokering. Wolfgang Schreiner 36

38 References MathBroker project MONET project /projects/basic/mathbroker Wolfgang Schreiner 37