Mathematical Service Trading Based on Equational Matching

Mathematical software libraries provide many computational services. Mathematical operators properties can be used to combine several services in order to provide more complex ones or to adapt a given service to a slightly different use. The computational grid provides users with access to most of the available software libraries. Service trading, that is searching for services able to fulfil a user requirements is therefore difficult as many different services and service combinations from different libraries can fulfil the same requirements. Usual proposals rely on the use of the service interface and/or domain specific meta-data and ontologies. The service semantics defined in these framework are either easy to use but too poor or application dependent (interface and meta-data); or too complex and sophisticated (ontologies logic) for the common user. The purpose of our work is to provide a trading framework which is both easy to use for specialist of application domains and precise enough to allow service adaptation and combination during the trading process. Our proposal is based on algebraic specification (related to OpenMath) for domain and service description and equational matching for service trading, adaptation and combination. This paper presents our framework proposal and the associated trading algorithm which is both sound and complete: it can find all the appropriate services and combinations according to the given semantics.