Sequential composition of schema mappings

A method for generating a schema mapping, said method comprising:

• providing a mapping M12 from a schema S1 to a schema S2, said mapping M12 relating the schema S2 to the schema S1, said schema S1 and schema S2 each comprising one or more elements, said mapping M12 being expressed in terms of at least one second-order nested tuple-generating dependency (SO nested tgd);
• providing a mapping M23 from the schema S2 to the schema S3, said mapping M23 relating the schema S3 to the schema S2, said schema S3 comprising one or more elements, said mapping M23 being expressed in terms of at least one SO nested tgd;
• and
• generating, by a processor of a computer system, a mapping M13 from the schema S1 to the schema S3, said mapping M13 relating the schema S3 to the schema S1 that does not expressly recite any element of the schema S2, said generating the mapping M13 comprising generating the mapping M13 as a composition of the mappings M12 and M23, wherein the mapping M13 defines the composition of the mappings M12 and M23 with respect to a transformation semantics such that M13 (I1)=M23 (M12 (I1)) for every instance b over S1, wherein said generating the mapping M13 as a composition of the marwincis M12 and M23 comprises:
• Skolemizinci each SO nested tcid of the marwinci M12;
• computing a rule RE for each element E in the schema S2 that is of set type, wherein the rule RE describes how data instances of the element E can be created based on the Skolemized SO target tcids that are relevant for the element E, and wherein R12 is a rule set denotin the set of all of said rules RE and
• replacing all references to the schema S2 in the mapping M23 with references to the schema S1 using the rule set R12, wherein said replacing all references to the schema S2 in the mapping M23 converts the mapping M23 to the mapping M13;
• after said replacing all references to the schema S2 in the mapping M23;
• eliminating in R all Skolem term equalities in which different Skolem functions are equated or in which a Skolem term is equated to a non Skolem term;
• and
• after said eliminating:
• reducing the number of variables to a minimal number of logically required variables in a FOR clause of each SO nested tgd in R.

A computer program product, comprising a computer readable storage medium having a computer readable program code stored therein, said computer readable program code configured to be executed by a processor of a computer system to implement a method for generating a schema mapping, said method comprising:

• providing a mapping M12 from a schema S1 to a schema S2, said mapping M12 relating the schema S2 to the schema S1, said schema S1 and schema S2 each comprising one or more elements, said mapping M12 being expressed in terms of at least one second-order nested tuple-generating dependency (SO nested tgd);
• providing a mapping M23 from the schema S2 to the schema S3, said mapping M23 relating the schema S3 to the schema S2, said schema S3 comprising one or more elements, said mapping M23 being expressed in terms of at least one SO nested tgd;
• and
• generating a mapping M13 from the schema S1 to the schema S3, said mapping M13 relating the schema S3 to the schema S1, said mapping M13 being expressed in terms of at least one SO nested tgd that does not expressly recite any element of the schema S2, said generating the mapping M13 comprising generating the mapping M13 as a composition of the mappings M12 and M23,wherein at least one schema of the schemas S1 and S2 comprises at least one complex type expression nested inside another complex type expression, wherein said generating the mapping M13 as a composition of the mappings M12 and M23 comprises:
• Skolemizing each SO nested tgd of the mapping M12;
• computing a rule RE for each element E in the schema S2 that is of set type, wherein the rule RE describes how data instances of the element E can be created based on the Skolemized SO target tgds that are relevant for the element E, and wherein R12 is a rule set denoting the set of all of said rules RE and
• replacing all references to the schema S2 in the mapping M23 with references to the schema S1 using the rule set R12, wherein said replacing all references to the schema S2 in the mapping M23 converts the mapping M23 to the mapping M13.

A computer program product, comprising a computer readable storage medium having a computer readable program code stored therein, said computer readable program code configured to be executed by a processor of a computer system to implement a method for generating a schema mapping, said method comprising:

• providing a mapping M12 from a schema S1 to a schema S2, said mapping M12 relating the schema S2 to the schema S1, said schema S1 and schema S2 each comprising one or more elements, said mapping M12 being expressed in terms of at least one second-order nested tuple-generating dependency (SO nested tgd);
• providing a mapping M23 from the schema S2 to the schema S3, said mapping M23 relating the schema S3 to the schema S2, said schema S3 comprising one or more elements, said mapping M23 being expressed in terms of at least one SO nested tgd;
• and
• generating a mapping M13 from the schema S1 to the schema S3, said mapping M13 relating the schema S3 to the schema S1 that does not expressly recite any element of the schema S2, said generating the mapping M13 comprising generating the mapping M13 as a composition of the mappings M12 and M23, wherein the mapping M13 defines the composition of the mappings M12 and M23 with respect to a transformation semantics such that M13 (I1)=M23 (M12 (Ii)) for every instance Ii over S1, wherein said generating the main M13 as a composition of the ma in s M12 and M23 comprises:
• Skolemizing each SO nested tgd of the mapping M12;
• computing a rule RE for each element E in the schema S2 that is of set type, wherein the rule RE describes how data instances of the element E can be created based on the Skolemized SO tarciet tcids that are relevant for the element E and wherein R12 is a rule set denoting the set of all of said rules RE and
• replacinci all references to the schema S2 in the mapping M23 with references to the schema S1 using the rule set R12, wherein said replacing all references to the schema S2 in the mapping M23 converts the mapping M23 to the mapping M13;
• after said replacing all references to the schema S2 in the mapping M23:
• eliminating in R all Skolem term equalities in which different Skolem functions are equated or in which a Skolem term is equated to a non Skolem term;
• and
• after said eliminating:
• reducing the number of variables to a minimal number of logically required variables in a FOR clause of each SO nested tgd in R.