Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry (Work-in-Progress) Pedro Quaresma CISUC, Mathematics Department University of Coimbra CICM 2012, 8-13 July 2012, Jacobs University, Bremen, Germany 1 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry DGSs & GATPs & Repositories of geometric constructions. ◮ loose coupling of tools; ◮ wide availability of their corpora; ◮ (+) describe constructions created with a DGS, allows sharing interactive geometry constructions across boundaries. ◮ (-) does not provide support for the conjectures. 2 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry DGSs & GATPs & Repositories of geometric constructions. ◮ loose coupling of tools; ◮ wide availability of their corpora; ◮ (+) describe constructions created with a DGS, allows sharing interactive geometry constructions across boundaries. ◮ (-) does not provide support for the conjectures. 3 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry DGSs & GATPs & Repositories of geometric constructions. ◮ loose coupling of tools; ◮ wide availability of their corpora; The Intergeo (i2g) file format. ◮ (+) describe constructions created with a DGS, allows sharing interactive geometry constructions across boundaries. ◮ (-) does not provide support for the conjectures. 4 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry DGSs & GATPs & Repositories of geometric constructions. ◮ loose coupling of tools; ◮ wide availability of their corpora; The Intergeo (i2g) file format. ◮ (+) describe constructions created with a DGS, allows sharing interactive geometry constructions across boundaries. ◮ (-) does not provide support for the conjectures. 5 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry The i2gatp format. ◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry Laboratory ◮ Supported by other tools DGSs, GATPs, . . . . 6 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry The i2gatp format. ◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry Laboratory ◮ Supported by other tools DGSs, GATPs, . . . . 7 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry The i2gatp format. ◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry Laboratory ◮ Supported by other tools DGSs, GATPs, . . . . 8 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry The i2gatp format. ◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry Laboratory ◮ Supported by other tools DGSs, GATPs, . . . . 9 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry The i2gatp format. ◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry Laboratory ◮ Supported by other tools DGSs, GATPs, . . . . 10 / 20
Introduction i2gatp XML-Format Conclusions and Further Work An XML-Format for Conjectures in Geometry The i2gatp format. ◮ An extension of the i2g format. ◮ support for geometric conjectures and proofs. ◮ Converters from/to the format. ◮ Integration with GeoThms & TGTP & Web Geometry Laboratory ◮ Supported by other tools DGSs, GATPs, . . . . 11 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture Overall Architecture I2GATP Format information construction (I2G) name description statement [bibrefs] [keywords] elements constraints display bibentry keyword conjecture proofInfo hypothesis ndg conclusion method status limits measures platform 12 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture Overall Architecture I2GATP Format information construction (I2G) name description statement [bibrefs] [keywords] elements constraints display bibentry keyword conjecture proofInfo hypothesis ndg conclusion method status limits measures platform intergeo.xsd; 13 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture Overall Architecture I2GATP Format information construction (I2G) name description statement [bibrefs] [keywords] elements constraints display bibentry keyword conjecture proofInfo hypothesis ndg conclusion method status limits measures platform intergeo.xsd; proofInfo.xsd; 14 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Overall Architecture Overall Architecture I2GATP Format information construction (I2G) name description statement [bibrefs] [keywords] elements constraints display bibentry keyword conjecture proofInfo hypothesis ndg conclusion method status limits measures platform intergeo.xsd; proofInfo.xsd; information.xsd; conjecture.xsd. 15 / 20
Introduction i2gatp XML-Format Conclusions and Further Work The Container The Container A zip file, superset of the i2g container. information/ mandatory information/information.xml optional construction/ mandatory construction/intergeo.xml mandatory construction/preview.pdf optional construction/preview.svg optional construction/(. . . ) conjecture/ mandatory conjecture/conjecture.xml optional proofs/ mandatory proofs/proof < GATP >< Version >< Method > / optional proofs/proof < GATP >< Version >< Method > /proofInfo.xml optional proofs/proof < GATP >< Version >< Method > /proofOutput.pdf optional proofs/proof < GATP >< Version >< Method > /(. . . ) metadata/ optional metadata/i2g-lom.xml optional resources/ optional resources/ < image files > optional resources/(. . . ) private/ optional private/ < domain-name > optional private/ < domain-name > / < files > optional 16 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Implementation Implementation Graphical Human−Language Rendering Rendering others (SVG) (HTML) GATP code DGS code (GCLC AM) (GCLC) 4 5 6 1 7 Container GATP code 8 DGS code 2 I2GATP (Coq AM) (GeoGebra) XML files 9 3 TGTP WGL GeoThms others others 1 − From/to GCLC to/from I2G(ATP) 4 − SVG rendering 7 − From/to I2GATP to/from GCLC AM 8 − From/to I2GATP to/from Coq AM 2 − From/to GeoGebra to/from I2G(ATP) 5 − HTML rendering 3 − From/to DGS to/from I2G(ATP) 6 − other: proofs; bibrefs., etc. 9 − From/to I2GATP to/from GATP 17 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Implementation Implementation Graphical Human−Language Rendering Rendering others (SVG) (HTML) GATP code DGS code (GCLC AM) (GCLC) 4 5 6 1 7 Container GATP code 8 DGS code 2 I2GATP (Coq AM) (GeoGebra) XML files 9 3 TGTP WGL GeoThms others others 1 − From/to GCLC to/from I2G(ATP) 4 − SVG rendering 7 − From/to I2GATP to/from GCLC AM 8 − From/to I2GATP to/from Coq AM 2 − From/to GeoGebra to/from I2G(ATP) 5 − HTML rendering 3 − From/to DGS to/from I2G(ATP) 6 − other: proofs; bibrefs., etc. 9 − From/to I2GATP to/from GATP 18 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Conclusions and Further Work This is a work-in-progress. Questions and future work to be addressed: ◮ The xml/xsd format must be complemented with an extensive set of converters allowing the exchange of information between as many geometric tools as possible. ◮ The databases queries, as in TGTP, raise the question of selecting appropriate keywords. A fine grain index and/or an appropriate geometry ontology should be addressed. ◮ The i2gatp format does not address proofs. Should we try to create such a format? The GATPs produce proofs in quite different formats, maybe the construction of such unifying format it is not possible and/or desirable in this area. 19 / 20
Introduction i2gatp XML-Format Conclusions and Further Work Thank You 20 / 20
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