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A content based mathematical search engine: whelp
 In: Postproceedings of the Types 2004 International Conference, Vol. 3839 of LNCS
, 2004
"... Abstract. The prototype of a content based search engine for mathematical knowledge supporting a small set of queries requiring matching and/or typing operations is described. The prototype — called Whelp — exploits a metadata approach for indexing the information that looks far more flexible than t ..."
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Abstract. The prototype of a content based search engine for mathematical knowledge supporting a small set of queries requiring matching and/or typing operations is described. The prototype — called Whelp — exploits a metadata approach for indexing the information that looks far more flexible than traditional indexing techniques for structured expressions like substitution, discrimination, or context trees. The prototype has been instantiated to the standard library of the Coq proof assistant extended with many user contributions. 1
Polynomial equality testing for terms with shared substructures. Frank report 21, Institut für Informatik
 FB Informatik und Mathematik. J. W. GoetheUniversität Frankfurt am Main
, 2005
"... Abstract. Sharing of substructures like subterms and subcontexts in terms is a common method for spaceefficient representation of terms, which allows for example to represent exponentially large terms in polynomial space, or to represent terms with iterated substructures in a compact form. We prese ..."
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Cited by 11 (4 self)
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Abstract. Sharing of substructures like subterms and subcontexts in terms is a common method for spaceefficient representation of terms, which allows for example to represent exponentially large terms in polynomial space, or to represent terms with iterated substructures in a compact form. We present singleton tree grammars as a general formalism for the treatment of sharing in terms. Singleton tree grammars (STG) are recursionfree contextfree tree grammars without alternatives for nonterminals and at most unary secondorder nonterminals. STGs generalize Plandowski’s singleton context free grammars to terms (trees). We show that the test, whether two different nonterminals in an STG generate the same term can be done in polynomial time, which implies that the equality test of terms with shared terms and contexts, where composition of contexts is permitted, can be done in polynomial time in the size of the representation. This will allow polynomialtime algorithms for terms exploiting sharing. We hope that this technique will lead to improved upper complexity bounds for variants of second order unification algorithms, in particular for variants of context unification and bounded second order unification.
Efficient Retrieval of Mathematical Statements
 In Proceeding of the Third International Conference on Mathematical Knowledge Management, MKM 2004. Bialowieza, Poland. LNCS 3119
, 2004
"... Abstract. The paper describes an innovative technique for efficient retrieval of mathematical statements from large repositories, developing and substantially improving the metadatabased approach introduced in [13]. 1 ..."
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Cited by 9 (2 self)
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Abstract. The paper describes an innovative technique for efficient retrieval of mathematical statements from large repositories, developing and substantially improving the metadatabased approach introduced in [13]. 1
Smart matching
"... One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given scientific domain (mostly expressed in the form of equalities or ..."
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One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given scientific domain (mostly expressed in the form of equalities or isomorphisms), are usually implicit in the mathematical discourse, and it would be highly desirable to obtain a similar behaviour in interactive provers. The paper describes the superpositionbased implementation of this feature inside the Matita interactive theorem prover, focusing in particular on the so called smart application tactic, supporting smart matching between a goal and a given result.
Searching Mathematics on the Web: State of the Art and Future Developments
 In: Proceedings of New Developments in Electronic Publishing of Mathematics, p. 918, Edited by FIZ
, 2004
"... Abstract. A huge amount of mathematical knowledge is nowadays available on the World Wide Web. Many different solutions and technologies for searching that knowledge have been developed as well. We present the state of the art of searching mathematics on the web, giving some insight on future develo ..."
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Abstract. A huge amount of mathematical knowledge is nowadays available on the World Wide Web. Many different solutions and technologies for searching that knowledge have been developed as well. We present the state of the art of searching mathematics on the web, giving some insight on future developments in this area. 1.
Higherorder term indexing using substitution trees
"... We present a higherorder term indexing strategy based on substitution trees for simply typed lambdaterms. The strategy is based in linear higherorder patterns where computationally expensive parts are delayed. While insertion of terms into the index is based on computing the most specific linear ..."
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We present a higherorder term indexing strategy based on substitution trees for simply typed lambdaterms. The strategy is based in linear higherorder patterns where computationally expensive parts are delayed. While insertion of terms into the index is based on computing the most specific linear generalization of two linear higherorder patterns, retrieval is based on matching two linear higherorder patterns. We give a theoretical framework for higherorder term indexing, describe insertion and retrieval algorithms and prove their correctness. This indexing structure is implemented as part of the Twelf system to speedup the execution of the tabled higherlogic programming interpreter.