Towards a Substitution Tree Based Index for Higher-order Resolution Theorem Provers

in Urban, Josef; Fontaine, Pascal; Schulz, Stephan (Eds.) Practical Aspects of Automated Reasoning (2016, July)

Effective Normalization Techniques for HOL

in Olivetti, Nicola; Tiwari, Ashish (Eds.) Automated Reasoning --- 8th International Joint Conference, IJCAR 2016, Coimbra, Portugal, June 27 -- July 2, 2016, Proceedings (2016, June)

Leo-III

Software (2016)

Embedding of Quantified Higher-Order Nominal Modal Logic into Classical Higher-Order Logic

in Benzmüller, Christpoh; Otten, Jens (Eds.) ARQNL 2014. Automated Reasoning in Quantified Non-Classical Logics (2015, December)

LeoPARD - A Generic Platform for the Implementation of Higher-Order Reasoners

in Kerber, Manfred; Carette, Jacques; Kaliszyk, Cezary (Eds.) et al Intelligent Computer Mathematics - International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings (2015, June)

Efficient Data Structures for Automated Theorem Proving in Expressive Higher-Order Logics

Bachelor/master dissertation (2014)

Church's Simple Theory of Types (STT), also referred to as classical higher-order logik, is an elegant and expressive formal system built on top of the simply typed λ-calculus. Its mechanisms of explicit ... [more ▼]

Church's Simple Theory of Types (STT), also referred to as classical higher-order logik, is an elegant and expressive formal system built on top of the simply typed λ-calculus. Its mechanisms of explicit binding and quantification over arbitrary sets and functions allow the representation of complex mathematical concepts and formulae in a concise and unambiguous manner. Higher-order automated theorem proving (ATP) has recently made major progress and several sophisticated ATP systems for higher-order logic have been developed, including Satallax, Osabelle/HOL and LEO-II. Still, higher-order theorem proving is not as mature as its first-order counterpart, and robust implementation techniques for efficient data structures are scarce. In this thesis, a higher-order term representation based upon the polymorphically typed λ-calculus is presented. This term representation employs spine notation, explicit substitutions and perfect term sharing for efficient term traversal, fast β-normalization and reuse of already constructed terms, respectively. An evaluation of the term representation is performed on the basis of a heterogeneous benchmark set. It shows that while the presented term data structure performs quite well in general, the normalization results indicate that a context dependent choice of reduction strategies is beneficial. A term indexing data structure for fast term retrieval based on various low-level criteria is presented and discussed. It supports symbol-based term retrieval, indexing of terms via structural properties, and subterm indexing. [less ▲]

Generation and State-Space Reduction of Program Graphs for Non-deterministic Programs

Bachelor/master dissertation (2013)