Term indexing theorem prover
theorem provers. Term indexing is also used in logic and functional program-ming languages implementation, but indexing in theorem provers has several distinctive features: 1. Indexes in theorem provers frequently store 105{106 complex terms, unlike a typically small number of shallow terms in functional and logic programs. 2. The problem of term indexing can be formulated abstractly as follows (see ). Given a set L of indexed terms, a binary relation R over terms (called the retrieval condition) and a term t (called the query term), identify the subset M of L that consists of the terms l such that R(l; t) holds. Terms in M will be called the candidate terms. Typical retrieval conditions used in first-order theorem proving are matching, generalization, unifiability, and syntactic equality. The theorem prover presented here explicitly aims at enforcing complete proofs. Also, it is intended to provide a framework for prototyping automated proof calculi while offering standard decision proce-dures like unification (e.g. [17, 18] and standard methods for optimisation like term indexing[19]). In a Theorem Prover Critical Pair Indexing Technique Binary Resolution Unit Clause These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. With directed automated theorem proving, algorithms like A* and greedy best-first search are integrated in a deductive system. As theorem provers draw inferences on top of axioms of an underlying logic, the state space is the set of proof trees. The basic theorem proving paradigms we plan to cover are tableaux and the inverse method, both of which are applicable to classical and non-classical logics. Time permitting we may also cover some aspects of equational and inductive reasoning.
ence on Theorem Proving in Higher Order Logics, 27{30 August. 1996, Turku the proper de Bruijn terms, that is, those with no dangling indexes. Sometimes.
More recently, Theiss and Benzmüller explore higher-order term indexing in their implementation of Leo-II, a higher-order resolution theorem prover [Theiss and Benzmüller 2006]. Their approach mated theorem proving in classical higher order logic. Key features of our indexing method are a shared representation of terms, the use of partial syntax trees to speedup logical computations and indexing of subterm occurrences. theorem provers. Term indexing is also used in logic and functional program-ming languages implementation, but indexing in theorem provers has several distinctive features: 1. Indexes in theorem provers frequently store 105{106 complex terms, unlike a typically small number of shallow terms in functional and logic programs. 2. Key features of our indexing method are a shared representation of terms, the use of partial syntax trees to speedup logical computations and indexing of subterm occurrences. For the implementation of explicit substitutions, additional support is offered by indexing of bound variable occurrences. 2.4 Refutational Theorem Proving. Theorem provers are procedures that can be used to check whether a given formula F (the “goal”) is a logical consequence of a set of formulas N (the “theory”). Refutational theorem provers deal with the equivalent problem of showing that the set N∪{¬F} is inconsistent.
Theorem Prover Critical Pair Indexing Technique Binary Resolution Unit Clause These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Additional Key Words and Phrases: Indexing, type theory, logical frameworks. 1. INTRODUCTION. First-order logic programming and theorem proving systems 2 Jul 2016 to higher-order term indexing: Theiß and Benzmüller designed a term index [22] for the LEO-II higher-order resolution theorem prover [3]. 15-815 Automated Theorem Proving. Lecture 28: Discrimination Trees. In path indexing, a term is stored via the set of paths from the root to the 3 Classi cations of Term Indexing Techniques. Relations on Terms and Substitutions. The main purpose of indexing techniques. in theorem provers is to achieve Theorem provers are procedures that can be used to check whether a given a large number of subsumption-checks per second without using term indexing is
resolution proof calculus like many leading automated theorem provers. Starting Indexes. Index terms control two important aspects of guided proof re-.
Contribute to HOL-Theorem-Prover/hol-guidebook development by creating an account on GitHub. The syntax of higher-order logic includes types and terms. These are It is the same as `List.nth` in ML, but indexes from `1` rather than `0`. Term indexing. In computer science, a term index is a data structure to facilitate fast lookup of terms and clauses in a logic program, deductive database, or automated theorem prover. More recently, Theiss and Benzmüller explore higher-order term indexing in their implementation of Leo-II, a higher-order resolution theorem prover [Theiss and Benzmüller 2006]. Their approach mated theorem proving in classical higher order logic. Key features of our indexing method are a shared representation of terms, the use of partial syntax trees to speedup logical computations and indexing of subterm occurrences.
Classical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces—often in the range of several billion clauses.
Term indexing. In computer science, a term index is a data structure to facilitate fast lookup of terms and clauses in a logic program, deductive database, or automated theorem prover. More recently, Theiss and Benzmüller explore higher-order term indexing in their implementation of Leo-II, a higher-order resolution theorem prover [Theiss and Benzmüller 2006]. Their approach mated theorem proving in classical higher order logic. Key features of our indexing method are a shared representation of terms, the use of partial syntax trees to speedup logical computations and indexing of subterm occurrences. theorem provers. Term indexing is also used in logic and functional program-ming languages implementation, but indexing in theorem provers has several distinctive features: 1. Indexes in theorem provers frequently store 105{106 complex terms, unlike a typically small number of shallow terms in functional and logic programs. 2. Key features of our indexing method are a shared representation of terms, the use of partial syntax trees to speedup logical computations and indexing of subterm occurrences. For the implementation of explicit substitutions, additional support is offered by indexing of bound variable occurrences. 2.4 Refutational Theorem Proving. Theorem provers are procedures that can be used to check whether a given formula F (the “goal”) is a logical consequence of a set of formulas N (the “theory”). Refutational theorem provers deal with the equivalent problem of showing that the set N∪{¬F} is inconsistent. The problem of term indexing can be formulated abstractly as follows (see ). Given a set L of indexed terms, a binary relation R over terms (called the retrieval condition) and a term t (called the query term), identify the subset M of L that consists of the terms l such that R(l; t) holds. Terms in M will be called the candidate terms. Typical retrieval conditions used in first-order theorem proving are matching, generalization, unifiability, and syntactic equality.
With directed automated theorem proving, algorithms like A* and greedy best-first search are integrated in a deductive system. As theorem provers draw inferences on top of axioms of an underlying logic, the state space is the set of proof trees. The basic theorem proving paradigms we plan to cover are tableaux and the inverse method, both of which are applicable to classical and non-classical logics. Time permitting we may also cover some aspects of equational and inductive reasoning. a first-order prover. Furthermore, the project investigates whether techniques that have proved very successful in automated first-order theorem proving, such as shared data structures and term indexing, can be lifted to the higher-order setting. Leo-II is implemented in OCAML; it is the successor of LEO [9,7], Classical automated theorem proving of today is based on ingenious search techniques to find a proof for a given theorem in very large search spaces—often in the range of several billion clauses. E (theorem prover) E is a high performance theorem prover for full first-order logic with equality. It is based on the equational superposition calculus and uses a purely equational paradigm. It has been integrated into other theorem provers and it has been among the best-placed systems in several theorem proving competitions.