scholarly journals Metis-based Paramodulation Tactic for HOL Light

10.29007/z9mz ◽  
2018 ◽  
Author(s):  
Michael Färber ◽  
Cezary Kaliszyk
Keyword(s):  
Theorem Prover ◽  
Reconstruction Method ◽  
Theorem Provers ◽  
Interactive Theorem Provers ◽  
Automated Theorem Prover ◽  
Hol Light

Metis is an automated theorem prover based on ordered paramodulation.It is widely employed in the interactive theorem provers Isabelle/HOL and HOL4to automate proofs as well as reconstruct proofs found by automated provers.For both these purposes, the tableaux-based MESON tactic is frequently usedin HOL Light. However, paramodulation-based provers such as Metisperform better on many problems involving equality.We created a Metis-based tactic in HOL Light which translates HOL problemsto Metis, runs an OCaml version of Metis, and reconstructs proofsin Metis' paramodulation calculus as HOL proofs.We evaluate the performance of Metis as proof reconstruction methodin HOL Light.

scholarly journals Leo-III Version 1.1 (System description)

10.29007/grmx ◽  
2018 ◽  
Author(s):  
Christoph Benzmüller ◽  
Alexander Steen ◽  
Max Wisniewski
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Higher Order Logic ◽  
System Description ◽  
Agent Based ◽  
First Order ◽  
Theorem Provers ◽  
Automated Theorem Prover ◽  
Ordering Constraints

Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives. It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers.Unlike LEO-II, asynchronous cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use.

scholarly journals Implementing Polymorphism in Zenon

10.29007/87vl ◽  
2018 ◽  
Author(s):  
Guillaume Bury ◽  
Raphaël Cauderlier ◽  
Pierre Halmagrand
Keyword(s):  
Search Algorithm ◽  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
First Order ◽  
Proof Search ◽  
Theorem Provers ◽  
Automated Theorem Prover

Extending first-order logic with ML-style polymorphism allows to definegeneric axioms dealing with several sorts. Until recently, mostautomated theorem provers relied on preprocess encodings intomono/many-sorted logic to reason within such theories. In this paper, wediscuss the implementation of polymorphism into thefirst-order tableau-based automated theorem prover Zenon. Thisimplementation leads to slightly modify some basic parts of the code,from the representation of expressions to the proof-search algorithm.

Tableaux Versus Resolution a Comparison

1993 ◽  
Vol 18 (2-4) ◽  
pp. 109-127
Author(s):  
W.M.J. Ophelders ◽  
H.C.M. De Swart
Keyword(s):  
Theorem Prover ◽  
Full Description ◽  
Test Results ◽  
Theorem Provers ◽  
Automatic Theorem Provers ◽  
Automated Theorem Prover ◽  
Main Ideas ◽  
Automatic Theorem

In [13] we have presented the ideas underlying an automated theorem prover based on tableaux extended with unification under restrictions. In [6] a full description of an implementation of this theorem prover in PROLOG is given. In this paper we first shortly repeat the main ideas, referring to [13] for more details. Next we present the test results of our theorem prover mainly with respect to Pelletier’s 75 problems for testing automatic theorem provers ([7]). We also give a comparison of our results with the results obtained by the resolution-based theorem provers PCPROVE and OTTER and by the tableau-based theorem provers of M. Fitting and S. Reeves. Short discussions of these theorem provers accompany the test results. For more elaborate discussions the reader is referred to [6].

scholarly journals Going Polymorphic - TH1 Reasoning for Leo-III

10.29007/jgkw ◽  
2018 ◽  
Author(s):  
Alexander Steen ◽  
Max Wisniewski ◽  
Christoph Benzmüller
Keyword(s):  
Type Systems ◽  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Proof Assistants ◽  
Interactive Proof ◽  
Higher Order Logic ◽  
Theorem Provers ◽  
Reasoning System ◽  
Automated Theorem Prover

While interactive proof assistants for higher-order logic (HOL) commonly admit reasoning within rich type systems, current theorem provers for HOL are mainly based on simply typed lambda-calculi and therefore do not allow such flexibility. In this paper, we present modifications to the higher-order automated theorem prover Leo-III for turning it into a reasoning system for rank-1 polymorphic HOL.To that end, a polymorphic version of HOL and a suitable paramodulation-based calculus are sketched. The implementation is evaluated using a set of polymorphic TPTP THF problems.

scholarly journals CSE_E 1.0: An Integrated Automated Theorem Prover for First-Order Logic

Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1142
Author(s):  
Feng Cao ◽  
Yang Xu ◽  
Jun Liu ◽  
Shuwei Chen ◽  
Xinran Ning
Keyword(s):  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Inference Mechanism ◽  
First Order ◽  
Proof Search ◽  
Interdisciplinary Field ◽  
Heuristic Strategies ◽  
Automated Theorem Prover ◽  
Hard Problems

First-order logic is an important part of mathematical logic, and automated theorem proving is an interdisciplinary field of mathematics and computer science. The paper presents an automated theorem prover for first-order logic, called C S E _ E 1.0, which is a combination of two provers contradiction separation extension (CSE) and E, where CSE is based on the recently-introduced multi-clause standard contradiction separation (S-CS) calculus for first-order logic and E is the well-known equational theorem prover for first-order logic based on superposition and rewriting. The motivation of the combined prover C S E _ E 1.0 is to (1) evaluate the capability, applicability and generality of C S E _ E , and (2) take advantage of novel multi-clause S-CS dynamic deduction of CSE and mature equality handling of E to solve more and harder problems. In contrast to other improvements of E, C S E _ E 1.0 optimizes E mainly from the inference mechanism aspect. The focus of the present work is given to the description of C S E _ E including its S-CS rule, heuristic strategies, and the S-CS dynamic deduction algorithm for implementation. In terms of combination, in order not to lose the capability of E and use C S E _ E to solve some hard problems which are unsolved by E, C S E _ E 1.0 schedules the running of the two provers in time. It runs plain E first, and if E does not find a proof, it runs plain CSE, then if it does not find a proof, some clauses inferred in the CSE run as lemmas are added to the original clause set and the combined clause set handed back to E for further proof search. C S E _ E 1.0 is evaluated through benchmarks, e.g., CASC-26 (2017) and CASC-J9 (2018) competition problems (FOFdivision). Experimental results show that C S E _ E 1.0 indeed enhances the performance of E to a certain extent.

CALL FOR PAPERS Journal of Functional Programming Special Issue on Theorem Provers and Functional Programming

1997 ◽  
Vol 7 (1) ◽  
pp. 125-126
Author(s):  
Tom Melham
Keyword(s):  
Interface Design ◽  
Functional Programming ◽  
Type Systems ◽  
Theory And Practice ◽  
Theorem Prover ◽  
Functional Languages ◽  
Special Issue ◽  
Theorem Provers ◽  
Problems And Solutions ◽  
Submission Deadline

A special issue of the Journal of Functional Programming will be devoted to the use of functional programming in theorem proving. The submission deadline is 31 August 1997.The histories of theorem provers and functional languages have been deeply intertwined since the advent of Lisp. A notable example is the ML family of languages, which are named for the meta language devised for the LCF theorem prover, and which provide both the implementation platform and interaction facilities for numerous later systems (such as Coq, HOL, Isabelle, NuPrl). Other examples include Lisp (as used for ACL2, PVS, Nqthm) and Haskell (as used for Veritas).This special issue is devoted to the theory and practice of using functional languages to implement theorem provers and using theorem provers to reason about functional languages. Topics of interest include, but are not limited to:– architecture of theorem prover implementations– interface design in the functional context– limits of the LCF methodology– impact of host language features– type systems– lazy vs strict languages– imperative (impure) features– performance problems and solutions– problems of scale– special implementation techniques– term representations (e.g. de Bruijn vs name carrying vs BDDs)– limitations of current functional languages– mechanised theories of functional programming

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