Proof Generation in the Touchstone Theorem Prover

2000 ◽  
pp. 25-44 ◽  
Author(s):  
George C. Necula ◽  
Peter Lee
Keyword(s):  
Theorem Prover

Evaluation Opportunities in Mechanized Theories

10.29007/7kx8 ◽  
2018 ◽  
Author(s):  
Joe Hurd
Keyword(s):  
Mathematical Theory ◽  
Theorem Prover ◽  
Mechanized Mathematics ◽  
Reasoning Tasks

This invited talk will look at logic solvers through the application lens of constructing and processing a theory library of mechanized mathematics. In fact, constructing and processing theories are two distinct applications, and each will be considered in turn. Construction is carried out by formalizing a mathematical theory using an interactive theorem prover, and logic solvers can remove much of the drudgery by automating common reasoning tasks. At the theory library level, logic solvers can provide assistance with theory engineering tasks such as compressing theories, managing dependencies, and constructing new theories from reusable theory components.

CSim 2

2021 ◽  
Vol 43 (1) ◽  
pp. 1-46
Author(s):  
David Sanan ◽  
Yongwang Zhao ◽  
Shang-Wei Lin ◽  
Liu Yang
Keyword(s):  
Programming Languages ◽  
Concurrent Systems ◽  
Theorem Prover ◽  
Compositional Techniques ◽  
Machine Code ◽  
Top Down ◽  
Hol Theorem Prover ◽  
High Level ◽  
High Degree

To make feasible and scalable the verification of large and complex concurrent systems, it is necessary the use of compositional techniques even at the highest abstraction layers. When focusing on the lowest software abstraction layers, such as the implementation or the machine code, the high level of detail of those layers makes the direct verification of properties very difficult and expensive. It is therefore essential to use techniques allowing to simplify the verification on these layers. One technique to tackle this challenge is top-down verification where by means of simulation properties verified on top layers (representing abstract specifications of a system) are propagated down to the lowest layers (that are an implementation of the top layers). There is no need to say that simulation of concurrent systems implies a greater level of complexity, and having compositional techniques to check simulation between layers is also desirable when seeking for both feasibility and scalability of the refinement verification. In this article, we present CSim 2 a (compositional) rely-guarantee-based framework for the top-down verification of complex concurrent systems in the Isabelle/HOL theorem prover. CSim 2 uses CSimpl, a language with a high degree of expressiveness designed for the specification of concurrent programs. Thanks to its expressibility, CSimpl is able to model many of the features found in real world programming languages like exceptions, assertions, and procedures. CSim 2 provides a framework for the verification of rely-guarantee properties to compositionally reason on CSimpl specifications. Focusing on top-down verification, CSim 2 provides a simulation-based framework for the preservation of CSimpl rely-guarantee properties from specifications to implementations. By using the simulation framework, properties proven on the top layers (abstract specifications) are compositionally propagated down to the lowest layers (source or machine code) in each concurrent component of the system. Finally, we show the usability of CSim 2 by running a case study over two CSimpl specifications of an Arinc-653 communication service. In this case study, we prove a complex property on a specification, and we use CSim 2 to preserve the property on lower abstraction layers.

Structural ambiguity in Montague Grammar and categorial grammar

2015 ◽  
Vol 32 (1) ◽  
Author(s):  
Glyn Morrill
Keyword(s):  
Categorial Grammar ◽  
Theorem Prover ◽  
Montague Grammar ◽  
Structural Ambiguity

AbstractWe give a type logical categorial grammar for the syntax and semantics of Montague's seminal fragment, which includes ambiguities of quantification and intensionality and their interactions, and we present the analyses assigned by a parser/theorem prover CatLog to the examples in the first half of Chapter 7 of the classic text

scholarly journals The foundation of a generic theorem prover

1989 ◽  
Vol 5 (3) ◽  
pp. 363-397 ◽  
Author(s):  
Lawrence C. Paulson
Keyword(s):  
Theorem Prover

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.

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