A generic proof checker

2002 ◽  
Author(s):  
◽  
Geoffrey Norman Watson
Keyword(s):  
Proof Checker ◽  
Generic Proof

The romulus proof checker

1990 ◽  
pp. 651-652
Author(s):  
Carl Eichenlaub ◽  
Bruce Esrig ◽  
James Hook ◽  
Carl Klapper ◽  
Garrel Pottinger
Keyword(s):  
Proof Checker

N.G. de Bruijn (1918–2012) and his Road to Automath, the Earliest Proof Checker

2012 ◽  
Vol 34 (4) ◽  
pp. 4-11 ◽  
Author(s):  
Francien Dechesne ◽  
Rob Nederpelt
Keyword(s):  
Proof Checker ◽  
De Bruijn

scholarly journals Enhancement of properties in Mizar

2020 ◽  
Vol 6 ◽  
pp. e320
Author(s):  
Artur Korniłowicz
Keyword(s):  
Proof Assistant ◽  
Current Implementation ◽  
Proof Checker ◽  
Mizar Mathematical Library ◽  
Specific Number ◽  
Symmetry Operations

A “property” in the Mizar proof-assistant is a construction that can be used to register chosen features of predicates (e.g., “reflexivity”, “symmetry”), operations (e.g., “involutiveness”, “commutativity”) and types (e.g., “sethoodness”) declared at the definition stage. The current implementation of Mizar allows using properties for notions with a specific number of visible arguments (e.g., reflexivity for a predicate with two visible arguments and involutiveness for an operation with just one visible argument). In this paper we investigate a more general approach to overcome these limitations. We propose an extension of the Mizar language and a corresponding enhancement of the Mizar proof-checker which allow declaring properties of notions of arbitrary arity with respect to explicitly indicated arguments. Moreover, we introduce a new property—the “fixedpoint-free” property of unary operations—meaning that the result of applying the operation to its argument always differs from the argument. Results of tests conducted on the Mizar Mathematical Library are presented.

scholarly journals Towards a Trustworthy Semantics-Based Language Framework via Proof Generation

2021 ◽  
pp. 477-499
Author(s):  
Xiaohong Chen ◽  
Zhengyao Lin ◽  
Minh-Thai Trinh ◽  
Grigore Roşu
Keyword(s):  
Programming Language ◽  
Innovative Approach ◽  
Experimental Result ◽  
Proof Checking ◽  
Complete Proof ◽  
Mathematical Proofs ◽  
Proof Checker ◽  
Ideal Language ◽  
Individual Task ◽  
Case Basis

AbstractWe pursue the vision of an ideal language framework, where programming language designers only need to define the formal syntax and semantics of their languages, and all language tools are automatically generated by the framework. Due to the complexity of such a language framework, it is a big challenge to ensure its trustworthiness and to establish the correctness of the autogenerated language tools. In this paper, we propose an innovative approach based on proof generation. The key idea is to generate proof objects as correctness certificates for each individual task that the language tools conduct, on a case-by-case basis, and use a trustworthy proof checker to check the proof objects. This way, we avoid formally verifying the entire framework, which is practically impossible, and thus can make the language framework both practical and trustworthy. As a first step, we formalize program execution as mathematical proofs and generate their complete proof objects. The experimental result shows that the performance of our proof object generation and proof checking is very promising.

scholarly journals Challenge to the proving of theorems of Euclid's elements of as ATP

2019 ◽  
Vol 3 (4) ◽  
pp. 9-13
Author(s):  
Keyword(s):  
Mathematical Logic ◽  
Mathematics Education ◽  
Theorem Proving ◽  
Automated Reasoning ◽  
Automated Theorem Proving ◽  
Euclidean Geometry ◽  
Proof Assistant ◽  
Weak Point ◽  
Euclid’S Elements ◽  
Generic Proof

Automated theorem proving (ATP) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. An Isabelle/HOL is a generic proof assistant. We perform the challenge for the proving theorems of Euclid's elements of geometry. We could prove some theorems of Euclid's elements of geometry. Technique of programing and mental conception interact. The mathematics education which prove theorems of the Euclidean geometry by using the Isabelle/HOL can correct the present weak point

scholarly journals A First Step Towards a Unified Proof Checker for QBF

2007 ◽  
pp. 201-214 ◽  
Author(s):  
Toni Jussila ◽  
Armin Biere ◽  
Carsten Sinz ◽  
Daniel Kröning ◽  
Christoph M. Wintersteiger
Keyword(s):  
Proof Checker
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