Results 1  10
of
654,702
Proof Checking
"... The aim of computer proof checking is not to find proofs, but to verify them. This is different from automated deduction, which is the use of computers to find proofs that humans have not devised first. Currently, checking a proof by computer is done by taking a known mathematical ..."
Abstract
 Add to MetaCart
The aim of computer proof checking is not to find proofs, but to verify them. This is different from automated deduction, which is the use of computers to find proofs that humans have not devised first. Currently, checking a proof by computer is done by taking a known mathematical
Interactive and probabilistic proofchecking
 Annals of Pure and Applied Logic
, 2000
"... The notion of efficient proofchecking has always been central to complexity theory, and it gave rise to the definition of the class NP. In the last 15 years there has been a number of exciting, unexpected and deep developments in complexity theory that exploited the notion of randomized and interac ..."
Abstract
 Add to MetaCart
The notion of efficient proofchecking has always been central to complexity theory, and it gave rise to the definition of the class NP. In the last 15 years there has been a number of exciting, unexpected and deep developments in complexity theory that exploited the notion of randomized
PVS: Combining Specification, Proof Checking, and Model Checking
, 1996
"... rem Proving and Typechecking The PVS specification language is based on classical, simply typed higherorder logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks for simp ..."
Abstract

Cited by 230 (5 self)
 Add to MetaCart
rem Proving and Typechecking The PVS specification language is based on classical, simply typed higherorder logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks
Proof Checking Using Experience
"... Checking Mathematics proofs is a complex task which needs experience. Yet most AI approaches to proof checking tend to use general methods rather than knowledge rich approaches. The program MU, Mathematics Understander, reads mathematics texts expressed in the Formal Expression Language (FEL), and p ..."
Abstract
 Add to MetaCart
Checking Mathematics proofs is a complex task which needs experience. Yet most AI approaches to proof checking tend to use general methods rather than knowledge rich approaches. The program MU, Mathematics Understander, reads mathematics texts expressed in the Formal Expression Language (FEL
Fast and Flexible Proof Checking for SMT
 In B. Dutertre and O. Strichman, editors, Workshop on Satisfiability Modulo Theories (SMT
, 2009
"... Abstract. Fast and flexible proof checking can be implemented for SMT using the Edinburgh Logical Framework with Side Conditions (LFSC). LFSC provides a declarative format for describing proof systems as signatures. We describe several optimizations for LFSC proof checking, and report experiments o ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
Abstract. Fast and flexible proof checking can be implemented for SMT using the Edinburgh Logical Framework with Side Conditions (LFSC). LFSC provides a declarative format for describing proof systems as signatures. We describe several optimizations for LFSC proof checking, and report experiments
An Integration of Model Checking with Automated Proof Checking
, 1995
"... Although automated proof checking tools for generalpurpose logics have been successfully employed in the verification of digital systems, there are inherent limits to the efficient automation of expressive logics. If the expressiveness is constrained, there are useful logic fragments for which effi ..."
Abstract

Cited by 100 (8 self)
 Add to MetaCart
Although automated proof checking tools for generalpurpose logics have been successfully employed in the verification of digital systems, there are inherent limits to the efficient automation of expressive logics. If the expressiveness is constrained, there are useful logic fragments for which
Towards Lean Proof Checking
 Proceedings of DISCO'96, volume 1128 of Lecture Notes in Computer Science
, 1996
"... . Logical formal systems are inefficient at computations. In order to increase their efficiency, we aim to extend these systems with computational power. In this paper, we suggest a general, powerful syntax, called oracle types, to extend type theories with computational power; the resulting systems ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
. Logical formal systems are inefficient at computations. In order to increase their efficiency, we aim to extend these systems with computational power. In this paper, we suggest a general, powerful syntax, called oracle types, to extend type theories with computational power; the resulting systems, which combine the logical abilities of logical formal systems and the computational power of term rewriting systems, provide a suitable environment for theorem proving. As a practical application, we present an extension of the theorem prover Lego with oracle types and illustrate the use of this new system in performing algebraic computations. Our implementation of oracle types is very flexible and allows rewriting to be performed either inside Lego or by Reduce, an efficient symbolic computation system. In our view, the main novelty of our approach is to combine a sound theoretical foundation with an efficient implementation. Besides, our work provides the first attempt to combine symboli...
Practical Proof Checking for Program Certification
 Proceedings of the CADE20 Workshop on Empirically Successful Classical Automated Reasoning (ESCAR’05
, 2005
"... Program certification aims to provide explicit evidence that a program meets a specified level of safety. This evidence must be independently reproducible and verifiable. We have developed a system, based on theorem proving, that generates proofs that autogenerated aerospace code adheres to a numbe ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
number of safety policies. For certification purposes, these proofs need to be verified by a proof checker. Here, we describe and evaluate a semantic derivation verification approach to proof checking. The evaluation is based on 109 safety obligations that are attempted by EP and SPASS. Our system
Static and UserExtensible Proof Checking
"... Despite recent successes, largescale proof development within proof assistants remains an arcane art that is extremely timeconsuming. We argue that this can be attributed to two profound shortcomings in the architecture of modern proof assistants. The first is that proofs need to include a large am ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
amount of minute detail; this is due to the rigidity of the proof checking process, which cannot be extended with domainspecific knowledge. In order to avoid these details, we rely on developing and using tactics, specialized procedures that produce proofs. Unfortunately, tactics are both hard to write
Parallel proof checking in Isabelle/Isar
 ACM SIGSAM Workshop on Programming Languages for Mechanized Mathematics Systems (PLMMS 2009). ACM Digital Library, 2009. Parallel Poly/ML and Isabelle 10 2009/9/28
"... We address the “multicore problem ” for mathematical assistants with full proof checking, with special focus on Isabelle/Isar and its main SML platform Poly/ML. On the one hand, working with explicit definitions, statements, and proofs requires significant runtime resources, so the question of paral ..."
Abstract

Cited by 18 (10 self)
 Add to MetaCart
We address the “multicore problem ” for mathematical assistants with full proof checking, with special focus on Isabelle/Isar and its main SML platform Poly/ML. On the one hand, working with explicit definitions, statements, and proofs requires significant runtime resources, so the question
Results 1  10
of
654,702