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.

Response to Intervention and Current Implementation

2008 ◽  
Vol 9 (3) ◽  
pp. 116-121
Author(s):  
Janet L. Proly
Keyword(s):  
Response To Intervention ◽  
Federal Regulations ◽  
Speech Language Pathologist ◽  
Current Implementation ◽  
Rti Implementation ◽  
Level Of Understanding

Abstract Response to Intervention (RTI) implementation is becoming more widespread due to the references of RTI components in the Federal Regulations. But everyone is not at the same level of understanding about RTI and its implementation. This article will answer several questions. What is RTI? Why are we hearing more and more about RTI? How are states implementing RTI components? How can the speech-language pathologist help in RTI implementation in the presence or absence of a specific RTI infrastructure? How is Florida Proceeding with RTI implementation? Are there any new resources available for principals and other educators who might want to learn more about RTI?

Verification of Content-Centric Networking Using Proof Assistant

2016 ◽  
Vol E99.B (11) ◽  
pp. 2297-2304
Author(s):  
Sosuke MORIGUCHI ◽  
Takashi MORISHIMA ◽  
Mizuki GOTO ◽  
Kazuko TAKAHASHI
Keyword(s):  
Proof Assistant ◽  
Content Centric Networking

Limits of the current implementation of incremental housing

2021 ◽  
pp. 1-10
Author(s):  
Goran Ivo Marinovic
Keyword(s):  
Middle Class ◽  
Housing Policy ◽  
Low Income ◽  
Bank Loans ◽  
Housing Project ◽  
Middle Income ◽  
Specific Location ◽  
Current Implementation ◽  
Incremental Housing

In the case of conventional public housing, urban planners and policymakers design the layout of a housing project in a specific location and then estimate how many households can afford a home. This housing policy has been pursued as a legitimate solution for housing low- and middle-income households where the houses are individually financed by bank loans or mortgages raised by the occupants. John Turner criticised conventional housing solutions by affirming that ‘developing governments take the perspective of the elite and act as if the process of low-income houses were the same as in high-income countries and the same as for the small upper-middle class of their own countries’. Bruce Ferguson and Jesus Navarrete extend this argument with their critique of distributing finished houses to low-income populations and then requiring long-term payments, which are harmful to the beneficiaries. They note that ‘governments think of housing as complete units built by developers that households must purchase with a long-term loan rather than as a progressive process’.

scholarly journals A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1913
Author(s):  
Yousef Navidtehrani ◽  
Covadonga Betegón ◽  
Emilio Martínez-Pañeda
Keyword(s):  
Phase Field ◽  
Crack Nucleation ◽  
Crack Density ◽  
Contact Problems ◽  
Element Mesh ◽  
Robust Implementation ◽  
Current Implementation ◽  
User Material Subroutine ◽  
Complex Crack ◽  
Monolithic Solution

We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus’ in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed is made freely available.

The Impact Assessment of the Managed Motorway on M25 Junction 5 to 7

2011 ◽  
Vol 66-68 ◽  
pp. 692-696
Author(s):  
Sui Chao ◽  
Ling Tao Wu ◽  
Jian Yun Chen
Keyword(s):  
Impact Assessment ◽  
State Of The Art ◽  
Technical State ◽  
Current Implementation ◽  
The Impact

This study introduces the transport situation and polices of the highway agency for the M25. Then the current implementation of the Managed Motorway on M25 between junction 5 and junction 7 is reviewed, and some examples are given in this paper. Then a technical state-of-the-art of application is also reviewed. After that, the requirements for integration with complementary systems and polices are presented. Finally, this paper discusses the arguments for and against taking this application forward.

scholarly journals CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

2011 ◽  
Vol 21 (4) ◽  
pp. 827-859 ◽  
Author(s):  
FRÉDÉRIC BLANQUI ◽  
ADAM KOPROWSKI
Keyword(s):  
Term Rewriting ◽  
Automated Verification ◽  
Proof Assistant ◽  
Proof Assistants ◽  
Active Subject ◽  
Turing Complete

Termination is an important property of programs, and is notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting. Over the years, many methods and tools have been developed to address the problem of deciding termination for specific problems (since it is undecidable in general). Ensuring the reliability of those tools is therefore an important issue.In this paper we present a library formalising important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools.The sources are freely available athttp://color.inria.fr/.

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