A mechanizable induction principle for equational specifications

2005 ◽  
pp. 162-181 ◽  
Author(s):  
Hantao Zhang ◽  
Deepak Kapur ◽  
Mukkai S. Krishnamoorthy
Keyword(s):  
Induction Principle ◽  
Equational Specifications

Theory Design Research and the Application Prospect of the Future for the Ever Moving Car

2013 ◽  
Vol 456 ◽  
pp. 142-145
Author(s):  
Guo Qiang Cao ◽  
Yuan Ji Li ◽  
Jiang Ning Liu
Keyword(s):  
Wind Power ◽  
Power Loss ◽  
Electromagnetic Induction ◽  
Energy Recovery ◽  
Design Research ◽  
Automobile Driving ◽  
The Other ◽  
Induction Principle ◽  
Energy Maximum ◽  
Set Up

Using faraday electromagnetic induction principle will car each wheel as a generator. For car generates its own energy recovery; In the front of car set up a blade, It can recovery the wind power what automobile driving produced, For wind power generation, So that it can recover the energy maximum for the car itself. Because of the two kinds of energy all are car generates its own energy, so it can not recovery completely, in addition to there is power loss in the other part of the car, So it needs to the energy loss and power loss for supplement, I choose the solar energy used as supplementary energy that finally achieve the purpose of "ever moving".

scholarly journals On the foundations of final coalgebra semantics: non-well-founded sets, partial orders, metric spaces

1998 ◽  
Vol 8 (5) ◽  
pp. 481-540 ◽  
Author(s):  
DANIELE TURI ◽  
JAN RUTTEN
Keyword(s):  
Computer Science ◽  
Mathematical Theory ◽  
Metric Spaces ◽  
Operational Semantics ◽  
Denotational Semantics ◽  
Partial Orders ◽  
Present Survey ◽  
Induction Principle ◽  
Structural Operational Semantics ◽  
Modern Mathematics

This paper, a revised version of Rutten and Turi (1993), is part of a programme aiming at formulating a mathematical theory of structural operational semantics to complement the established theory of domains and denotational semantics to form a coherent whole (Turi 1996; Turi and Plotkin 1997). The programme is based on a suitable interplay between the induction principle, which pervades modern mathematics, and a dual, non-standard ‘coinduction principle’, which underlies many of the recursive phenomena occurring in computer science.The aim of the present survey is to show that the elementary categorical notion of a final coalgebra is a suitable foundation for such a coinduction principle. The properties of coalgebraic coinduction are studied both at an abstract categorical level and in some specific categories used in semantics, namely categories of non-well-founded sets, partial orders and metric spaces.

scholarly journals A duality between proof systems for cyclic term graphs

2007 ◽  
Vol 17 (3) ◽  
pp. 439-484 ◽  
Author(s):  
CLEMENS GRABMAYER
Keyword(s):  
Close Connection ◽  
Proof System ◽  
Consistency Checking ◽  
Duality Result ◽  
First Order ◽  
Proof Systems ◽  
Similar Proof ◽  
Equational Specifications ◽  
Cyclic Term

This paper presents a proof-theoretic observation about two kinds of proof systems for bisimilarity between cyclic term graphs.First we consider proof systems for demonstrating that μ term specifications of cyclic term graphs have the same tree unwinding. We establish a close connection between adaptations for μ terms over a general first-order signature of the coinductive axiomatisation of recursive type equivalence by Brandt and Henglein (Brandt and Henglein 1998) and of a proof system by Ariola and Klop (Ariola and Klop 1995) for consistency checking. We show that there exists a simple duality by mirroring between derivations in the former system and formalised consistency checks, which are called ‘consistency unfoldings', in the latter. This result sheds additional light on the axiomatisation of Brandt and Henglein: it provides an alternative soundness proof for the adaptation considered here.We then outline an analogous duality result that holds for a pair of similar proof systems for proving that equational specifications of cyclic term graphs are bisimilar.

Contact-less revolving stage using transverse flux induction principle

2009 ◽  
Vol 33 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Kwang Suk Jung ◽  
Sang Heon Lee
Keyword(s):  
Induction Principle ◽  
Transverse Flux
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