Head Normal Form Bisimulation for Pairs and the \lambda\mu-Calculus

2006 ◽  
Author(s):  
S.B. Lassen
Keyword(s):  
Normal Form ◽  
Head Normal Form

scholarly journals The evaluation strategy for head normal form with and without on-demand flags

2000 ◽  
Vol 36 ◽  
pp. 212-228 ◽  
Author(s):  
Masaki Nakamura ◽  
Kazuhiro Ogata
Keyword(s):  
Normal Form ◽  
Evaluation Strategy ◽  
On Demand ◽  
Head Normal Form

An environment machine for the λμ-calculus

1998 ◽  
Vol 8 (6) ◽  
pp. 637-669 ◽  
Author(s):  
PHILIPPE de GROOTE
Keyword(s):  
Normal Form ◽  
Natural Deduction ◽  
Soundness And Completeness ◽  
Head Normal Form

We introduce a natural deduction-like formalisation of Parigot's λμ-calculus. From this, we derive an environment machine that allows any well-typed λμ-term to be reduced to its weak head normal form. The soundness and completeness of the machine is proved.

scholarly journals Simply typed fixpoint calculus and collapsible pushdown automata

2015 ◽  
Vol 26 (7) ◽  
pp. 1304-1350 ◽  
Author(s):  
SYLVAIN SALVATI ◽  
IGOR WALUKIEWICZ
Keyword(s):  
Normal Form ◽  
Intermediate Step ◽  
Program Semantics ◽  
The Relationship ◽  
Head Normal Form ◽  
Pushdown Automata

Simply typed λ-calculus with fixpoint combinators, λY-calculus, offers an interesting method for approximating program semantics. The Böhm tree of a λY-term represents the meaning of the program up to the meaning of built-in constants. It is much easier to reason about properties of such trees than properties of interpreted programs. Moreover, some interesting properties of programs are already expressible on the level of these trees.Collapsible pushdown automata (CPDA) give another way of generating the same class of trees as λY-terms. We clarify the relationship between the two models. In particular, we present two relatively simple translations from λY-terms to CPDA using Krivine machines as an intermediate step. The latter are general machines for describing computation of the weak head normal form in the λ-calculus. They provide the notions of closure and environment that facilitate reasoning about computation.

Closing the GAP—A 5Å Scanning Microscope

1969 ◽  
Vol 27 ◽  
pp. 6-7
Author(s):  
A. V. Crewe
Keyword(s):  
Normal Form ◽  
The Other ◽  
Resolving Power ◽  
Scanning Microscope ◽  
Conventional Microscope ◽  
Other Hand ◽  
Closing The Gap ◽  
Thermal Sources ◽  
Better Than ◽  
Transmission Microscope

We have become accustomed to differentiating between the scanning microscope and the conventional transmission microscope according to the resolving power which the two instruments offer. The conventional microscope is capable of a point resolution of a few angstroms and line resolutions of periodic objects of about 1Å. On the other hand, the scanning microscope, in its normal form, is not ordinarily capable of a point resolution better than 100Å. Upon examining reasons for the 100Å limitation, it becomes clear that this is based more on tradition than reason, and in particular, it is a condition imposed upon the microscope by adherence to thermal sources of electrons.

A 3D Field Expression in Multilayered Structures using Jordan Normal Form

2012 ◽  
Vol 132 (8) ◽  
pp. 698-699 ◽  
Author(s):  
Hideaki Wakabayashi ◽  
Jiro Yamakita
Keyword(s):  
Normal Form ◽  
Jordan Normal Form ◽  
Multilayered Structures

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

Analysis of a 2DOF Nonlinear Mechanical System Using the Normal Form Method

2019 ◽  
Author(s):  
David Julian Gonzalez Maldonado ◽  
Peter Hagedorn ◽  
Thiago Ritto ◽  
Rubens Sampaio ◽  
Artem Karev
Keyword(s):  
Normal Form ◽  
Mechanical System ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Normal Form Method

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

The Logic of Normal-Form Games

2015 ◽  
Author(s):  
Gabriel Frahm
Keyword(s):  
Normal Form ◽  
Normal Form Games
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