scholarly journals Polytypic Functions Over Nested Datatypes

1999 ◽  
Vol Vol. 3 no. 4 ◽  
Author(s):  
Ralf Hinze
Keyword(s):  
Recent Work ◽  
Theory And Practice ◽  
Basic Knowledge ◽  
Central Idea ◽  
Underlying Theory ◽  
Initial Algebra ◽  
International Audience ◽  
Initial Algebra Semantics

International audience The theory and practice of polytypic programming is intimately connected with the initial algebra semantics of datatypes. This is both a blessing and a curse. It is a blessing because the underlying theory is beautiful and well developed. It is a curse because the initial algebra semantics is restricted to so-called regular datatypes. Recent work by R. Bird and L. Meertens [3] on the semantics of non-regular or nested datatypes suggests that an extension to general datatypes is not entirely straightforward. Here we propose an alternative that extends polytypism to arbitrary datatypes, including nested datatypes and mutually recursive datatypes. The central idea is to use rational trees over a suitable set of functor symbols as type arguments for polytypic functions. Besides covering a wider range of types the approach is also simpler and technically less involving than previous ones. We present several examples of polytypic functions, among others polytypic reduction and polytypic equality. The presentation assumes some background in functional and in polytypic programming. A basic knowledge of monads is required for some of the examples.

Initial Algebra Semantics and Continuous Algebras

1977 ◽  
Vol 24 (1) ◽  
pp. 68-95 ◽  
Author(s):  
J. A. Goguen ◽  
J. W. Thatcher ◽  
E. G. Wagner ◽  
J. B. Wright
Keyword(s):  
Initial Algebra ◽  
Initial Algebra Semantics

scholarly journals Crisp-determinization of weighted tree automata over strong bimonoids

2021 ◽  
Vol vol. 23 no. 1 (Automata, Logic and Semantics) ◽  
Author(s):  
Zoltán Fülöp ◽  
Dávid Kószó ◽  
Heiko Vogler
Keyword(s):  
Finite Order ◽  
Positive Answer ◽  
Order Property ◽  
Sufficient Condition ◽  
Tree Automata ◽  
Weighted Tree ◽  
Bottom Up ◽  
Initial Algebra ◽  
Initial Algebra Semantics ◽  
Weighted Tree Automata

We consider weighted tree automata (wta) over strong bimonoids and their initial algebra semantics and their run semantics. There are wta for which these semantics are different; however, for bottom-up deterministic wta and for wta over semirings, the difference vanishes. A wta is crisp-deterministic if it is bottom-up deterministic and each transition is weighted by one of the unit elements of the strong bimonoid. We prove that the class of weighted tree languages recognized by crisp-deterministic wta is the same as the class of recognizable step mappings. Moreover, we investigate the following two crisp-determinization problems: for a given wta ${\cal A}$, (a) does there exist a crisp-deterministic wta which computes the initial algebra semantics of ${\cal A}$ and (b) does there exist a crisp-deterministic wta which computes the run semantics of ${\cal A}$? We show that the finiteness of the Nerode algebra ${\cal N}({\cal A})$ of ${\cal A}$ implies a positive answer for (a), and that the finite order property of ${\cal A}$ implies a positive answer for (b). We show a sufficient condition which guarantees the finiteness of ${\cal N}({\cal A})$ and a sufficient condition which guarantees the finite order property of ${\cal A}$. Also, we provide an algorithm for the construction of the crisp-deterministic wta according to (a) if ${\cal N}({\cal A})$ is finite, and similarly for (b) if ${\cal A}$ has finite order property. We prove that it is undecidable whether an arbitrary wta ${\cal A}$ is crisp-determinizable. We also prove that both, the finiteness of ${\cal N}({\cal A})$ and the finite order property of ${\cal A}$ are undecidable.

scholarly journals TRANSCRITICAL FLOW PAST AN OBSTACLE

2010 ◽  
Vol 52 (1) ◽  
pp. 2-26 ◽  
Author(s):  
R. GRIMSHAW
Keyword(s):  
Numerical Simulations ◽  
Recent Work ◽  
Vries Equation ◽  
Steady Solution ◽  
Underlying Theory ◽  
Flow Past ◽  
Transcritical Flow ◽  
De Vries ◽  
Large Width ◽  
Asymptotic Analyses

AbstractIt is well known that transcritical flow past an obstacle may generate undular bores propagating away from the obstacle. This flow has been successfully modelled in the framework of the forced Korteweg–de Vries equation, where numerical simulations and asymptotic analyses have shown that the unsteady undular bores are connected by a locally steady solution over the obstacle. In this paper we present an overview of the underlying theory, together with some recent work on the case where the obstacle has a large width.

Rhetoric and Rights: Citizenship and the Politics of Persuasion

2021 ◽  
pp. 003232172110637
Author(s):  
Peter Rees
Keyword(s):  
Human Rights ◽  
Recent Work ◽  
Rhetorical Analysis ◽  
Theory And Practice ◽  
Political Situation ◽  
Political Communities

This article examines the relevance of rhetorical analysis for the theory and practice of rights-claiming. Recent work in the field of human rights proposes that what is important about rights is not what they ‘are’ but what they ‘do’. Utilising performative theory, they suggest that rights-claiming is best understood as a perlocutionary practice of persuasion. The question is, ‘How might rights claims be most persuasive?’ This article applies insights from the field of rhetoric to investigate how practices of rights-claiming by migrants in France contest French citizenship. It argues that rights claims are ethico-political negotiations of a political situation and that such practices are persuasive when they mobilise transcendent principles embedded within particular political communities. Rhetorical analysis explains how rights can be both inventive and efficacious. In so doing, this article extends the human rights literature by providing a refined rights-claiming analytic.

scholarly journals Production of the Growth Factors GM-CSF, G-CSF, and VEGF by Human Peripheral Blood Cells Induced with Metal Complexes of Human Serumγ-Globulin Formed with Copper or Zinc Ions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Sergey B. Cheknev ◽  
Maria A. Apresova ◽  
Nadezhda A. Moryakova ◽  
Irina E. Efremova ◽  
Anna S. Mezdrokhina ◽  
...  
Keyword(s):  
Metal Complexes ◽  
Peripheral Blood ◽  
Blood Cells ◽  
Human Peripheral Blood ◽  
Theory And Practice ◽  
Basic Knowledge ◽  
Peripheral Blood Cells ◽  
Zinc Ions ◽  
Gm Csf ◽  
Copper And Zinc

As it was established in our previous studies, the proteins of human serumγ-globulin fraction could interact with copper or zinc ions distributed in the periglobular space, form metal complexes, and become able to perform effector functions differing due to the conformational shifts from those mediated by them in native conformation of their Fc regions. In the present work we have evaluated ability of theγ-globulin metal complexes formed with copper or zinc ions in the conditions like to the physiological ones to induce production or to regulate induction in the culture of freshly isolated human peripheral blood cells (PBC) of granulocyte (G) and granulocyte-macrophage (GM) colony-stimulating factors (CSF) as well as of vascular endothelial growth factor (VEGF). Theγ-globulin metal complexes formed with both copper and zinc ions were found to similarly reduce production of GM-CSF, G-CSF, and VEGF induced in normal human PBC cultures by the controlγ-globulins or by copper and zinc ions used alone. In context of theory and practice of inflammation the properties of theγ-globulin metal complexes might impact the basic knowledge in search of novel approaches to anti-inflammatory drugs development.

scholarly journals The Transrational Numbers as an Abstract Data Type

2020 ◽  
Author(s):  
Jan Aldert Bergstra ◽  
John V. Tucker
Keyword(s):  
Rational Numbers ◽  
Data Type ◽  
Abstract Data Type ◽  
Constant Symbol ◽  
Total Function ◽  
Initial Algebra ◽  
Abstract Data ◽  
Initial Algebra Semantics

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to its opposite, and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.

scholarly journals Generalized monotone triangles

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Lukas Riegler
Keyword(s):  
Recent Work ◽  
Computational Experiments ◽  
Combinatorial Interpretation ◽  
Alternating Sign Matrices ◽  
Round Numbers ◽  
International Audience

International audience In a recent work, the combinatorial interpretation of the polynomial $\alpha (n; k_1,k_2,\ldots,k_n)$ counting the number of Monotone Triangles with bottom row $k_1 < k_2 < ⋯< k_n$ was extended to weakly decreasing sequences $k_1 ≥k_2 ≥⋯≥k_n$. In this case the evaluation of the polynomial is equal to a signed enumeration of objects called Decreasing Monotone Triangles. In this paper we define Generalized Monotone Triangles – a joint generalization of both ordinary Monotone Triangles and Decreasing Monotone Triangles. As main result of the paper we prove that the evaluation of $\alpha (n; k_1,k_2,\ldots,k_n)$ at arbitrary $(k_1,k_2,\ldots,k_n) ∈ \mathbb{Z}^n$ is a signed enumeration of Generalized Monotone Triangles with bottom row $(k_1,k_2,\ldots,k_n)$. Computational experiments indicate that certain evaluations of the polynomial at integral sequences yield well-known round numbers related to Alternating Sign Matrices. The main result provides a combinatorial interpretation of the conjectured identities and could turn out useful in giving bijective proofs.

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