Directed Containers as Categories

Directed containers make explicit the additional structure of those containers whose set functor interpretation carries a comonad structure. The data and laws of a directed container resemble those of a monoid, while the data and laws of a directed container morphism those of a monoid morphism in the reverse direction. With some reorganization, a directed container is the same as a small category, but a directed container morphism is opcleavage-like. We draw some conclusions for comonads from this observation, considering in particular basic constructions and concepts like the opposite category and a groupoid.Comment: In Proceedings MSFP 2016, arXiv:1604.0038

When is a container a comonad?

Abbott, Altenkirch, Ghani and others have taught us that many parameterized datatypes (set functors) can be usefully analyzed via container representations in terms of a set of shapes and a set of positions in each shape. This paper builds on the observation that datatypes often carry additional structure that containers alone do not account for. We introduce directed containers to capture the common situation where every position in a data-structure determines another data-structure, informally, the sub-data-structure rooted by that position. Some natural examples are non-empty lists and node-labelled trees, and data-structures with a designated position (zippers). While containers denote set functors via a fully-faithful functor, directed containers interpret fully-faithfully into comonads. But more is true: every comonad whose underlying functor is a container is represented by a directed container. In fact, directed containers are the same as containers that are comonads. We also describe some constructions of directed containers. We have formalized our development in the dependently typed programming language Agda

Adolescents Strength Profile of Hope Based on Demographic Factors

This research aims to reveal ‘hope' of Indonesian adolescents especially in Bantul regency of Special Region of Yogyakarta. Data were gathered from 106 adolescents consisting of 38 males and 68 females (16 -18 years old) from high schools.The instruments of this study was a hope scale in the form of semantic deferential scale ranged from 1 to 8 (1= very inappropriate, 8 = very appropriate). The data analysis of this study was descriptive statistics. The result of the study showed that the hope of female students is higher than male students. In agency thinking, male students are higher than female students, otherwise, in pathways thinking, female students are higher than male students. Based on the parents' occupation, those who work in private sector have high hope. Conversely, the students whose parents are farmers have a low hope. The lowest scale of pathways thinking was obtained by the students whose parents are farmers as well as in the agency showed that the students whose parents are labours obtained the lowest scal

Handling Fibred Algebraic Effects

International audienceWe study algebraic computational effects and their handlers in the dependently typed setting. We describecomputational effects using a generalisation of Plotkin and Pretnar’s effect theories, whose dependentlytyped operations allow us to capture precise notions of computation, e.g., state with location-dependent storetypes and dependently typed update monads. Our treatment of handlers is based on an observation that theirconventional term-level definition leads to unsound program equivalences being derivable in languages thatinclude a notion of homomorphism. We solve this problem by giving handlers a novel type-based treatmentvia a new computation type, the user-defined algebra type, which pairs a value type (the carrier) with a set ofvalue terms (the operations), capturing Plotkin and Pretnar’s insight that effect handlers denote algebras. Wethen show that the conventional presentation of handlers can be routinely derived, and demonstrate that thistype-based treatment of handlers provides a useful mechanism for reasoning about effectful computations.We also equip the resulting language with a sound denotational semantics based on families fibrations

The Pathology of Heart Failure

The topic I have chosen to research is heart failure. I have chosen this topic because I have treated many patients in the ICU with this condition, and find it an interesting pathology. Heart failure affects a significant portion of the patient population, and the rates are increasing. 5.1 million Americans ≥20 years of age have heart failure, projections show that by 2030, the prevalence of HF will increase 25% from 2013 estimates. At 40 years of age, the lifetime risk of developing HF for both men and women is 1 in 5. At 80 years of age, remaining lifetime risk for development of new HF remains at 20% for men and women, even in the face of a much shorter life expectancy. While patients are now living longer after initial diagnosis, about half of the patients diagnosed die within five years. Projections from the American Heart Association show in 15 years, the total cost of HF will increase almost 120% to $70 billion from the current estimated total cost of$32 billion

Climate and Agriculture of Jordan

The primary objective of this study is to identify, analyze, and explain existing and potential patterns of agricultural development in Jordan as they relate to the country\u27s environmental resource base. Once established, an understanding of the intricate relationships that exist between environment and agriculture can enhance agricultural development planning and increase Jordan\u27s agricultural potential. Analysis of the variable patterns of the man (culture) and land (environment) relationship long has been a primary focus of geographic, study. This study is limited to those relationships which exist between agriculture in Jordan and those environmental elements which directly influence this vital aspect of the country\u27s economy, namely climate, soil, water, and vegetation. In attempting to develop a comprehensive overview of Jordan\u27s agriculture-environment relationship patterns, this study will focus/address four major factors. They are: 1) a survey of existing agricultural patterns in relation to environmental conditions, 2) an examination of both the environmental and technical problems which hinder agricultural development, 3) identifying potential means of expanding agricultural lands, and 4) to suggest means by which agricultural production can be increased . Agriculture has been the primary occupation of Jordanian people for centuries. Agricultural production is dependent upon· numerous factors, including climate, soil type, plant and animal genetics, insects, disease, and such cultural considerations as technology, capital, perceptions of the environment, traditional crops and farming practices, available land, and economic needs. Although Jordan can never be self-sufficient in all of its agricultural needs, production can be increased by adopting modern farming methods such as machinery and the use of fertilizers and chemicals. The non-irrigated agricultural areas are more affected by the variation of rain totals than are the irrigated areas. An increase in agricultural production can be achieved by expanding the arable area and with the use of new technology. The Jordan Valley is the main agricultural area in Jordan because of its climate, soil, topography and the availability of water. By using modern agricultural methods in irrigated as well as in non-irrigated areas, Jordan is pinning its hopes of increasing agricultural productivity 300 percent by the 1980s

Decomposing Comonad Morphisms

The analysis of set comonads whose underlying functor is a container functor in terms of directed containers makes it a simple observation that any morphism between two such comonads factors through a third one by two comonad morphisms, whereof the first is identity on shapes and the second is identity on positions in every shape. This observation turns out to generalize into a much more involved result about comonad morphisms to comonads whose underlying functor preserves Cartesian natural transformations to itself on any category with finite limits. The bijection between comonad coalgebras and comonad morphisms from costate comonads thus also yields a decomposition of comonad coalgebras

Coalgebraic Update Lenses

AbstractLenses are mathematical structures used in the context of bidirectional transformations.In this paper, we introduce update lenses as a refinement of ordinary (asymmetric) lenses in which we distinguish between views and updates. In addition to the set of views, there is a monoid of updates and an action of the monoid on the set of views. Decoupling updates from views allows for other ways of changing the source than just merging a view into the source. We also consider a yet finer dependently typed version of update lenses.We give a number of characterizations of update lenses in terms of bialgebras and coalgebras, including analogs to O'Connor's coalgebraic and Johnson, Rosebrugh and Wood's algebraic characterizations of ordinary lenses. We consider conversion of views and updates, a tensor product of update lenses and composition of update lenses