scholarly journals Reverse AD at Higher Types: Pure, Principled and Denotationally Correct

2021 ◽  
Author(s):  
Matthijs Vákár
Keyword(s):  
Higher Types

On the Pituitary of the Perch (Peroa Fluviatilis)

1942 ◽  
Vol s2-83 (331) ◽  
pp. 299-316
Author(s):  
T. KERR
Keyword(s):  
Connective Tissue ◽  
Blood Vessels ◽  
Perca Fluviatilis ◽  
Cell Types ◽  
Anterior Lobe ◽  
Intermediate Lobe ◽  
General Description ◽  
Perch Perca Fluviatilis ◽  
Higher Types ◽  
Different Cell Types

1. A general description is given of the pituitary of the perch (Perca fluviatilis L.), and histological details of its various parts. The subdivisions of the glandular component are confluent with each other but distinguished by their different cell types. The nervous lobe makes contact with all three of the subdivisions, but is separated from them by a layer of connective tissue, incomplete in particular areas. 2. The anterior glandular region (anterior lobe) has an anterior chromophil and a posterior chromophobe zone. The middle glandular region (transitional lobe) possesses brightly staining acidophils and basophils as well as chromophobes. The acidophils form a dorsal sheet, deeply indented by processes of the nervous lobe, the basophils lie ventrally and posteriorly, and chromophobes are common towards the extremities of the indentations. The posterior glandular region (intermediate lobe) is elaborately penetrated by nervous lobe processes; the cells are small and consist of amphiphils, dull basophils, and occasional dull acidophils. The possible homologies of these regions to the lobes of higher types are discussed. The nervous lobe is of loose glial tissue with many nuclei and blood vessels and some reticular and collagenous fibres. 3. Strongly acidophil spheres of various sizes and in various numbers occur in the middle glandular region. They originate in ‘sphere cells’ resembling eosinophil leucocytes and after enlarging become free in the tissues of the region. Later they appear to pass into the posterior processes of the nervous lobe to be the larger bodies of the Herring material. Finally these larger elements appear to break down to form a fine granulation, whose further fate could not be followed.

scholarly journals Croonian lecture : The origin of mammals

1913 ◽  
Vol 87 (592) ◽  
pp. 87-88
Keyword(s):  
Single Case ◽  
Lower Jurassic ◽  
Upper Permian ◽  
Occipital Condyle ◽  
Steady Increase ◽  
Lower Permian ◽  
Secondary Palate ◽  
Middle And Upper Permian ◽  
Higher Types ◽  
Evolution Of Mammals

An endeavour is made to trace the evolution of mammals from Cotylosaurian ancestors through the carnivorous Therapsida. In Upper Carboniferous times the line probably passed through some primitive generalised Pelycosaurs; in Lower Permian through primitive, probably Therocephalian, Therapsids. In Middle and Upper Permian the line passed through the Gorgonopsia. In Triassic times the mammalian ancestors were small generalised Cynodonts. In Lower Jurassic the mammals are so Cynodont-like, and the Cynodonts so mammal-like, that in no single case are we absolutely certain which is which. In the Therocephalia, the Gorgonopsia, and the Cynodontia, the skull is very mammal-like. The zygomatic arch is, as in mammals, formed by the jugal and the squamosal. The teeth are divided into incisors, canines and molars. In the later Gorgonopsians there is an imperfect secondary palate; in Cynodonts a complete secondary palate as in mammals. In Permian Therapsids there is a single occipital condyle; in the Triassic Cynodonts there may he a single condyle slightly divided or two exoccipital condyles. There is, on passing from earlier to later types, a steady increase in the size of the dentary and decrease in the size of the other elements of the jaw. The quadrate also becomes much reduced in the higher types. In Gorgonopsians and probably all earlier types the arch of the atlas is a pair of bones; in Cynodonts, as in mammals, there is a single arch.

Computing with Functionals—Computability Theory or Computer Science?

2006 ◽  
Vol 12 (1) ◽  
pp. 43-59 ◽  
Author(s):  
Dag Normann
Keyword(s):  
Computer Science ◽  
Computability Theory ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Active Subject ◽  
Higher Types ◽  
History Of

AbstractWe review some of the history of the computability theory of functionals of higher types, and we will demonstrate how contributions from logic and theoretical computer science have shaped this still active subject.

Colimit completions and the effective topos

1990 ◽  
Vol 55 (2) ◽  
pp. 678-699 ◽  
Author(s):  
Edmund Robinson ◽  
Giuseppe Rosolini
Keyword(s):  
Order Type ◽  
Higher Order ◽  
Type Structure ◽  
The Family ◽  
Higher Types ◽  
Polymorphic Type ◽  
Original Approach ◽  
Effective Operators

The family of readability toposes, of which the effective topos is the best known, was discovered by Martin Hyland in the late 1970's. Since then these toposes have been used for several purposes. The effective topos itself was originally intended as a category in which various recursion-theoretic or effective constructions would live as natural parts of the higher-order type structure. For example the hereditary effective operators become the higher types over N (Hyland [1982]), and effective domains become the countably-based domains in the topos (McCarty [1984], Rosolini [1986]). However, following the discovery by Moggi and Hyland that it contained nontrivial small complete categories, the effective topos has also been used to provide natural models of polymorphic type theories, up to and including the theory of constructions (Hyland [1987], Hyland, Robinson and Rosolini [1987], Scedrov [1987], Bainbridge et al. [1987]).Over the years there have also been several different constructions of the topos. The original approach, as in Hyland [1982], was to construct the topos by first giving a notion of Pω-valued set. A Pω-valued set is a set X together with a function =x: X × X → Pω. The elements of X are to be thought of as codes, or as expressions denoting elements of some “real underlying” set in the topos. Given a pair (x,x′) of elements of X, the set =x (x,x′) (generally written ) is the set of codes of proofs that the element denoted by x is equal to the element denoted by x′.

The countably based functionals

1983 ◽  
Vol 48 (2) ◽  
pp. 458-474 ◽  
Author(s):  
John P. Hartley
Keyword(s):  
Finite Type ◽  
Recursion Theory ◽  
Type Structure ◽  
Topological Properties ◽  
Natural Numbers ◽  
Finite Amount ◽  
Amount Of Information ◽  
Natural Concept ◽  
Higher Types

In [5], Kleene extended previous notions of computations to objects of higher finite type in the maximal type-structure of functionals given by:Tp(0) = N = the natural numbers,Tp(n + 1) = NTp(n) = the set of total maps from Tp(n) to N.He gave nine schemata, S1–S9, for describing algorithms for computations from a finite list of functionals, and indices to denote these algorithms. It is generally agreed that S1-S9 give a natural concept of computations in higher types.The type-structure of countable functions, Ct(n) for n ϵ N, was first developed by Kleene [6] and Kreisel [7]. It arises from the notions of ‘constructivity’, and has been extensively studied as a domain for higher type recursion theory. Each countable functional is globally described by a countable amount of information coded in its associate, and it is determined locally by a finite amount of information about its argument. The countable functionals are well summarised in Normann [9], and treated in detail in Normann [8].The purpose of this paper is to discuss a generalisation of the countable functionals, which we shall call the countably based functions, Cb(n) for n ϵ N. It is suggested by the notions of ‘predicativity’, in which we view N as a completed totality, and build higher types on it in a constructive manner. So we shall allow quantification over N and include application of 2E in our schemata. Each functional is determined locally by a countable amount of information about its argument, and so is globally described by a continuum of information coded in its associate, which will now be a type-2 object. This generalisation, obtained via associates, was proposed by Wainer, and seems to reflect topological properties of the countable functionals.

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