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A Theory of Higher-Order Subtyping with Type Intervals (Extended Version)

Sandro Stucki, Paolo G. Giarrusso
<span title="2021-07-05">2021</span> <span class="release-stage" >pre-print</span>
The result is a flexible and general theory of higher-order subtyping. We prove type and kind safety of F^ω_.., as well as weak normalization of types and undecidability of subtyping.  ...  F^ω_.. extends F^ω_<: with interval kinds, which afford a unified treatment of important type- and kind-level abstraction mechanisms found in Scala, such as bounded quantification, bounded operator abstractions  ...  CONCLUSIONS We have described ·· , a formal theory of higher-order subtyping with type intervals. In ·· , type intervals are represented through interval kinds.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3473574">doi:10.1145/3473574</a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2107.01883v1">arXiv:2107.01883v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tkhg5gwjqffkfpbactizkaw63i">fatcat:tkhg5gwjqffkfpbactizkaw63i</a> </span>
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Page 2858 of Mathematical Reviews Vol. , Issue 94e [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Summary: “Intersection types and bounded quantification are com- plementary extensions of a first-order statically typed programming language with subtyping.  ...  with overloading and subtyping.  ... 
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Lazy functional algorithms for exact real functionals [chapter]

Alex K. Simpson
<span title="">1998</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The algorithms are a practical application of a method, due to Berger, for computing quanti ers over streams. Correctness proofs for the algorithms make essential use of domain theory.  ...  We concentrate on two useful functionals: de nite integration, and the functional returning the maximum value of a continuous function over a closed interval.  ...  Acknowledgements I have bene ted from discussions with Pietro Di Gianantonio, Gordon Plotkin and, especially, Mart n Escard o.  ... 
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Page 6019 of Mathematical Reviews Vol. , Issue 2000i [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This theory can be obtained from a many-sorted first-order version of higher-order logic by relativizing quantifiers and replacing typing predicates by membership of some sets.  ...  The author gives a formulation of simple type theory a la Church [A. Church, J. Symbolic logic 5 (1940), 56-68; MR 1, 321d], also called higher order logic, in which types are sets.  ... 
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Page 2236 of Mathematical Reviews Vol. , Issue 88e [page]

<span title="">1988</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper the PL theories of part I [same journal 8 (1986), no. 2, 135-139; see the preceding review] are extended with subtypes and equality types Eaa’ (with intended interpretation {b:a(b) = a'(b  ...  McCracken, “An investigation of a programming language with a polymorphic type structure”, Ph.D. Thesis, Syracuse Univ., Syracuse, N.Y., 1979; per bibl.] inside the graph model Pw [D. S.  ... 
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General Homomorphic Overloading [chapter]

Alex Shafarenko, Sven-Bodo Scholz
<span title="">2005</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
A general homomorphic overloading in a first-order type system is discussed. Type inference is applied within predefined classes each containing an arbitrary first-order subtyping hierarchy.  ...  We propose a computationally efficient type inference algorithm by converting the attendant constraint-satisfaction problem into the algebraic path problem for a constraint graph weighted with elements  ...  , with a higher output type.  ... 
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A Formal System: Rigorous Constructions of Computer Models [article]

Garry Pantelis
<span title="2017-04-13">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A simple formal system based on a language of functional programs is employed as a tool of analysis.  ...  Such models are highly compatible with the operational parameters of the real world computer on which they are executed and hence their validation can be associated with the allowable computations on the  ...  of a higher order program list.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1510.04469v3">arXiv:1510.04469v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7rdf4jobjfbsfgpzijwtfivsai">fatcat:7rdf4jobjfbsfgpzijwtfivsai</a> </span>
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Generics of a higher kind

Adriaan Moors, Frank Piessens, Martin Odersky
<span title="2008-10-27">2008</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xu5bk2lj5rbdxlx6222nw7tsxi" style="color: black;">SIGPLAN notices</a> </i> &nbsp;
Although the first-order variant of generics is very useful, it also imposes some restrictions: it is possible to abstract over a type, but the resulting type constructor cannot be abstracted over.  ...  With Java 5 and C # 2.0, first-order parametric polymorphism was introduced in mainstream object-oriented programming languages under the name of generics.  ...  An older version of this paper was presented at the MPOOL workshop [38] . The first author is supported by a grant from the Flemish IWT.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449955.1449798">doi:10.1145/1449955.1449798</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y5ekiy7tjnbqjbevtyyeyp44qq">fatcat:y5ekiy7tjnbqjbevtyyeyp44qq</a> </span>
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Generics of a higher kind

Adriaan Moors, Frank Piessens, Martin Odersky
<span title="">2008</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6y3m32grtnfktkp2oo6oqjbvta" style="color: black;">Proceedings of the 23rd ACM SIGPLAN conference on Object oriented programming systems languages and applications - OOPSLA &#39;08</a> </i> &nbsp;
Although the first-order variant of generics is very useful, it also imposes some restrictions: it is possible to abstract over a type, but the resulting type constructor cannot be abstracted over.  ...  With Java 5 and C # 2.0, first-order parametric polymorphism was introduced in mainstream object-oriented programming languages under the name of generics.  ...  An older version of this paper was presented at the MPOOL workshop [38] . The first author is supported by a grant from the Flemish IWT.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449764.1449798">doi:10.1145/1449764.1449798</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/oopsla/MoorsPO08.html">dblp:conf/oopsla/MoorsPO08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4mxwju4lf5f5fddvx2exk6cuh4">fatcat:4mxwju4lf5f5fddvx2exk6cuh4</a> </span>
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Page 8753 of Mathematical Reviews Vol. , Issue 99m [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
between Kruskal and Dershowitz theorems (518-529); Daria Walukiewicz, A total AC-compatible reduction ordering on higher-order terms (530-542); Thomas A.  ...  Giménez, Structural recursive defi- nitions in type theory (397-408); D.  ... 
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Page 4498 of Mathematical Reviews Vol. , Issue 97G [page]

<span title="">1997</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Abstract reduction is able to find strictness information in a language with higher-order functions and structured data types.  ...  Specifically, we take four type systems from the literature (involving simple types, subtypes and recursion) and conservatively extend them to reason about control- flow information.  ... 
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Object-oriented programming versus abstract data types [chapter]

William R. Cook
<span title="">1991</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
(m) and x = head(m) and equal(l , tail(m)) Figure 3: Behavior of equal(l, m) with cases only for l. © © © tail(s) head(s) null?(s)  ...  Object-oriented programming and abstract data types can also be viewed as complementary implementation techniques: objects are centered around the constructors of a data abstraction, while abstract data  ...  Acknowledgment I would like to thank the sponsors and participants of the school/workshop on the foundations of objectoriented programming for providing a forum for the initial presentation of these ideas  ... 
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Programs as the Language of Science [article]

Garry Pantelis
<span title="2020-11-05">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This book does not examine any specific application in detail but rather attempts to lay down a foundation for the validation of such theories by employing the inference scheme based on computability logic  ...  Such models, it is argued, not only offer alternative simulation tools, as opposed to those based on discrete approximations of conventional continuum theories, but in themselves can be regarded as a language  ...  of a higher-order program list.  ... 
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The pathology of lumbosacral lipomas: macroscopic and microscopic disparity have implications for embryogenesis and mode of clinical deterioration

Victoria Jones, Victoria Wykes, Nicki Cohen, Dominic Thompson, Tom S Jacques
<span title="2018-03-15">2018</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uxv6qrdvtngyfnxtwbqkjbbbgi" style="color: black;">Histopathology</a> </i> &nbsp;
Charity, Medical Research Council and Smiles with Grace.  ...  Acknowledgements The study was supported by the Institute of Child Health, University College London and the Great Ormond Street Hospital NHS Trust, with funding from the Great Ormond Street Children's  ...  The presence of a higher frequency of tissue types within our series may be due to the level of sectioning and analysis.  ... 
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Conceptual Knowledge Markup Language: An Introduction [article]

Robert E. Kent
<span title="2018-10-10">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Among other things, this allows diverse communities of discourse to compare their own information structures, as coded in logical theories, with that of other communities that share a common generic ontology  ...  CKML incorporates the CKP ideas of concept lattice and formal context, along with the IF ideas of classification (= formal context), infomorphism, theory, interpretation and local logic.  ...  In describing the OML/CKML version of reification, all reified binary relations are instances of the CKML:Relation type, a subtype of the CKML:Object type.  ... 
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