منابع مشابه
Totality of product completions
Categories whose Yoneda embedding has a left adjoint are known as total categories and are characterized by a strong cocompleteness property. We introduce the notion of multitotal category A by asking the Yoneda embedding A → [Aop,Set] to be right multiadjoint and prove that this property is equivalent to totality of the formal product completion ΠA of A. We also characterize multitotal categor...
متن کاملTotality of colimit closures
Adámek, Herrlich, and Reiterman showed that a cocomplete category A is cocomplete if there exists a small (full) subcategory B such that every A-object is a colimit of B-objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the...
متن کاملTotality in arena games
We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland & Melliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed λ-calculus...
متن کاملTotality in Applicative Theories
In this paper we study applicative theories of operations and numbers with (and without) the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system ((0 1-CA) <"0 of second order arithmetic. Essential use will be made of so-called x...
متن کاملOn Strictness and Totality
Abs t rac t . In this paper we present a revised and extended version of the strictness and totality type assignment system introduced by Solberg, Nielson and Nielson in the Static Analysis Symposium '9~. Our main result is that (w.r.t. the possibility of replacing safely a lazy application by a strict one) the strictness and totality information given by this system is equivalent to the inform...
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ژورنال
عنوان ژورنال: Proceedings of the Aristotelian Society
سال: 1908
ISSN: 0066-7374,1467-9264
DOI: 10.1093/aristotelian/8.1.95