منابع مشابه
Totality 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 کاملTotality 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 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: Annals of Pure and Applied Logic
سال: 2010
ISSN: 0168-0072
DOI: 10.1016/j.apal.2009.07.016