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...

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...

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...

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...

The totality principle applies in cases of multiple offending to reduce the total effective sentence that is imposed on offenders. This is normally achieved by either making some or all of the individual sentences concurrent, or by reducing the length of the individual sentences. Although totality is a well-established sentencing doctrine, its scope and its impact on the overall sentence are un...

This commentary reflects on the contribution of this editorial and its “Three Challenges That Global Health Networks Face” to the totality of the framework developed over the past decade by Shiffman and his collaborators. It reviews the earlier works to demonstrate that the whole is greater than the sum of the parts in providing a package of tools for analysis of network effectiveness.   Additi...

We investigate domains with totality where density in general does not hold. We define three categories of domains X with totality X̄ satisfying certain structural properties. We then define the ordered set of evaluation structures. These will induce domains with totality. We show that the set of evaluation structures in a natural way is closed under dependent sums and products and under direct ...