We prove that Morel-Voevodsky's stable $\mathbb{A}^1$-homotopy theory affords the universal coefficient system, giving rise to Grothendieck's six operations.

1 The Basic UNITY Theory 7 1.0.1 The abstract type of programs . . . . . . . . . . . . . . . 8 1.0.2 Inspectors for type ”program” . . . . . . . . . . . . . . . 8 1.0.3 Equality for UNITY programs . . . . . . . . . . . . . . . 8 1.0.4 co . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.0.5 Union . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.0.6 Intersection . . ...

This document describes Version 2.2 of SRI’s Act formalism. The Act formalism is a domain-independent language for representing task networks whose actions manipulate both an external world and an internal database. It is intended to serve as an interchange language that will enable a broad range of action-related technologies to share information. The most recent version of the Act specificati...

The impact parameter formalism of the single-center close-coupling, first-, and second-order Born approximations have been applied to investigate direct excitations of Helium He+(2s) and Lithium Li++(2s) ions by colliding with protons or antiprotons. The total 3s, 3p, and 3d scaled excitation cross sections are calculated in the scaled impact energy region (2 to 1000 keV). The present work aims...

Formal reasoning is notoriously long and arduous; in order to use it to reason eeectively in the construction of programs it is, therefore, paramount that we design our notations to be both clear and economical. Taking examples from AI, from imperative programming, from the use of the Bird-Meertens formalism and from category theory we demonstrate how the right choice of what to denote and how ...