  Ehrhard, Pagani and Tasson proposed a model of probabilistic functional
programming in a category of normed positive cones and stable measurable cone
maps, which can be seen as a coordinate-free generalization of probabilistic
coherence spaces. However, unlike the case of probabilistic coherence spaces,
it remained unclear if the model could be refined to a model of classical
linear logic.
  In this work we consider a somewhat similar category which gives indeed a
coordinate-free model of full propositional linear logic with nondegenerate
interpretation of additives and sound interpretation of exponentials. Objects
are dual pairs of normed cones satisfying certain specific completeness
properties, such as existence of norm-bounded monotone weak limits, and
morphisms are bounded (adjointable) positive maps. Norms allow us a distinct
interpretation of dual additive connectives as product and coproduct.
Exponential connectives are modelled using real analytic functions and
distributions that have representations as power series with positive
coefficients.
  Unlike the familiar case of probabilistic coherence spaces, there is no
reference or need for a preferred basis; in this sense the model is invariant.
Probabilistic coherence spaces form a full subcategory, whose objects, seen as
posets, are lattices. Thus we get a model fitting in the tradition of
interpreting linear logic in a linear algebraic setting, which arguably is free
from the drawbacks of its predecessors.
  Relations with constructions of Ehrhard, Pagani and Tasson's work are left
for future research.
