  We investigate the phenomenon that "every monad is a linear state monad". We
do this by studying a fully-complete state-passing translation from an impure
call-by-value language to a new linear type theory: the enriched call-by-value
calculus. The results are not specific to store, but can be applied to any
computational effect expressible using algebraic operations, even to effects
that are not usually thought of as stateful. There is a bijective
correspondence between generic effects in the source language and state access
operations in the enriched call-by-value calculus. From the perspective of
categorical models, the enriched call-by-value calculus suggests a refinement
of the traditional Kleisli models of effectful call-by-value languages. The new
models can be understood as enriched adjunctions.
