  Recent trends in AI verification and Explainable AI have raised the question
of whether AI planning techniques can be verified. In this paper, we present a
novel resource logic, the Proof Carrying Plans (PCP) logic that can be used to
verify plans produced by AI planners. The PCP logic takes inspiration from
existing resource logics (such as Linear logic and Separation logic) as well as
Hoare logic when it comes to modelling states and resource-aware plan
execution. It also capitalises on the Curry-Howard approach to logics, in its
treatment of plans as functions and plan pre- and post-conditions as types.
This paper presents two main results. From the theoretical perspective, we show
that the PCP logic is sound relative to the standard possible world semantics
used in AI planning. From the practical perspective, we present a complete Agda
formalisation of the PCP logic and of its soundness proof. Moreover, we
showcase the Curry-Howard, or functional, value of this implementation by
supplementing it with the library that parses AI plans into Agda's proofs
automatically. We provide evaluation of this library and the resulting Agda
functions.
