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Modelling and reasoning about dynamic memory allocation is one of thewell-established strands of theoretical computer science, which is particularlywell-known as a source of notorious challenges in semantics, reasoning, andproof theory. We capitalize on recent progress on categorical semantics of fullground store, in terms of a full ground store monad, to build a correspondingsemantics of a higher order logic over the corresponding programs. Our mainresult is a construction of an (intuitionistic) BI-hyperdoctrine, which isarguably the semantic core of higher order logic over local store. Although wehave made an extensive use of the existing generic tools, certain principledchanges had to be made to enable the desired construction: while the originalmonad works over total heaps (to disable dangling pointers), our versioninvolves partial heaps (heaplets) to enable compositional reasoning usingseparating conjunction. Another remarkable feature of our construction is that,in contrast to the existing generic approaches, our BI-algebra does notdirectly stem from an internal categorical partial commutative monoid.

Local Local Reasoning: A BI-Hyperdoctrine for Full Ground Store