Proof Pearl: Magic Wand as Frame

Separation logic adds two connectives to assertion languages: separating conjunction * ("star") and its adjoint, separating implication -* ("magic wand"). Comparatively, separating implication is less widely used. This paper demonstrates that by using magic wand to express frames that relate mutable local portions of data structures to global portions, we can exploit its power while proofs are still easily understandable. Many useful separation logic theorems about partial data structures can now be proved by simple automated tactics, which were usually proved by induction. This magic-wand-as-frame technique is especially useful when formalizing the proofs by a high order logic. We verify binary search tree insert in Coq as an example to demonstrate this proof technique.