Fractional resources in unbounded separation logic

Many separation logics support fractional permissions to distinguish between read and write access a heap location, for instance, allow concurrent reads while enforcing exclusive writes. Fractional extend composite assertions such as (co)inductive predicates magic wands by allowing those be multiplied fraction. Typical logic proofs require that this multiplication has three key properties: it needs distribute over assertions, should permit fractions factored out from two of the same assertion combinable into one larger Existing formal semantics incorporating define semantically (via models), resulting in which distributivity combinability do not hold resource wands, cannot separating conjunction. By contrast, existing automatic verifiers syntactically, different is unknown whether all assertions. In paper, we present novel allows states more than full permission location during evaluation an assertion. reimposing upper bounds on held per at statement boundaries, retain properties logic, particular, frame rule. Our unifies semantic syntactic thereby reconciles discrepancy theory tools enjoys distributivity, factorisability, combinability. We have formalised our proved its Isabelle/HOL.