Binding bigraphs as symmetric monoidal closed theories

We reconstruct Milner’s [1] category of abstract binding bigraphs Bbg(K) over a signature K as the free (or initial) symmetric monoidal closed (smc) category S(TK) generated by a derived theory TK. The morphisms of S(TK) are essentially proof nets from the Intuitionistic Multiplicative fragment (imll) of Linear Logic [2]. Formally, we construct a faithful, essentially injective on objects functor Bbg(K) → S(TK), which is surjective on closed bigraphs (i.e., bigraphs without free names or sites). The functor is not full, which we view as a gain in modularity: we maintain the scoping discipline for whole programs (bound names never escape their scope) but allow more program fragments, including a large class of binding contexts, thanks to richer interfaces. Possible applications include bigraphical programming languages [3] and Rathke and Sobociński’s derived labelled transition systems [4].