diff --git a/theories/bi/interface.v b/theories/bi/interface.v index 9901452818f1ea0a2c21578f97e903d80141367e..cf3780875ac4eeff67415fb4f7b1c87ea7cbd541 100644 --- a/theories/bi/interface.v +++ b/theories/bi/interface.v @@ -42,6 +42,16 @@ Section bi_mixin. Local Notation "x ≡ y" := (sbi_internal_eq _ x y). Local Notation "▷ P" := (sbi_later P). + (** * Axioms for a general BI (logic of bunched implications) *) + + (** The following axioms are satisifed by both affine and linear BIs, and BIs + that combine both kinds of resources. In particular, we have an "ordered RA" + model satisfying all these axioms. For this model, we extend RAs with an + arbitrary partial order, and up-close resources wrt. that order (instead of + extension order). We demand composition to be monotone wrt. the order. We + define [emp := λ r, ε ≼ r]; persisently is still defined with the core: [□ P + := λ r, P (core r)]. *) + Record BiMixin := { bi_mixin_entails_po : PreOrder bi_entails; bi_mixin_equiv_spec P Q : equiv P Q ↔ (P ⊢ Q) ∧ (Q ⊢ P);