Module Memperm

Require Import Coqlib.

Memory states are accessed by addresses b, ofs: pairs of a block identifier b and a byte offset ofs within that block. Each address is associated to permissions, also known as access rights. The following permissions are expressible: The first four cases are represented by the following type of permissions. Being empty is represented by the absence of any permission.

Inductive permission: Type :=
  | Freeable: permission
  | Writable: permission
  | Readable: permission
  | Nonempty: permission.

In the list, each permission implies the other permissions further down the list. We reflect this fact by the following order over permissions.

Inductive perm_order: permission -> permission -> Prop :=
  | perm_refl: forall p, perm_order p p
  | perm_F_any: forall p, perm_order Freeable p
  | perm_W_R: perm_order Writable Readable
  | perm_any_N: forall p, perm_order p Nonempty.

Hint Constructors perm_order: mem.

Lemma perm_order_trans:
  forall p1 p2 p3, perm_order p1 p2 -> perm_order p2 p3 -> perm_order p1 p3.
  intros. inv H; inv H0; constructor.

Each address has not one, but two permissions associated with it. The first is the current permission. It governs whether operations (load, store, free, etc) over this address succeed or not. The other is the maximal permission. It is always at least as strong as the current permission. Once a block is allocated, the maximal permission of an address within this block can only decrease, as a result of free or drop_perm operations, or of external calls. In contrast, the current permission of an address can be temporarily lowered by an external call, then raised again by another external call.

Inductive perm_kind: Type :=
  | Max: perm_kind
  | Cur: perm_kind.