More nits and consistency of CoqDoc

theories/channel/proto_model.v

@@ -9,14 +9,14 @@ The main difference is that the protocols are defined over predicates,
 in place of types.
 
 Dependent Separation Protocols are modelled as the following type:
-- [proto] := 1 + ([action] * (V → (▶ [proto] → PROP) → PROP))
+- [proto := 1 + (action * (V → (▶ proto → PROP) → PROP))]
 
 Here the left-hand side of the sum is used for the terminated process,
 while the right-hand side is used for the communication constructors.
 [action] is an inductively defined datatype with two constructors,
 that is used to differentiate between sending and received, rather than
 having two distinct sums in [proto].
-- [action] := [Send] | [Receive]
+- [action := Send | Receive]
 
 The remainder (V → (▶ [proto] → PROP) → PROP)) is a continuation that
 depends on the communicated value V and the dependent tail (▶ proto → PROP)

theories/utils/auth_excl.v

 (** This file provides utility for defining and using
-the commonly used ghost functor over authoritative exclusive ownership. *)
+a commonly used ghost functor over authoritative exclusive ownership.
+[AuthExcl A := Auth (Option (Excl A))]
+
+This is isomorphic to a half-ownership, with an intuitive
+use-case, being putting the authoritative part in an
+invariant, while giving the other fragment to the client
+with write permissions.  *)
 From iris.proofmode Require Import tactics.
 From iris.algebra Require Import excl auth.
 From iris.base_logic.lib Require Import own.

theories/utils/contribution.v

 (** This file defines a ghost functor for tracking
 "contributions" made to a shared concurrent effort.
 It is ultimately defined as:
-contribution := Auth (Option ((Pos * A) + Excl 1))
-
-Intuitively it allows one to allocate a [server] and
-a number of [client] fragments. The server keeps track
-of the number of active clients, and what resources they
-are currently holding.
-To deallocate a client it must hold no resources.
-To deallocate a server there must be no remaining clients.
+[contribution := Auth (Option ((Pos * A) + Excl 1))]
+
+Intuitively it allows one to allocate a [server] and a
+number of [client] fragments, where the server keeps
+track of the number of active clients, and what resources
+they are currently holding.
 *)
 From iris.base_logic Require Export base_logic lib.iprop lib.own.
 From iris.proofmode Require Export tactics.