In this file we construct the type iProp of propositions of the Iris logic. This is done by solving the following recursive domain equation: iProp ≈ uPred (∀ i : gid, gname -fin-> (Σ i) iProp) where: Σ : gFunctors := lists of locally constractive functors i : gid := indexes addressing individual functors in Σ γ : gname := ghost variable names The Iris logic is parametrized by a list of locally contractive functors Σ from the category of COFEs to the category of CMRAs. These functors are instantiated with iProp, the type of Iris propositions, which allows one to construct impredicate CMRAs, such as invariants and stored propositions using the agreement CMRA.

Locally contractive functors

The type gFunctor bundles a functor from the category of COFEs to the category of CMRAs with a proof that it is locally contractive.

The type gFunctors describes the parameters Σ of the Iris logic: lists of gFunctors. Note that gFunctors is isomorphic to list gFunctor, but defined in an alternative way to avoid universe inconsistencies with respect to the universe monomorphic list type. Defining gFunctors as a dependent record instead of a sigT avoids other universe inconsistencies.

The resources functor iResF Σ A := ∀ i : gid, gname -fin→ (Σ i) A.

We define functions for the empty list of functors, the singleton list of functors, and the append operator on lists of functors. These are used to compose gFunctors out of smaller pieces.

Subfunctors

In order to make proofs in the Iris logic modular, they are not done with respect to some concrete list of functors Σ, but are instead parametrized by an arbitrary list of functors Σ that contains at least certain functors. For example, the lock library is parameterized by a functor Σ that should have the functors corresponding to the heap and the exclusive monoid to manage to lock invariant. The contraints to can be expressed using the type class subG Σ1 Σ2, which expresses that the functors Σ1 are contained in Σ2.

Avoid trigger happy type class search: this line ensures that type class search is only triggered if the arguments of subG do not contain evars. Since instance search for subG is restrained, instances should persistently have subG as their first parameter to avoid loops. For example, the instances subG_authΣ and auth_discrete otherwise create a cycle that pops up arbitrarily.

Solution of the recursive domain equation

We first declare a module type and then an instance of it so as to seal all of the construction, this way we are sure we do not use any properties of the construction, and also avoid Coq from blindly unfolding it.

Properties of the solution to the recursive domain equation