Commit 3897eaf4 authored by Robbert Krebbers's avatar Robbert Krebbers
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Move global functor construction to its own file and define notations.

I made the list of iFunctors monomorphic to avoid having to deal with
universe polymorphism, that is still somewhat flaky.
parent e0d0f8dd
From program_logic Require Export ghost_ownership.
Module iFunctors.
Inductive iFunctors :=
| nil : iFunctors
| cons : iFunctor iFunctors iFunctors.
Coercion singleton (F : iFunctor) : iFunctors := cons F nil.
End iFunctors.
Notation iFunctors := iFunctors.iFunctors.
Delimit Scope iFunctors_scope with iFunctors.
Bind Scope iFunctors_scope with iFunctors.
Arguments iFunctors.cons _ _%iFunctors.
Notation "[ ]" := iFunctors.nil (format "[ ]") : iFunctors_scope.
Notation "[ F ]" := (iFunctors.cons F iFunctors.nil) : iFunctors_scope.
Notation "[ F ; .. ; F' ]" :=
(iFunctors.cons F .. (iFunctors.cons F' iFunctors.nil) ..) : iFunctors_scope.
Module iFunctorG.
Definition nil : iFunctorG := const (constF unitRA).
Definition cons (F : iFunctor) (Σ : iFunctorG) : iFunctorG :=
λ n, match n with O => F | S n => Σ n end.
Fixpoint app (Fs : iFunctors) (Σ : iFunctorG) : iFunctorG :=
match Fs with
| iFunctors.nil => Σ
| iFunctors.cons F Fs => cons F (app Fs Σ)
End iFunctorG.
(** Cannot bind this scope with the [iFunctorG] since [iFunctorG] is a
notation hiding a more complex type. *)
Notation "#[ ]" := iFunctorG.nil (format "#[ ]").
Notation "#[ Fs ]" := ( Fs iFunctorG.nil).
Notation "#[ Fs ; .. ; Fs' ]" :=
( Fs .. ( Fs' iFunctorG.nil) ..).
(** We need another typeclass to identify the *functor* in the Σ. Basing inG on
the functor breaks badly because Coq is unable to infer the correct
typeclasses, it does not unfold the functor. *)
Class inGF (Λ : language) (Σ : iFunctorG) (F : iFunctor) := InGF {
inGF_id : gid;
inGF_prf : F = Σ inGF_id;
(* Avoid eager type class search: this line ensures that type class search
is only triggered if the first two arguments of inGF do not contain evars. Since
instance search for [inGF] is restrained, instances should always have [inGF] as
their first argument to avoid loops. For example, the instances [authGF_inGF]
and [auth_identity] otherwise create a cycle that pops up arbitrarily. *)
Hint Mode inGF + + - : typeclass_instances.
Lemma inGF_inG `{inGF Λ Σ F} : inG Λ Σ (F (laterC (iPreProp Λ (globalF Σ)))).
Proof. exists inGF_id. by rewrite -inGF_prf. Qed.
Instance inGF_here {Λ Σ} (F: iFunctor) : inGF Λ (iFunctorG.cons F Σ) F.
Proof. by exists 0. Qed.
Instance inGF_further {Λ Σ} (F F': iFunctor) :
inGF Λ Σ F inGF Λ (iFunctorG.cons F' Σ) F.
Proof. intros [i ?]. by exists (S i). Qed.
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