break the dependency chain from iris_core to metric_rec

world_prop.v

-(** In this file, we show how we can use the solution of the recursive
+(** In this file, we we define what it means to be a solution of the recursive
     domain equations to build a higher-order separation logic *)
-Require Import ModuRes.PreoMet ModuRes.MetricRec ModuRes.CBUltInst.
+Require Import ModuRes.PreoMet.
 Require Import ModuRes.Finmap ModuRes.Constr.
 Require Import ModuRes.RA ModuRes.UPred.
 
@@ -31,92 +31,3 @@ Module Type WORLD_PROP (Res : RA_T).
   Axiom iso : forall P, ı' (ı P) == P.
   Axiom isoR: forall T, ı (ı' T) == T.
 End WORLD_PROP.
-
-
-(* Now we come to the actual implementation *)
-Module WorldProp (Res : RA_T) : WORLD_PROP Res.
-
-  (** The construction is parametric in the monoid we choose *)
-  Definition pres := ra_pos Res.res.
-
-  (** We need to build a functor that would describe the following
-      recursive domain equation:
-        Prop ≃ (Loc -f> Prop) -m> UPred (Res)
-      As usual, we split the negative and (not actually occurring)
-      positive occurrences of Prop. *)
-
-  Section Definitions.
-    (** We'll be working with complete metric spaces, so whenever
-        something needs an additional preorder, we'll just take a
-        discrete one. *)
-    Local Instance pt_disc P `{cmetric P} : preoType P | 2000 := disc_preo P.
-    Local Instance pcm_disc P `{cmetric P} : pcmType P | 2000 := disc_pcm P.
-
-    Definition FProp P `{cmP : cmetric P} :=
-      (nat -f> P) -m> UPred pres.
-
-    Context {U V} `{cmU : cmetric U} `{cmV : cmetric V}.
-
-    Definition PropMorph (m : V -n> U) : FProp U -n> FProp V :=
-      fdMap (disc_m m) ▹.
-
-  End Definitions.
-
-  Module F <: SimplInput (CBUlt).
-    Import CBUlt.
-    Open Scope cat_scope.
-
-    Definition F (T1 T2 : cmtyp) := cmfromType (FProp T1).
-    Program Instance FArr : BiFMap F :=
-      fun P1 P2 P3 P4 => n[(PropMorph)] <M< Mfst.
-    Next Obligation.
-      intros m1 m2 Eqm; unfold PropMorph, equiv in *.
-      rewrite Eqm; reflexivity.
-    Qed.
-
-    Instance FFun : BiFunctor F.
-    Proof.
-      split; intros; unfold fmorph; simpl morph; unfold PropMorph.
-      - rewrite disc_m_comp, <- fdMap_comp, <- ucomp_precomp.
-        intros x; simpl morph; reflexivity.
-      - rewrite disc_m_id, fdMap_id, pid_precomp.
-        intros x; simpl morph; reflexivity.
-    Qed.
-
-    Definition F_ne : 1 -t> F 1 1 :=
-      umconst (pcmconst (up_cr (const True))).
-  End F.
-
-  Module F_In := InputHalve(F).
-  Module Import Fix := Solution(CBUlt)(F_In).
-
-  (** Now we can name the two isomorphic spaces of propositions, and
-      the space of worlds. We'll store the actual solutions in the
-      worlds, and use the action of the FPropO on them as the space we
-      normally work with. *)
-  Definition PreProp := DInfO.
-  Definition Props   := FProp PreProp.
-  Definition Wld     := (nat -f> PreProp).
-
-  (* Define an order on PreProp. *)
-  Instance PProp_preo: preoType PreProp   := disc_preo PreProp.
-  Instance PProp_pcm : pcmType PreProp    := disc_pcm PreProp.
-  Instance PProp_ext : extensible PreProp := disc_ext PreProp.
-
-  (* Give names to the things for Props, so the terms can get shorter. *)
-  Instance Props_ty   : Setoid Props     := _.
-  Instance Props_m    : metric Props     := _.
-  Instance Props_cm   : cmetric Props    := _.
-  Instance Props_preo : preoType Props   := _.
-  Instance Props_pcm  : pcmType Props    := _.
-
-  (* Establish the isomorphism *)
-  Definition ı  : PreProp -t> halve (cmfromType Props) := Unfold.
-  Definition ı' : halve (cmfromType Props) -t> PreProp := Fold.
-
-  Lemma iso P : ı' (ı P) == P.
-  Proof. apply (FU_id P). Qed.
-  Lemma isoR T : ı (ı' T) == T.
-  Proof. apply (UF_id T). Qed.
-
-End WorldProp.

world_prop_recdom.v

+(** In this file, we show how we can obtain a solution of the recursive
+    domain equations to build a higher-order separation logic *)
+Require Import ModuRes.PreoMet ModuRes.MetricRec ModuRes.CBUltInst.
+Require Import ModuRes.Finmap ModuRes.Constr.
+Require Import ModuRes.RA ModuRes.UPred.
+Require Import world_prop.
+
+(* Now we come to the actual implementation *)
+Module WorldProp (Res : RA_T) : WORLD_PROP Res.
+
+  (** The construction is parametric in the monoid we choose *)
+  Definition pres := ra_pos Res.res.
+
+  (** We need to build a functor that would describe the following
+      recursive domain equation:
+        Prop ≃ (Loc -f> Prop) -m> UPred (Res)
+      As usual, we split the negative and (not actually occurring)
+      positive occurrences of Prop. *)
+
+  Section Definitions.
+    (** We'll be working with complete metric spaces, so whenever
+        something needs an additional preorder, we'll just take a
+        discrete one. *)
+    Local Instance pt_disc P `{cmetric P} : preoType P | 2000 := disc_preo P.
+    Local Instance pcm_disc P `{cmetric P} : pcmType P | 2000 := disc_pcm P.
+
+    Definition FProp P `{cmP : cmetric P} :=
+      (nat -f> P) -m> UPred pres.
+
+    Context {U V} `{cmU : cmetric U} `{cmV : cmetric V}.
+
+    Definition PropMorph (m : V -n> U) : FProp U -n> FProp V :=
+      fdMap (disc_m m) ▹.
+
+  End Definitions.
+
+  Module F <: SimplInput (CBUlt).
+    Import CBUlt.
+    Open Scope cat_scope.
+
+    Definition F (T1 T2 : cmtyp) := cmfromType (FProp T1).
+    Program Instance FArr : BiFMap F :=
+      fun P1 P2 P3 P4 => n[(PropMorph)] <M< Mfst.
+    Next Obligation.
+      intros m1 m2 Eqm; unfold PropMorph, equiv in *.
+      rewrite Eqm; reflexivity.
+    Qed.
+
+    Instance FFun : BiFunctor F.
+    Proof.
+      split; intros; unfold fmorph; simpl morph; unfold PropMorph.
+      - rewrite disc_m_comp, <- fdMap_comp, <- ucomp_precomp.
+        intros x; simpl morph; reflexivity.
+      - rewrite disc_m_id, fdMap_id, pid_precomp.
+        intros x; simpl morph; reflexivity.
+    Qed.
+
+    Definition F_ne : 1 -t> F 1 1 :=
+      umconst (pcmconst (up_cr (const True))).
+  End F.
+
+  Module F_In := InputHalve(F).
+  Module Import Fix := Solution(CBUlt)(F_In).
+
+  (** Now we can name the two isomorphic spaces of propositions, and
+      the space of worlds. We'll store the actual solutions in the
+      worlds, and use the action of the FPropO on them as the space we
+      normally work with. *)
+  Definition PreProp := DInfO.
+  Definition Props   := FProp PreProp.
+  Definition Wld     := (nat -f> PreProp).
+
+  (* Define an order on PreProp. *)
+  Instance PProp_preo: preoType PreProp   := disc_preo PreProp.
+  Instance PProp_pcm : pcmType PreProp    := disc_pcm PreProp.
+  Instance PProp_ext : extensible PreProp := disc_ext PreProp.
+
+  (* Give names to the things for Props, so the terms can get shorter. *)
+  Instance Props_ty   : Setoid Props     := _.
+  Instance Props_m    : metric Props     := _.
+  Instance Props_cm   : cmetric Props    := _.
+  Instance Props_preo : preoType Props   := _.
+  Instance Props_pcm  : pcmType Props    := _.
+
+  (* Establish the isomorphism *)
+  Definition ı  : PreProp -t> halve (cmfromType Props) := Unfold.
+  Definition ı' : halve (cmfromType Props) -t> PreProp := Fold.
+
+  Lemma iso P : ı' (ı P) == P.
+  Proof. apply (FU_id P). Qed.
+  Lemma isoR T : ı (ı' T) == T.
+  Proof. apply (UF_id T). Qed.
+
+End WorldProp.