update to new coq-categories, base ND_Relation on inert sequences

[coq-hetmet.git] / src / ProgrammingLanguageArrow.v

diff --git a/src/ProgrammingLanguageArrow.v b/src/ProgrammingLanguageArrow.v
index 6bf0f24..b613455 100644 (file)
--- a/src/ProgrammingLanguageArrow.v
+++ b/src/ProgrammingLanguageArrow.v
@@ -31,38 +31,48 @@ Require Import ProgrammingLanguage.
 Require Import ProgrammingLanguageGeneralizedArrow.
 Require Import FreydCategories.
 
+Require Import GeneralizedArrow.
+
 Section ArrowInLanguage.
 
-  Section ArrowInLanguage.
-    Context {MF}{mn:MonoidalCat TypesL (fun x => (fst_obj _ _ x),,(snd_obj _ _ x)) MF []} (CC:CartesianCat mn).
-    Context {Kehom}(K:@ECategory _ _ TypesL _ mn [] mn TypesL Kehom).
-    Context {bc:BinoidalCat (Underlying K) (@T_Branch _)}.
-    Context (pmc:@PreMonoidalCat _ _ _ _ bc (@one _ _ _ (car_terminal(CartesianCat:=CC)))).
-    Definition ArrowInProgrammingLanguage := @FreydCategory _ _ _ _ _ _ mn _ _ _ _ pmc.
-  End ArrowInLanguage.
+  (* an Arrow In A Programming Language consists of... *)
+
+  (* a host language: *)
+  Context `(Host:ProgrammingLanguage).
+
+  (* ... for which Types(L) is cartesian: *)
+  Context {MF}(center_of_TypesL:MonoidalCat (TypesL _ _ Host) (fun x => (fst_obj _ _ x),,(snd_obj _ _ x)) MF []).
+
+  (* along with a monoidal subcategory of Z(Types(L)) *)
+  Context (VK:MonoidalSubCat center_of_TypesL).
 
-  Definition ArrowsAreGeneralizedArrows (Host:ProgrammingLanguageSMME)
-    {mf}{mn}{cc}{kehom}{CC}
-    (arrow:ArrowInProgrammingLanguage Host _ _ CC mf mn cc kehom) :  GeneralizedArrowInLanguage.
+  (* a premonoidal category enriched in aforementioned full subcategory *)
+  Context (Kehom:center_of_TypesL -> center_of_TypesL -> @ob _ _ VK).
 
-  Definition TwoLevelLanguage := Reification Guest Host (me_i Host).
+  Context (KE:@ECategory (@ob _ _ VK) (@hom _ _ VK) VK _ VK
+               (mon_i (full_subcat_is_monoidal VK)) (full_subcat_is_monoidal VK) center_of_TypesL Kehom).
 
-  Context (GuestHost:TwoLevelLanguage).
+  Context {kbo:center_of_TypesL -> center_of_TypesL -> center_of_TypesL}.
 
-  Definition FlatObject (x:TypesL _ _ Host) :=
-    forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x).
+  Context (kbc:@BinoidalCat center_of_TypesL _ (Underlying KE) kbo).
 
-  Definition FlatSubCategory := FullSubcategory (TypesL _ _ Host) FlatObject.
+  Check (@PreMonoidalCat)
+  Definition one' := @one _ _ _ (car_terminal(CartesianCat:=CC))
+  Context (K:@PreMonoidalCat _ _ KE kbo kbc ).
+  Context (CC:CartesianCat center_of_TypesL).
 
-  Section Flattening.
+  (*
+  Definition K_enrichment : Enrichment.
+    refine {| enr_c := KE |}.
+    Defined.
+  Context (K_surjective:SurjectiveEnrichment K_enrichment).
+    *)
 
-    Context  (F:Retraction (TypesL _ _ Host) FlatSubCategory).
-    Definition FlatteningOfReification := garrow_from_reification Guest Host GuestHost >>>> F.
-    Lemma FlatteningIsNotDestructive : 
-      FlatteningOfReification >>>> retraction_retraction F >>>> HomFunctor _ (me_i Host) ~~~~ GuestHost.
-      admit.
-      Qed.
+  Definition ArrowInProgrammingLanguage :=
+    @FreydCategory _ _ _ _ _ _ center_of_TypesL _ _ _ _ K.
 
-  End Flattening.
+  Definition ArrowsAreGeneralizedArrows (arrow:ArrowInProgrammingLanguage) : GeneralizedArrow K_enrichment Host.
+    refine {| ga_functor_monoidal := inclusion_functor_monoidal VK |}.
+    Defined.
 
 End GArrowInLanguage.