X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FProgrammingLanguageArrow.v;h=f6a3940a864d22edcb0e4fd5306da07c7baaf987;hp=a4f40e3b3287847268912f5cbd73f30196557fc1;hb=2d963cf6994fa510fe67d5bf3852ffcc8090496c;hpb=c3b1fb9622a65ad01e54b6e35785cee672d25bdc

diff --git a/src/ProgrammingLanguageArrow.v b/src/ProgrammingLanguageArrow.v
index a4f40e3..f6a3940 100644
--- a/src/ProgrammingLanguageArrow.v
+++ b/src/ProgrammingLanguageArrow.v
@@ -18,6 +18,9 @@ Require Import Enrichment_ch2_8.
 Require Import Subcategories_ch7_1.
 Require Import NaturalTransformations_ch7_4.
 Require Import NaturalIsomorphisms_ch7_5.
+Require Import BinoidalCategories.
+Require Import PreMonoidalCategories.
+Require Import PreMonoidalCenter.
 Require Import MonoidalCategories_ch7_8.
 Require Import Coherence_ch7_8.
 Require Import Enrichment_ch2_8.
@@ -33,91 +36,6 @@ Require Import FreydCategories.
 
 Require Import GeneralizedArrow.
 
-Section ExtendFunctor.
-
-  Context `(F:Functor).
-  Context  (P:c1 -> Prop).
-
-  Definition domain_subcat := FullSubcategory c1 P.
-
-  Definition functor_restricts_to_full_subcat_on_domain_fobj (a:domain_subcat) : c2 :=
-    F (projT1 a).
-
-  Definition functor_restricts_to_full_subcat_on_domain_fmor (a b:domain_subcat)(f:a~~{domain_subcat}~~>b) :
-    (functor_restricts_to_full_subcat_on_domain_fobj a)~~{c2}~~>(functor_restricts_to_full_subcat_on_domain_fobj b) :=
-    F \ (projT1 f).
-
-  Lemma functor_restricts_to_full_subcat_on_domain : Functor domain_subcat c2 functor_restricts_to_full_subcat_on_domain_fobj.
-    refine {| fmor := functor_restricts_to_full_subcat_on_domain_fmor |};
-      unfold functor_restricts_to_full_subcat_on_domain_fmor; simpl; intros.
-    setoid_rewrite H; reflexivity.
-    setoid_rewrite fmor_preserves_id; reflexivity.
-    setoid_rewrite <- fmor_preserves_comp; reflexivity.
-    Defined.
-
-End ExtendFunctor.
-
-Section MonoidalSubCat.
-
-  (* a monoidal subcategory is a full subcategory, closed under tensor and containing the unit object *)
-  Class MonoidalSubCat {Ob}{Hom}{C:Category Ob Hom}{MFobj}{MF}{MI}(MC:MonoidalCat C MFobj MF MI) :=
-  { msc_P                   :  MC -> Prop
-  ; msc_closed_under_tensor :  forall o1 o2, msc_P o1 -> msc_P o2 -> msc_P (MC (pair_obj o1 o2))
-  ; msc_contains_unit       :  msc_P (mon_i MC)
-  ; msc_subcat              := FullSubcategory MC msc_P
-  }.
-  Local Coercion msc_subcat : MonoidalSubCat >-> SubCategory.
-
-  Context `(MSC:MonoidalSubCat).
-
-  (* any full subcategory of a monoidal category, , is itself monoidal *)
-  Definition mf_restricts_to_full_subcat_on_domain_fobj (a:MSC ×× MSC) : MSC.
-    destruct a.
-    destruct o.
-    destruct o0.
-    set (MC (pair_obj x x0)) as m'.
-    exists m'.
-    apply msc_closed_under_tensor; auto.
-    Defined.
-
-  Definition mf_restricts_to_full_subcat_on_domain_fmor
-    {a}{b}
-    (f:a~~{MSC ×× MSC}~~>b)
-    :
-    (mf_restricts_to_full_subcat_on_domain_fobj a)~~{MSC}~~>(mf_restricts_to_full_subcat_on_domain_fobj b).
-    destruct a as [[a1 a1pf] [a2 a2pf]].
-    destruct b as [[b1 b1pf] [b2 b2pf]].
-    destruct f as [[f1 f1pf] [f2 f2pf]].
-    simpl in *.
-    exists (MC \ (pair_mor (pair_obj a1 a2) (pair_obj b1 b2) f1 f2)); auto.
-    Defined.
-
-  Lemma mf_restricts_to_full_subcat_on_domain : Functor (MSC ×× MSC) MSC
-    mf_restricts_to_full_subcat_on_domain_fobj.
-    refine {| fmor := fun a b f => mf_restricts_to_full_subcat_on_domain_fmor f |};
-      unfold functor_restricts_to_full_subcat_on_domain_fmor; simpl; intros.
-    admit.
-    admit.
-    admit.
-    Defined.
-
-  Definition subcat_i : MSC.
-    exists (mon_i MC).
-    apply msc_contains_unit.
-    Defined.
-
-  Lemma full_subcat_is_monoidal : MonoidalCat MSC _ mf_restricts_to_full_subcat_on_domain subcat_i.
-    admit.
-    Defined.
-
-  Lemma inclusion_functor_monoidal : MonoidalFunctor full_subcat_is_monoidal MC (InclusionFunctor _ MSC).
-    admit.
-    Defined.
-
-End MonoidalSubCat.
-Coercion full_subcat_is_monoidal : MonoidalSubCat >-> MonoidalCat.
-
-(*
 Section ArrowInLanguage.
 
   (* an Arrow In A Programming Language consists of... *)
@@ -126,41 +44,31 @@ Section ArrowInLanguage.
   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).
-
-  (* a premonoidal category enriched in aforementioned full subcategory *)
-  Context (Kehom:center_of_TypesL -> center_of_TypesL -> @ob _ _ VK).
-Check (@ECategory).
-  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 (center_of_TypesL:MonoidalCat (TypesL_PreMonoidal Host)).
 
-Check (Underlying KE).
+  (* along with a full subcategory of Z(Types(L)) *)
+  Context {P}(VK:FullSubcategory (Center (TypesL_PreMonoidal Host)) P).
 
-  Context {kbo:center_of_TypesL -> center_of_TypesL -> center_of_TypesL}.
+  Context (Pobj_unit   : P []).
+  Context (Pobj_closed : forall a b, P a → P b → P (bin_obj(BinoidalCat:=Center_is_PreMonoidal (TypesL_PreMonoidal Host)) a b)).
+  Definition VKM :=
+    PreMonoidalFullSubcategory_PreMonoidal (Center_is_PreMonoidal (TypesL_PreMonoidal Host)) VK Pobj_unit Pobj_closed.
 
-  Context (kbc:@BinoidalCat center_of_TypesL _ (Underlying KE) kbo).
+  (* a premonoidal category enriched in aforementioned full subcategory *)
+  Context (Kehom:(Center (TypesL_PreMonoidal Host)) -> (Center (TypesL_PreMonoidal Host)) -> @ob _ _ VK).
+  Context (KE   :@ECategory (@ob _ _ VK) (@hom _ _ VK) VK _ VKM (pmon_I VKM) VKM (Center (TypesL_PreMonoidal Host)) Kehom).
+  Context {kbo  :(Center (TypesL_PreMonoidal Host)) -> (Center (TypesL_PreMonoidal Host)) -> (Center (TypesL_PreMonoidal Host))}.
+  Context (kbc  :@BinoidalCat (Center (TypesL_PreMonoidal Host)) _ (Underlying KE) kbo).
 
-  Check (@PreMonoidalCat)
   Definition one' := @one _ _ _ (car_terminal(CartesianCat:=CC))
-  Context (K:@PreMonoidalCat _ _ KE kbo kbc ).
-  Context (CC:CartesianCat center_of_TypesL).
-
-  (*
-  Definition K_enrichment : Enrichment.
-    refine {| enr_c := KE |}.
-    Defined.
-  Context (K_surjective:SurjectiveEnrichment K_enrichment).
-    *)
-Check (@FreydCategory).
+  Context (K :@PreMonoidalCat _ _ KE kbo kbc ).
+  Context (CC:CartesianCat (Center (TypesL_PreMonoidal Host))).
 
   Definition ArrowInProgrammingLanguage :=
-    @FreydCategory _ _ _ _ _ _ center_of_TypesL _ _ _ _ K.
+    @FreydCategory _ _ _ _ _ _ (Center (TypesL_PreMonoidal Host)) _ _ _ _ K.
 
   Definition ArrowsAreGeneralizedArrows (arrow:ArrowInProgrammingLanguage) : GeneralizedArrow K_enrichment Host.
     refine {| ga_functor_monoidal := inclusion_functor_monoidal VK |}.
     Defined.
 
 End GArrowInLanguage.
-*)
\ No newline at end of file