clean up hints for NaturalDeduction, split ProgrammingLanguage into multiple files

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

diff --git a/src/ProgrammingLanguageArrow.v b/src/ProgrammingLanguageArrow.v
index b613455..5386d3e 100644 (file)
--- 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.
@@ -27,10 +30,9 @@ Require Import FunctorCategories_ch7_7.
 Require Import NaturalDeduction.
 Require Import NaturalDeductionCategory.
 
-Require Import ProgrammingLanguage.
-Require Import ProgrammingLanguageGeneralizedArrow.
+Require Import ProgrammingLanguageCategory.
 Require Import FreydCategories.
-
+Require Import Enrichments.
 Require Import GeneralizedArrow.
 
 Section ArrowInLanguage.
@@ -38,41 +40,36 @@ Section 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 []).
+  Context `(Host         : ProgrammingLanguage).
 
-  (* along with a monoidal subcategory of Z(Types(L)) *)
-  Context (VK:MonoidalSubCat center_of_TypesL).
+  Context  (Host_Monoidal  : MonoidalCat  (TypesL_PreMonoidal Host)).
+  Context  (Host_Cartesian : CartesianCat Host_Monoidal).
 
-  (* a premonoidal category enriched in aforementioned full subcategory *)
-  Context (Kehom:center_of_TypesL -> center_of_TypesL -> @ob _ _ VK).
+  Context
+    {P}
+    (Pobj_unit   : P [])
+    (Pobj_closed : forall a b, P a → P b → P (bin_obj(BinoidalCat:=Center_is_PreMonoidal (TypesL_PreMonoidal Host)) a b)).
 
-  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 (VK : FullSubcategory Host_Cartesian P).
 
-  Context {kbo:center_of_TypesL -> center_of_TypesL -> center_of_TypesL}.
+  Context  ehom KE (K_bin:@EBinoidalCat _ _ VK _ _ _
+          (PreMonoidalFullSubcategory_PreMonoidal Host_Cartesian VK Pobj_unit Pobj_closed)
+          (TypesL Host) ehom KE (bin_obj(BinoidalCat:=Host_Monoidal))).
 
-  Context (kbc:@BinoidalCat center_of_TypesL _ (Underlying KE) kbo).
+  Context (K_premonoidal:PreMonoidalCat K_bin (one(TerminalObject:=Host_Cartesian))).
 
-  Check (@PreMonoidalCat)
-  Definition one' := @one _ _ _ (car_terminal(CartesianCat:=CC))
-  Context (K:@PreMonoidalCat _ _ KE kbo kbc ).
-  Context (CC:CartesianCat center_of_TypesL).
+  Definition ArrowInProgrammingLanguage :=
+    @FreydCategory _ _ _ _ _ _ _ _ Host_Cartesian _ _ K_bin K_premonoidal.
 
-  (*
   Definition K_enrichment : Enrichment.
-    refine {| enr_c := KE |}.
-    Defined.
-  Context (K_surjective:SurjectiveEnrichment K_enrichment).
-    *)
-
-  Definition ArrowInProgrammingLanguage :=
-    @FreydCategory _ _ _ _ _ _ center_of_TypesL _ _ _ _ K.
+    refine
+      {| enr_c_pm  := K_premonoidal
+       ; enr_v_mon := MonoidalFullSubcategory_Monoidal Host_Cartesian _ _ VK
+      |}.
+      Defined.
 
-  Definition ArrowsAreGeneralizedArrows (arrow:ArrowInProgrammingLanguage) : GeneralizedArrow K_enrichment Host.
-    refine {| ga_functor_monoidal := inclusion_functor_monoidal VK |}.
-    Defined.
+  Instance ArrowsAreGeneralizedArrows : GeneralizedArrow K_enrichment (TypesEnrichedInJudgments Host) :=
+    { ga_functor_monoidal :=
+        PreMonoidalFullSubcategoryInclusionFunctor_PreMonoidal Host_Cartesian VK Pobj_unit Pobj_closed Host_Cartesian }.
 
-End GArrowInLanguage.
+End ArrowInLanguage.