clean up demo code

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

diff --git a/src/ProgrammingLanguageArrow.v b/src/ProgrammingLanguageArrow.v
index 6bf0f24..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.
@@ -27,42 +30,46 @@ 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.
 
-  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... *)
 
-  Definition ArrowsAreGeneralizedArrows (Host:ProgrammingLanguageSMME)
-    {mf}{mn}{cc}{kehom}{CC}
-    (arrow:ArrowInProgrammingLanguage Host _ _ CC mf mn cc kehom) :  GeneralizedArrowInLanguage.
+  (* a host language: *)
+  Context `(Host         : ProgrammingLanguage).
 
-  Definition TwoLevelLanguage := Reification Guest Host (me_i Host).
+  Context  (Host_Monoidal  : MonoidalCat  (TypesL_PreMonoidal Host)).
+  Context  (Host_Cartesian : CartesianCat Host_Monoidal).
 
-  Context (GuestHost:TwoLevelLanguage).
+  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)).
 
-  Definition FlatObject (x:TypesL _ _ Host) :=
-    forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x).
+  Context (VK : FullSubcategory Host_Cartesian P).
 
-  Definition FlatSubCategory := FullSubcategory (TypesL _ _ Host) FlatObject.
+  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))).
 
-  Section Flattening.
+  Context (K_premonoidal:PreMonoidalCat K_bin (one(TerminalObject:=Host_Cartesian))).
 
-    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 _ _ _ _ _ _ _ _ Host_Cartesian _ _ K_bin K_premonoidal.
 
-  End Flattening.
+  Definition K_enrichment : Enrichment.
+    refine
+      {| enr_c_pm  := K_premonoidal
+       ; enr_v_mon := MonoidalFullSubcategory_Monoidal Host_Cartesian _ _ VK
+      |}.
+      Defined.
 
-End GArrowInLanguage.
+  Instance ArrowsAreGeneralizedArrows : GeneralizedArrow K_enrichment (TypesEnrichedInJudgments Host) :=
+    { ga_functor_monoidal :=
+        PreMonoidalFullSubcategoryInclusionFunctor_PreMonoidal Host_Cartesian VK Pobj_unit Pobj_closed Host_Cartesian }.
+
+End ArrowInLanguage.