lots of cleanup

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

diff --git a/src/ProgrammingLanguageArrow.v b/src/ProgrammingLanguageArrow.v
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+(*********************************************************************************************************************************)
+(* ProgrammingLanguageArrow                                                                                                      *)
+(*                                                                                                                               *)
+(*   Arrows in ProgrammingLanguages.                                                                                             *)
+(*                                                                                                                               *)
+(*********************************************************************************************************************************)
+
+Generalizable All Variables.
+Require Import Preamble.
+Require Import General.
+Require Import Categories_ch1_3.
+Require Import InitialTerminal_ch2_2.
+Require Import Functors_ch1_4.
+Require Import Isomorphisms_ch1_5.
+Require Import ProductCategories_ch1_6_1.
+Require Import OppositeCategories_ch1_6_2.
+Require Import Enrichment_ch2_8.
+Require Import Subcategories_ch7_1.
+Require Import NaturalTransformations_ch7_4.
+Require Import NaturalIsomorphisms_ch7_5.
+Require Import MonoidalCategories_ch7_8.
+Require Import Coherence_ch7_8.
+Require Import Enrichment_ch2_8.
+Require Import RepresentableStructure_ch7_2.
+Require Import FunctorCategories_ch7_7.
+
+Require Import NaturalDeduction.
+Require Import NaturalDeductionCategory.
+
+Require Import ProgrammingLanguage.
+Require Import ProgrammingLanguageGeneralizedArrow.
+Require Import FreydCategories.
+
+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.
+
+  Definition ArrowsAreGeneralizedArrows (Host:ProgrammingLanguageSMME)
+    {mf}{mn}{cc}{kehom}{CC}
+    (arrow:ArrowInProgrammingLanguage Host _ _ CC mf mn cc kehom) :  GeneralizedArrowInLanguage.
+
+  Definition TwoLevelLanguage := Reification Guest Host (me_i Host).
+
+  Context (GuestHost:TwoLevelLanguage).
+
+  Definition FlatObject (x:TypesL _ _ Host) :=
+    forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x).
+
+  Definition FlatSubCategory := FullSubcategory (TypesL _ _ Host) FlatObject.
+
+  Section Flattening.
+
+    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.
+
+  End Flattening.
+
+End GArrowInLanguage.