src/ProgrammingLanguageArrow.v

   1 (*********************************************************************************************************************************)
   2 (* ProgrammingLanguageArrow                                                                                                      *)
   3 (*                                                                                                                               *)
   4 (*   Arrows in ProgrammingLanguages.                                                                                             *)
   5 (*                                                                                                                               *)
   6 (*********************************************************************************************************************************)
   7
   8 Generalizable All Variables.
   9 Require Import Preamble.
  10 Require Import General.
  11 Require Import Categories_ch1_3.
  12 Require Import InitialTerminal_ch2_2.
  13 Require Import Functors_ch1_4.
  14 Require Import Isomorphisms_ch1_5.
  15 Require Import ProductCategories_ch1_6_1.
  16 Require Import OppositeCategories_ch1_6_2.
  17 Require Import Enrichment_ch2_8.
  18 Require Import Subcategories_ch7_1.
  19 Require Import NaturalTransformations_ch7_4.
  20 Require Import NaturalIsomorphisms_ch7_5.
  21 Require Import MonoidalCategories_ch7_8.
  22 Require Import Coherence_ch7_8.
  23 Require Import Enrichment_ch2_8.
  24 Require Import RepresentableStructure_ch7_2.
  25 Require Import FunctorCategories_ch7_7.
  26
  27 Require Import NaturalDeduction.
  28 Require Import NaturalDeductionCategory.
  29
  30 Require Import ProgrammingLanguage.
  31 Require Import ProgrammingLanguageGeneralizedArrow.
  32 Require Import FreydCategories.
  33
  34 Section ArrowInLanguage.
  35
  36   Section ArrowInLanguage.
  37     Context {MF}{mn:MonoidalCat TypesL (fun x => (fst_obj _ _ x),,(snd_obj _ _ x)) MF []} (CC:CartesianCat mn).
  38     Context {Kehom}(K:@ECategory _ _ TypesL _ mn [] mn TypesL Kehom).
  39     Context {bc:BinoidalCat (Underlying K) (@T_Branch _)}.
  40     Context (pmc:@PreMonoidalCat _ _ _ _ bc (@one _ _ _ (car_terminal(CartesianCat:=CC)))).
  41     Definition ArrowInProgrammingLanguage := @FreydCategory _ _ _ _ _ _ mn _ _ _ _ pmc.
  42   End ArrowInLanguage.
  43
  44   Definition ArrowsAreGeneralizedArrows (Host:ProgrammingLanguageSMME)
  45     {mf}{mn}{cc}{kehom}{CC}
  46     (arrow:ArrowInProgrammingLanguage Host _ _ CC mf mn cc kehom) :  GeneralizedArrowInLanguage.
  47
  48   Definition TwoLevelLanguage := Reification Guest Host (me_i Host).
  49
  50   Context (GuestHost:TwoLevelLanguage).
  51
  52   Definition FlatObject (x:TypesL _ _ Host) :=
  53     forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x).
  54
  55   Definition FlatSubCategory := FullSubcategory (TypesL _ _ Host) FlatObject.
  56
  57   Section Flattening.
  58
  59     Context  (F:Retraction (TypesL _ _ Host) FlatSubCategory).
  60     Definition FlatteningOfReification := garrow_from_reification Guest Host GuestHost >>>> F.
  61     Lemma FlatteningIsNotDestructive :
  62       FlatteningOfReification >>>> retraction_retraction F >>>> HomFunctor _ (me_i Host) ~~~~ GuestHost.
  63       admit.
  64       Qed.
  65
  66   End Flattening.
  67
  68 End GArrowInLanguage.