src/ProgrammingLanguageGeneralizedArrow.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 FreydCategories.
  31
  32 Require Import GeneralizedArrowFromReification.
  33 Section GArrowInLanguage.
  34
  35   Definition GeneralizedArrowInLanguage (Guest:ProgrammingLanguageSMME) (Host :ProgrammingLanguageSMME)
  36     := GeneralizedArrow Guest Host.
  37
  38   Definition ArrowsAreGeneralizedArrows (Host:ProgrammingLanguageSMME)
  39     {mf}{mn}{cc}{kehom}{CC}
  40     (arrow:ArrowInProgrammingLanguage Host _ _ CC mf mn cc kehom) :  GeneralizedArrowInLanguage.
  41
  42   Definition TwoLevelLanguage := Reification Guest Host (me_i Host).
  43
  44   Context (GuestHost:TwoLevelLanguage).
  45
  46   Definition FlatObject (x:TypesL _ _ Host) :=
  47     forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x).
  48
  49   Definition FlatSubCategory := FullSubcategory (TypesL _ _ Host) FlatObject.
  50
  51   Section Flattening.
  52
  53     Context  (F:Retraction (TypesL _ _ Host) FlatSubCategory).
  54     Definition FlatteningOfReification := garrow_from_reification Guest Host GuestHost >>>> F.
  55     Lemma FlatteningIsNotDestructive :
  56       FlatteningOfReification >>>> retraction_retraction F >>>> HomFunctor _ (me_i Host) ~~~~ GuestHost.
  57       admit.
  58       Qed.
  59
  60   End Flattening.
  61
  62 End GArrowInLanguage.