Require Import NaturalDeduction.
Require Import NaturalDeductionCategory.
-Require Import FreydCategories.
+Require Import Enrichments.
+Require Import Reification.
+Require Import GeneralizedArrow.
+Require Import ProgrammingLanguageEnrichment.
-Require Import GeneralizedArrowFromReification.
-Section GArrowInLanguage.
+Section ProgrammingLanguageGeneralizedArrow.
- Definition GeneralizedArrowInLanguage (Guest:ProgrammingLanguageSMME) (Host :ProgrammingLanguageSMME)
- := GeneralizedArrow Guest Host.
+ Context
+ `(Guest : ProgrammingLanguage)
+ `(Host : ProgrammingLanguage)
+ (HostMonoidal : MonoidalEnrichment (TypesEnrichedInJudgments Host))
+ (HostMonic : MonicEnrichment (TypesEnrichedInJudgments Host)).
- Definition ArrowsAreGeneralizedArrows (Host:ProgrammingLanguageSMME)
- {mf}{mn}{cc}{kehom}{CC}
- (arrow:ArrowInProgrammingLanguage Host _ _ CC mf mn cc kehom) : GeneralizedArrowInLanguage.
+ Definition GeneralizedArrowInLanguage
+ := GeneralizedArrow (TypesEnrichedInJudgments Guest) HostMonoidal.
- Definition TwoLevelLanguage := Reification Guest Host (me_i Host).
+End ProgrammingLanguageGeneralizedArrow.
- 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.