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.
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.