src/ProgrammingLanguageReification.v

   1 (*********************************************************************************************************************************)
   2 (* ProgrammingLanguageReification                                                                                                *)
   3 (*                                                                                                                               *)
   4 (*   Reifications 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 Reification.
  28 Require Import NaturalDeduction.
  29 Require Import NaturalDeductionCategory.
  30 Require Import ProgrammingLanguage.
  31 Require Import ProgrammingLanguageCategory.
  32 Require Import Enrichments.
  33
  34 Section ProgrammingLanguageReification.
  35
  36   Definition TwoLevelLanguage `(Guest:ProgrammingLanguage) `(Host:ProgrammingLanguage)
  37     := Reification (TypesEnrichedInJudgments Guest) (TypesEnrichedInJudgments Host) [].
  38
  39   Inductive NLevelLanguage : forall (n:nat) `(PL:ProgrammingLanguage), Type :=
  40   | NLevelLanguage_zero : forall `(lang:ProgrammingLanguage),
  41                             NLevelLanguage O lang
  42   | NLevelLanguage_succ : forall `(L1:ProgrammingLanguage) `(L2:ProgrammingLanguage) n,
  43                             TwoLevelLanguage L1 L2 -> NLevelLanguage n L1 -> NLevelLanguage (S n) L2.
  44
  45   (*
  46   Definition OmegaLevelLanguage : Type :=
  47     { f : nat -> ProgrammingLanguage
  48     & forall n, TwoLevelLanguage (f n) (f (S n)) }.
  49     *)
  50
  51 End ProgrammingLanguageReification.
  52
  53 (*
  54   Structure ProgrammingLanguage :=
  55   { plsmme_t       : Type
  56   ; plsmme_judg    : Type
  57   ; plsmme_sequent : Tree ??plsmme_t -> Tree ??plsmme_t -> plsmme_judg
  58   ; plsmme_rule    : Tree ??plsmme_judg -> Tree ??plsmme_judg -> Type
  59   ; plsmme_pl      : @ProgrammingLanguage plsmme_t plsmme_judg plsmme_sequent plsmme_rule
  60   ; plsmme_smme    : SurjectiveEnrichment (TypesEnrichedInJudgments _ _ plsmme_pl)
  61   }.
  62   Coercion plsmme_pl   : ProgrammingLanguage >-> ProgrammingLanguage.
  63   Coercion plsmme_smme : ProgrammingLanguage >-> SurjectiveMonicMonoidalEnrichment.
  64 *)