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
  32 Definition TwoLevelLanguage (Guest Host:ProgrammingLanguageSMME)
  33   := Reification Guest Host (me_i Host).
  34
  35 Inductive NLevelLanguage : nat -> ProgrammingLanguageSMME -> Type :=
  36 | NLevelLanguage_zero : forall lang,    NLevelLanguage O lang
  37 | NLevelLanguage_succ : forall (L1 L2:ProgrammingLanguageSMME) n,
  38                           TwoLevelLanguage L1 L2 -> NLevelLanguage n L1 -> NLevelLanguage (S n) L2.
  39
  40 Definition OmegaLevelLanguage : Type :=
  41   { f : nat -> ProgrammingLanguageSMME
  42   & forall n, TwoLevelLanguage (f n) (f (S n)) }.
  43