lots of cleanup

[coq-hetmet.git] / src / ProgrammingLanguageReification.v

diff --git a/src/ProgrammingLanguageReification.v b/src/ProgrammingLanguageReification.v
new file mode 100644 (file)
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--- /dev/null
+++ b/src/ProgrammingLanguageReification.v
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+(*********************************************************************************************************************************)
+(* ProgrammingLanguageReification                                                                                                *)
+(*                                                                                                                               *)
+(*   Reifications in ProgrammingLanguages.                                                                                       *)
+(*                                                                                                                               *)
+(*********************************************************************************************************************************)
+
+Generalizable All Variables.
+Require Import Preamble.
+Require Import General.
+Require Import Categories_ch1_3.
+Require Import InitialTerminal_ch2_2.
+Require Import Functors_ch1_4.
+Require Import Isomorphisms_ch1_5.
+Require Import ProductCategories_ch1_6_1.
+Require Import OppositeCategories_ch1_6_2.
+Require Import Enrichment_ch2_8.
+Require Import Subcategories_ch7_1.
+Require Import NaturalTransformations_ch7_4.
+Require Import NaturalIsomorphisms_ch7_5.
+Require Import MonoidalCategories_ch7_8.
+Require Import Coherence_ch7_8.
+Require Import Enrichment_ch2_8.
+Require Import RepresentableStructure_ch7_2.
+Require Import FunctorCategories_ch7_7.
+
+Require Import Reification.
+Require Import NaturalDeduction.
+Require Import NaturalDeductionCategory.
+Require Import ProgrammingLanguage.
+
+Inductive NLevelLanguage : nat -> ProgrammingLanguageSMME -> Type :=
+| NLevelLanguage_zero : forall lang,    NLevelLanguage O lang
+| NLevelLanguage_succ : forall (L1 L2:ProgrammingLanguageSMME) n,
+                          TwoLevelLanguage L1 L2 -> NLevelLanguage n L1 -> NLevelLanguage (S n) L2.
+
+Definition OmegaLevelLanguage : Type :=
+  { f : nat -> ProgrammingLanguageSMME
+  & forall n, TwoLevelLanguage (f n) (f (S n)) }.