Require Import NaturalDeduction.
Require Import NaturalDeductionCategory.
Require Import ProgrammingLanguage.
+Require Import ProgrammingLanguageCategory.
+Require Import Enrichments.
-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.
+Section ProgrammingLanguageReification.
-Definition OmegaLevelLanguage : Type :=
- { f : nat -> ProgrammingLanguageSMME
- & forall n, TwoLevelLanguage (f n) (f (S n)) }.
+ Definition TwoLevelLanguage `(Guest:ProgrammingLanguage) `(Host:ProgrammingLanguage)
+ := Reification (TypesEnrichedInJudgments Guest) (TypesEnrichedInJudgments Host) [].
+
+ Inductive NLevelLanguage : forall (n:nat) `(PL:ProgrammingLanguage), Type :=
+ | NLevelLanguage_zero : forall `(lang:ProgrammingLanguage),
+ NLevelLanguage O lang
+ | NLevelLanguage_succ : forall `(L1:ProgrammingLanguage) `(L2:ProgrammingLanguage) n,
+ TwoLevelLanguage L1 L2 -> NLevelLanguage n L1 -> NLevelLanguage (S n) L2.
+
+ (*
+ Definition OmegaLevelLanguage : Type :=
+ { f : nat -> ProgrammingLanguage
+ & forall n, TwoLevelLanguage (f n) (f (S n)) }.
+ *)
+
+End ProgrammingLanguageReification.
+
+(*
+ Structure ProgrammingLanguage :=
+ { plsmme_t : Type
+ ; plsmme_judg : Type
+ ; plsmme_sequent : Tree ??plsmme_t -> Tree ??plsmme_t -> plsmme_judg
+ ; plsmme_rule : Tree ??plsmme_judg -> Tree ??plsmme_judg -> Type
+ ; plsmme_pl : @ProgrammingLanguage plsmme_t plsmme_judg plsmme_sequent plsmme_rule
+ ; plsmme_smme : SurjectiveEnrichment (TypesEnrichedInJudgments _ _ plsmme_pl)
+ }.
+ Coercion plsmme_pl : ProgrammingLanguage >-> ProgrammingLanguage.
+ Coercion plsmme_smme : ProgrammingLanguage >-> SurjectiveMonicMonoidalEnrichment.
+*)