(*********************************************************************************************************************************) (* 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. (* Structure ProgrammingLanguageSMME := { 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 : ProgrammingLanguageSMME >-> ProgrammingLanguage. Coercion plsmme_smme : ProgrammingLanguageSMME >-> SurjectiveMonicMonoidalEnrichment. *) Context `(Guest : ProgrammingLanguage) `(Host : ProgrammingLanguage) (HostMonoidal : MonoidalEnrichment (TypesEnrichedInJudgments Host)) (HostMonic : MonicEnrichment (TypesEnrichedInJudgments Host)). Definition TwoLevelLanguage (Guest Host:ProgrammingLanguageSMME) := Reification Guest Host (me_i Host). 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)) }.