1 (*********************************************************************************************************************************)
2 (* ProgrammingLanguageReification *)
4 (* Reifications in ProgrammingLanguages. *)
6 (*********************************************************************************************************************************)
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.
27 Require Import Reification.
28 Require Import NaturalDeduction.
29 Require Import NaturalDeductionCategory.
30 Require Import ProgrammingLanguage.
33 Structure ProgrammingLanguageSMME :=
36 ; plsmme_sequent : Tree ??plsmme_t -> Tree ??plsmme_t -> plsmme_judg
37 ; plsmme_rule : Tree ??plsmme_judg -> Tree ??plsmme_judg -> Type
38 ; plsmme_pl : @ProgrammingLanguage plsmme_t plsmme_judg plsmme_sequent plsmme_rule
39 ; plsmme_smme : SurjectiveEnrichment (TypesEnrichedInJudgments _ _ plsmme_pl)
41 Coercion plsmme_pl : ProgrammingLanguageSMME >-> ProgrammingLanguage.
42 Coercion plsmme_smme : ProgrammingLanguageSMME >-> SurjectiveMonicMonoidalEnrichment.
46 `(Guest : ProgrammingLanguage)
47 `(Host : ProgrammingLanguage)
48 (HostMonoidal : MonoidalEnrichment (TypesEnrichedInJudgments Host))
49 (HostMonic : MonicEnrichment (TypesEnrichedInJudgments Host)).
51 Definition TwoLevelLanguage (Guest Host:ProgrammingLanguageSMME)
52 := Reification Guest Host (me_i Host).
54 Inductive NLevelLanguage : nat -> ProgrammingLanguageSMME -> Type :=
55 | NLevelLanguage_zero : forall lang, NLevelLanguage O lang
56 | NLevelLanguage_succ : forall (L1 L2:ProgrammingLanguageSMME) n,
57 TwoLevelLanguage L1 L2 -> NLevelLanguage n L1 -> NLevelLanguage (S n) L2.
59 Definition OmegaLevelLanguage : Type :=
60 { f : nat -> ProgrammingLanguageSMME
61 & forall n, TwoLevelLanguage (f n) (f (S n)) }.