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.
31 Require Import Enrichments.
33 Section ProgrammingLanguageReification.
35 Definition TwoLevelLanguage `(Guest:ProgrammingLanguage) `(Host:ProgrammingLanguage)
36 := Reification (TypesEnrichedInJudgments Guest) (TypesEnrichedInJudgments Host) [].
38 Inductive NLevelLanguage : forall (n:nat) `(PL:ProgrammingLanguage), Type :=
39 | NLevelLanguage_zero : forall `(lang:ProgrammingLanguage),
41 | NLevelLanguage_succ : forall `(L1:ProgrammingLanguage) `(L2:ProgrammingLanguage) n,
42 TwoLevelLanguage L1 L2 -> NLevelLanguage n L1 -> NLevelLanguage (S n) L2.
45 Definition OmegaLevelLanguage : Type :=
46 { f : nat -> ProgrammingLanguage
47 & forall n, TwoLevelLanguage (f n) (f (S n)) }.
50 End ProgrammingLanguageReification.
53 Structure ProgrammingLanguage :=
56 ; plsmme_sequent : Tree ??plsmme_t -> Tree ??plsmme_t -> plsmme_judg
57 ; plsmme_rule : Tree ??plsmme_judg -> Tree ??plsmme_judg -> Type
58 ; plsmme_pl : @ProgrammingLanguage plsmme_t plsmme_judg plsmme_sequent plsmme_rule
59 ; plsmme_smme : SurjectiveEnrichment (TypesEnrichedInJudgments _ _ plsmme_pl)
61 Coercion plsmme_pl : ProgrammingLanguage >-> ProgrammingLanguage.
62 Coercion plsmme_smme : ProgrammingLanguage >-> SurjectiveMonicMonoidalEnrichment.