X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FProgrammingLanguage.v;h=3a8ce8eb188211dff503518b4769e5483c927a1f;hp=657a69f216befb695d3518a36efa0138cde48468;hb=9eb30966bc3fdf52921925079331f25de339a36c;hpb=61fb093700aab006b77998d1cbd30235e144ca1f diff --git a/src/ProgrammingLanguage.v b/src/ProgrammingLanguage.v index 657a69f..3a8ce8e 100644 --- a/src/ProgrammingLanguage.v +++ b/src/ProgrammingLanguage.v @@ -1,7 +1,7 @@ (*********************************************************************************************************************************) (* ProgrammingLanguage *) (* *) -(* Basic assumptions about programming languages . *) +(* Basic assumptions about programming languages. *) (* *) (*********************************************************************************************************************************) @@ -34,15 +34,6 @@ Require Import GeneralizedArrow. Require Import GeneralizedArrowFromReification. Require Import ReificationFromGeneralizedArrow. -(* - * Everything in the rest of this section is just groundwork meant to - * build up to the definition of the ProgrammingLanguage class, which - * appears at the end of the section. References to "the instance" - * mean instances of that class. Think of this section as being one - * big Class { ... } definition, except that we declare most of the - * stuff outside the curly brackets in order to take advantage of - * Coq's section mechanism. - *) Section Programming_Language. Context {T : Type}. (* types of the language *) @@ -50,12 +41,6 @@ Section Programming_Language. Context (Judg : Type). Context (sequent : Tree ??T -> Tree ??T -> Judg). Notation "cs |= ss" := (sequent cs ss) : pl_scope. - (* Because of term irrelevance we need only store the *erased* (def - * 4.4) trees; for this reason there is no Coq type directly - * corresponding to productions $e$ and $x$ of 4.1.1, and TreeOT can - * be used for productions $\Gamma$ and $\Sigma$ *) - - (* to do: sequent calculus equals natural deduction over sequents, theorem equals sequent with null antecedent, *) Context {Rule : Tree ??Judg -> Tree ??Judg -> Type}. @@ -65,24 +50,6 @@ Section Programming_Language. Open Scope nd_scope. Open Scope pl_scope. - (* - * - * Note that from this abstract interface, the terms (expressions) - * in the proof are not accessible at all; they don't need to be -- - * so long as we have access to the equivalence relation upon - * proof-conclusions. Moreover, hiding the expressions actually - * makes the encoding in CiC work out easier for two reasons: - * - * 1. Because the denotation function is provided a proof rather - * than a term, it is a total function (the denotation function is - * often undefined for ill-typed terms). - * - * 2. We can define arr_composition of proofs without having to know how - * to compose expressions. The latter task is left up to the client - * function which extracts an expression from a completed proof. - * - * This also means that we don't need an explicit proof obligation for 4.1.2. - *) Class ProgrammingLanguage := { pl_eqv : @ND_Relation Judg Rule where "pf1 === pf2" := (@ndr_eqv _ _ pl_eqv _ _ pf1 pf2) ; pl_tsr :> @TreeStructuralRules Judg Rule T sequent @@ -179,70 +146,68 @@ Section Programming_Language. Defined. End LanguageCategory. +End Programming_Language. - Structure ProgrammingLanguageSMME := - { plsmme_pl : ProgrammingLanguage - ; plsmme_smme : SurjectiveMonicMonoidalEnrichment (TypesEnrichedInJudgments plsmme_pl) - }. - Coercion plsmme_pl : ProgrammingLanguageSMME >-> ProgrammingLanguage. - Coercion plsmme_smme : ProgrammingLanguageSMME >-> SurjectiveMonicMonoidalEnrichment. - - Section ArrowInLanguage. - Context (Host:ProgrammingLanguageSMME). - Context `(CC:CartesianCat (me_mon Host)). - Context `(K:@ECategory _ _ _ _ _ _ (@car_mn _ _ _ _ _ _ _ CC) C Kehom). - Context `(pmc:PreMonoidalCat K bobj mobj (@one _ _ _ (cartesian_terminal C))). - (* FIXME *) - (* - Definition ArrowInProgrammingLanguage := - @FreydCategory _ _ _ _ _ _ (@car_mn _ _ _ _ _ _ _ CC) _ _ _ _ pmc. - *) - End ArrowInLanguage. - - Section GArrowInLanguage. - Context (Guest:ProgrammingLanguageSMME). - Context (Host :ProgrammingLanguageSMME). - Definition GeneralizedArrowInLanguage := GeneralizedArrow Guest Host. - - (* FIXME - Definition ArrowsAreGeneralizedArrows : ArrowInProgrammingLanguage -> GeneralizedArrowInLanguage. - *) - Definition TwoLevelLanguage := Reification Guest Host (me_i Host). - - Context (GuestHost:TwoLevelLanguage). - - Definition FlatObject (x:TypesL Host) := - forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x). - - Definition FlatSubCategory := FullSubcategory (TypesL Host) FlatObject. - - Section Flattening. - - Context (F:Retraction (TypesL Host) FlatSubCategory). - Definition FlatteningOfReification := garrow_from_reification Guest Host GuestHost >>>> F. - Lemma FlatteningIsNotDestructive : - FlatteningOfReification >>>> retraction_retraction F >>>> RepresentableFunctor _ (me_i Host) ~~~~ GuestHost. - admit. - Qed. - - End Flattening. - - End GArrowInLanguage. - - 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)) }. - - Close Scope temporary_scope3. - Close Scope pl_scope. - Close Scope nd_scope. - Close Scope pf_scope. +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 : SurjectiveMonicMonoidalEnrichment (TypesEnrichedInJudgments _ _ plsmme_pl) +}. +Coercion plsmme_pl : ProgrammingLanguageSMME >-> ProgrammingLanguage. +Coercion plsmme_smme : ProgrammingLanguageSMME >-> SurjectiveMonicMonoidalEnrichment. + +Section ArrowInLanguage. + Context (Host:ProgrammingLanguageSMME). + Context `(CC:CartesianCat (me_mon Host)). + Context `(K:@ECategory _ _ _ _ _ _ (@car_mn _ _ _ _ _ _ _ CC) C Kehom). + Context `(pmc:PreMonoidalCat K bobj mobj (@one _ _ _ (cartesian_terminal C))). + (* FIXME *) + (* + Definition ArrowInProgrammingLanguage := + @FreydCategory _ _ _ _ _ _ (@car_mn _ _ _ _ _ _ _ CC) _ _ _ _ pmc. + *) +End ArrowInLanguage. + +Section GArrowInLanguage. + Context (Guest:ProgrammingLanguageSMME). + Context (Host :ProgrammingLanguageSMME). + Definition GeneralizedArrowInLanguage := GeneralizedArrow Guest Host. + + (* FIXME + Definition ArrowsAreGeneralizedArrows : ArrowInProgrammingLanguage -> GeneralizedArrowInLanguage. + *) + Definition TwoLevelLanguage := Reification Guest Host (me_i Host). + + Context (GuestHost:TwoLevelLanguage). + + Definition FlatObject (x:TypesL _ _ Host) := + forall y1 y2, not ((reification_r_obj GuestHost y1 y2)=x). + + Definition FlatSubCategory := FullSubcategory (TypesL _ _ Host) FlatObject. + + Section Flattening. + + Context (F:Retraction (TypesL _ _ Host) FlatSubCategory). + Definition FlatteningOfReification := garrow_from_reification Guest Host GuestHost >>>> F. + Lemma FlatteningIsNotDestructive : + FlatteningOfReification >>>> retraction_retraction F >>>> RepresentableFunctor _ (me_i Host) ~~~~ GuestHost. + admit. + Qed. -End Programming_Language. + End Flattening. + +End GArrowInLanguage. + +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)) }. + Implicit Arguments ND [ Judgment ].