X-Git-Url: http://git.megacz.com/?p=coq-hetmet.git;a=blobdiff_plain;f=src%2FProgrammingLanguage.v;h=de7c7f0597ef6326645372d410a8978cbc33ffcd;hp=6dd9c714bbe28ca22f8a09634d18d5f7c667c5e0;hb=9444d329585e0dc3400a3bbb8155900f9ad62b92;hpb=e15a8b6d72e0b28af765acfda7ddad21b50704ee diff --git a/src/ProgrammingLanguage.v b/src/ProgrammingLanguage.v index 6dd9c71..de7c7f0 100644 --- a/src/ProgrammingLanguage.v +++ b/src/ProgrammingLanguage.v @@ -1,7 +1,7 @@ (*********************************************************************************************************************************) (* ProgrammingLanguage *) (* *) -(* Basic assumptions about programming languages . *) +(* Basic assumptions about programming languages. *) (* *) (*********************************************************************************************************************************) @@ -32,17 +32,7 @@ Require Import FreydCategories. Require Import Reification. 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 +40,6 @@ 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 +49,6 @@ 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 @@ -128,13 +94,13 @@ Section Programming_Language. Defined. Definition Types_first c : EFunctor TypesL TypesL (fun x => x,,c ). - refine {| efunc := fun x y => (nd_rule (@se_expand_right _ _ _ _ _ _ _ (@pl_sequent_join PL) c x y)) |}. + refine {| efunc := fun x y => (@se_expand_right _ _ _ _ _ _ _ (@pl_sequent_join PL) c x y) |}. intros; apply MonoidalCat_all_central. intros. unfold ehom. unfold hom. unfold identityProof. unfold eid. simpl. unfold identityProof. apply se_reflexive_right. intros. unfold ehom. unfold comp. simpl. unfold cutProof. - rewrite <- (@ndr_prod_preserves_comp _ _ pl_eqv _ _ [#se_expand_right _ c#] _ _ (nd_id1 (b|=c0)) - _ (nd_id1 (a,,c |= b,,c)) _ [#se_expand_right _ c#]). + rewrite <- (@ndr_prod_preserves_comp _ _ pl_eqv _ _ (se_expand_right _ c) _ _ (nd_id1 (b|=c0)) + _ (nd_id1 (a,,c |= b,,c)) _ (se_expand_right _ c)). setoid_rewrite (@ndr_comp_right_identity _ _ pl_eqv _ [a,, c |= b,, c]). setoid_rewrite (@ndr_comp_left_identity _ _ pl_eqv [b |= c0]). apply se_cut_right. @@ -142,13 +108,13 @@ Section Programming_Language. Definition Types_second c : EFunctor TypesL TypesL (fun x => c,,x). eapply Build_EFunctor. - instantiate (1:=(fun x y => (nd_rule (@se_expand_left _ _ _ _ _ _ _ (@pl_sequent_join PL) c x y)))). + instantiate (1:=(fun x y => ((@se_expand_left _ _ _ _ _ _ _ (@pl_sequent_join PL) c x y)))). intros; apply MonoidalCat_all_central. intros. unfold ehom. unfold hom. unfold identityProof. unfold eid. simpl. unfold identityProof. apply se_reflexive_left. intros. unfold ehom. unfold comp. simpl. unfold cutProof. - rewrite <- (@ndr_prod_preserves_comp _ _ pl_eqv _ _ [#se_expand_left _ c#] _ _ (nd_id1 (b|=c0)) - _ (nd_id1 (c,,a |= c,,b)) _ [#se_expand_left _ c#]). + rewrite <- (@ndr_prod_preserves_comp _ _ pl_eqv _ _ (se_expand_left _ c) _ _ (nd_id1 (b|=c0)) + _ (nd_id1 (c,,a |= c,,b)) _ (se_expand_left _ c)). setoid_rewrite (@ndr_comp_right_identity _ _ pl_eqv _ [c,,a |= c,,b]). setoid_rewrite (@ndr_comp_left_identity _ _ pl_eqv [b |= c0]). apply se_cut_left. @@ -161,10 +127,39 @@ Section Programming_Language. |}. Defined. - Definition Types_PreMonoidal : PreMonoidalCat Types_binoidal []. + Definition Types_assoc a b : Types_second a >>>> Types_first b <~~~> Types_first b >>>> Types_second a. + admit. + Defined. + + Definition Types_cancelr : Types_first [] <~~~> functor_id _. + admit. + Defined. + + Definition Types_cancell : Types_second [] <~~~> functor_id _. admit. Defined. + Definition Types_assoc_ll a b : Types_second (a,,b) <~~~> Types_second b >>>> Types_second a. + admit. + Defined. + + Definition Types_assoc_rr a b : Types_first (a,,b) <~~~> Types_first a >>>> Types_first b. + admit. + Defined. + + Instance Types_PreMonoidal : PreMonoidalCat Types_binoidal [] := + { pmon_assoc := Types_assoc + ; pmon_cancell := Types_cancell + ; pmon_cancelr := Types_cancelr + ; pmon_assoc_rr := Types_assoc_rr + ; pmon_assoc_ll := Types_assoc_ll + }. + admit. (* pentagon law *) + admit. (* triangle law *) + admit. (* assoc_rr/assoc coherence *) + admit. (* assoc_ll/assoc coherence *) + Defined. + Definition TypesEnrichedInJudgments : Enrichment. refine {| enr_c := TypesL |}. Defined.