Context {T : Type}. (* types of the language *)
- Context (Judg : Type).
- Context (sequent : Tree ??T -> Tree ??T -> Judg).
+ Definition PLJudg := (Tree ??T) * (Tree ??T).
+ Definition sequent := @pair (Tree ??T) (Tree ??T).
Notation "cs |= ss" := (sequent cs ss) : pl_scope.
- Context {Rule : Tree ??Judg -> Tree ??Judg -> Type}.
+ Context {Rule : Tree ??PLJudg -> Tree ??PLJudg -> Type}.
Notation "H /⋯⋯/ C" := (ND Rule H C) : pl_scope.
Open Scope pl_scope.
Class ProgrammingLanguage :=
- { pl_eqv0 : @ND_Relation Judg Rule
- ; pl_snd :> @SequentND Judg Rule _ sequent
- ; pl_cnd :> @ContextND Judg Rule T sequent pl_snd
- ; pl_eqv1 :> @SequentND_Relation Judg Rule _ sequent pl_snd pl_eqv0
- ; pl_eqv :> @ContextND_Relation Judg Rule _ sequent pl_snd pl_cnd pl_eqv0 pl_eqv1
+ { pl_eqv0 : @ND_Relation PLJudg Rule
+ ; pl_snd :> @SequentND PLJudg Rule _ sequent
+ ; pl_cnd :> @ContextND PLJudg Rule T sequent pl_snd
+ ; pl_eqv1 :> @SequentND_Relation PLJudg Rule _ sequent pl_snd pl_eqv0
+ ; pl_eqv :> @ContextND_Relation PLJudg Rule _ sequent pl_snd pl_cnd pl_eqv0 pl_eqv1
}.
Notation "pf1 === pf2" := (@ndr_eqv _ _ pl_eqv _ _ pf1 pf2) : temporary_scope3.
simpl; eapply cndr_inert. apply pl_eqv. auto. auto.
Defined.
- Definition Types_binoidal : EBinoidalCat TypesL.
+ Definition Types_binoidal : EBinoidalCat TypesL (@T_Branch _).
refine
{| ebc_first := Types_first
; ebc_second := Types_second
auto.
Defined.
+ (* this tactical searches the environment; setoid_rewrite doesn't seem to be able to do that properly sometimes *)
+ Ltac nd_swap_ltac P EQV :=
+ match goal with
+ [ |- context [ (?F ** nd_id _) ;; (nd_id _ ** ?G) ] ] =>
+ set (@nd_swap _ _ EQV _ _ _ _ F G) as P
+ end.
+
Instance Types_assoc a b : Types_second a >>>> Types_first b <~~~> Types_first b >>>> Types_second a :=
{ ni_iso := fun c => Types_assoc_iso a c b }.
- intros; unfold eqv; simpl.
- admit.
- Defined.
+ intros.
+ Opaque nd_id.
+ simpl.
+ Transparent nd_id.
+
+ rename A into X.
+ rename B into Y.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) f) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+
+ clear q.
+ set (ni_commutes' (jud_mon_cancell pl_eqv) f) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects; try reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ Defined.
+
+ Instance Types_assoc_ll a b : Types_second (a,,b) <~~~> Types_second b >>>> Types_second a :=
+ { ni_iso := fun c => Types_assoc_iso a b c }.
+ intros.
+ Opaque nd_id.
+ simpl.
+ Transparent nd_id.
+
+ rename A into X.
+ rename B into Y.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) f) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+
+ clear q.
+ set (ni_commutes' (jud_mon_cancell pl_eqv) f) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects; try reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ Defined.
+
+ Instance Types_assoc_rr a b : Types_first (a,,b) <~~~> Types_first a >>>> Types_first b :=
+ { ni_iso := fun c => iso_inv _ _ (Types_assoc_iso c a b) }.
+ intros.
+ Opaque nd_id.
+ simpl.
+ Transparent nd_id.
+
+ rename A into X.
+ rename B into Y.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) f) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+
+ clear q.
+ set (ni_commutes' (jud_mon_cancell pl_eqv) f) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects; try reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ Defined.
Instance Types_cancelr : Types_first [] <~~~> functor_id _ :=
{ ni_iso := Types_cancelr_iso }.
- intros; simpl.
- admit.
+ intros.
+ Opaque nd_id.
+ simpl.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) f) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) f) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects; try reflexivity.
+ Transparent nd_id.
+ simpl.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
Defined.
Instance Types_cancell : Types_second [] <~~~> functor_id _ :=
{ ni_iso := Types_cancell_iso }.
- admit.
- Defined.
-
- Instance Types_assoc_ll a b : Types_second (a,,b) <~~~> Types_second b >>>> Types_second a :=
- { ni_iso := fun c => Types_assoc_iso a b c }.
- admit.
- Defined.
-
- Instance Types_assoc_rr a b : Types_first (a,,b) <~~~> Types_first a >>>> Types_first b :=
- { ni_iso := fun c => iso_inv _ _ (Types_assoc_iso c a b) }.
- admit.
+ intros.
+ Opaque nd_id.
+ simpl.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) f) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) f) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+
+ apply ndr_comp_respects; try reflexivity.
+ Transparent nd_id.
+ simpl.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
Defined.
- Instance Types_PreMonoidal : PreMonoidalCat Types_binoidal [] :=
+ Lemma TypesL_assoc_central a b c : CentralMorphism(H:=Types_binoidal) #((Types_assoc a b) c).
+ intros.
+ apply Build_CentralMorphism.
+ Opaque nd_id.
+ intros.
+ unfold bin_obj.
+ unfold ebc_bobj.
+ simpl.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) g) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) g) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects.
+ reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+
+ Opaque nd_id.
+ intros.
+ unfold bin_obj.
+ unfold ebc_bobj.
+ simpl.
+ unfold ehom.
+ symmetry.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) g) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) g) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects.
+ reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ Qed.
+
+ Lemma TypesL_cancell_central a : CentralMorphism(H:=Types_binoidal) #(Types_cancell a).
+ intros.
+ apply Build_CentralMorphism.
+ Opaque nd_id.
+ intros.
+ unfold bin_obj.
+ unfold ebc_bobj.
+ simpl.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) g) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) g) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects.
+ reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+
+ Opaque nd_id.
+ intros.
+ unfold bin_obj.
+ unfold ebc_bobj.
+ simpl.
+ unfold ehom.
+ symmetry.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) g) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) g) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects.
+ reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ Qed.
+
+ Lemma TypesL_cancelr_central a : CentralMorphism(H:=Types_binoidal) #(Types_cancelr a).
+ intros.
+ apply Build_CentralMorphism.
+ Opaque nd_id.
+ intros.
+ unfold bin_obj.
+ unfold ebc_bobj.
+ simpl.
+ unfold ehom.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) g) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) g) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects.
+ reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+
+ Opaque nd_id.
+ intros.
+ unfold bin_obj.
+ unfold ebc_bobj.
+ simpl.
+ unfold ehom.
+ symmetry.
+ nd_swap_ltac p pl_eqv.
+ setoid_rewrite p.
+ clear p.
+ setoid_rewrite (@nd_prod_split_left _ Rule pl_eqv _ _ _ []).
+ setoid_rewrite (@nd_prod_split_right _ Rule pl_eqv _ _ _ []).
+ repeat setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ setoid_rewrite <- (@ndr_comp_associativity _ Rule pl_eqv).
+
+ set (ni_commutes' (jud_mon_cancelr pl_eqv) g) as q.
+ Opaque nd_id.
+ simpl in q.
+ setoid_rewrite <- q.
+ clear q.
+
+ set (ni_commutes' (jud_mon_cancell pl_eqv) g) as q.
+ simpl in q.
+ set (coincide (pmon_triangle(PreMonoidalCat:=(Judgments_Category_premonoidal pl_eqv)))) as q'.
+ set (isos_forward_equal_then_backward_equal _ _ q') as qq.
+ simpl in qq.
+ setoid_rewrite qq in q.
+ clear q' qq.
+ setoid_rewrite <- q.
+
+ setoid_rewrite (@ndr_comp_associativity _ Rule pl_eqv).
+ apply ndr_comp_respects.
+ reflexivity.
+
+ Transparent nd_id.
+ apply (cndr_inert pl_cnd); auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ apply ndpc_comp; auto.
+ Qed.
+
+ Instance TypesL_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
}.
-(*
apply Build_Pentagon.
intros; simpl.
eapply cndr_inert. apply pl_eqv.
auto.
auto.
auto.
+
apply Build_Triangle; intros; simpl.
eapply cndr_inert. apply pl_eqv.
auto.
auto.
eapply cndr_inert. apply pl_eqv. auto.
auto.
-*)
-admit.
-admit.
intros; simpl; reflexivity.
intros; simpl; reflexivity.
- admit. (* assoc central *)
- admit. (* cancelr central *)
- admit. (* cancell central *)
+ apply TypesL_assoc_central.
+ apply TypesL_cancelr_central.
+ apply TypesL_cancell_central.
Defined.
- Definition TypesEnrichedInJudgments : Enrichment.
+ Definition TypesEnrichedInJudgments : SurjectiveEnrichment.
refine
- {| enr_v_mon := Judgments_Category_monoidal _
- ; enr_c_pm := Types_PreMonoidal
- ; enr_c_bin := Types_binoidal
+ {| senr_c_pm := TypesL_PreMonoidal
+ ; senr_v := JudgmentsL
+ ; senr_v_bin := Judgments_Category_binoidal _
+ ; senr_v_pmon := Judgments_Category_premonoidal _
+ ; senr_v_mon := Judgments_Category_monoidal _
+ ; senr_c_bin := Types_binoidal
+ ; senr_c := TypesL
|}.
Defined.
- Structure HasProductTypes :=
- {
- }.
-
- (*
- Lemma CartesianEnrMonoidal (e:PreMonoidalEnrichment)
- `(C:CartesianCat(Ob:= _)(Hom:= _)(C:=Underlying (enr_c e))) : MonoidalEnrichment e.
- admit.
- Defined.
- *)
-
- (* need to prove that if we have cartesian tuples we have cartesian contexts *)
- (*
- Definition LanguagesWithProductsAreSMME : HasProductTypes -> SurjectiveMonicMonoidalEnrichment TypesEnrichedInJudgments.
- admit.
- Defined.
- *)
End LanguageCategory.
End Programming_Language.
-(*
-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.
-*)
Implicit Arguments ND [ Judgment ].
projects / coq-hetmet.git / blobdiff