+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
-
-notation "hvbox( ⦃ term 46 h , break term 46 L ⦄ ⊢ break term 46 T1 •* break [ term 46 g ] break term 46 T2 )"
- non associative with precedence 45
- for @{ 'StaticTypeStar $h $g $L $T1 $T2 }.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦃ term 46 G , break term 46 L ⦄ ⊢ break term 46 T1 •* break [ term 46 h, break term 46 g ] break term 46 T2 )"
+ non associative with precedence 45
+ for @{ 'StaticTypeStar $h $g $G $L $T1 $T2 }.
+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||M|| *)
-(* ||A|| A project by Andrea Asperti *)
-(* ||T|| *)
-(* ||I|| Developers: *)
-(* ||T|| The HELM team. *)
-(* ||A|| http://helm.cs.unibo.it *)
-(* \ / *)
-(* \ / This file is distributed under the terms of the *)
-(* v GNU General Public License Version 2 *)
-(* *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
-
-notation "hvbox( L1 ⊢ ⧫ * break term 46 T ≡ break term 46 L2 )"
- non associative with precedence 45
- for @{ 'Unfold $L1 $T $L2 }.
--- /dev/null
+(**************************************************************************)
+(* ___ *)
+(* ||M|| *)
+(* ||A|| A project by Andrea Asperti *)
+(* ||T|| *)
+(* ||I|| Developers: *)
+(* ||T|| The HELM team. *)
+(* ||A|| http://helm.cs.unibo.it *)
+(* \ / *)
+(* \ / This file is distributed under the terms of the *)
+(* v GNU General Public License Version 2 *)
+(* *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM λδ ****************************************)
+
+notation "hvbox( ⦃ term 46 G, break term 46 L1 ⦄ ⊢ ⧫ * break term 46 T ≡ break term 46 L2 )"
+ non associative with precedence 45
+ for @{ 'Unfold $G $L1 $T $L2 }.
(* *)
(**************************************************************************)
-include "basic_2/notation/relations/statictypestar_5.ma".
+include "basic_2/notation/relations/statictypestar_6.ma".
include "basic_2/static/ssta.ma".
(* ITERATED STRATIFIED STATIC TYPE ASSIGNMENT FOR TERMS *********************)
(* Note: includes: stass_refl *)
-definition sstas: ∀h. sd h → lenv → relation term ≝
- λh,g,L. star … (ssta_step h g L).
+definition sstas: ∀h. sd h → genv → lenv → relation term ≝
+ λh,g,G,L. star … (ssta_step h g G L).
interpretation "iterated stratified static type assignment (term)"
- 'StaticTypeStar h g L T U = (sstas h g L T U).
+ 'StaticTypeStar h g G L T U = (sstas h g G L T U).
(* Basic eliminators ********************************************************)
-lemma sstas_ind: ∀h,g,L,T. ∀R:predicate term.
+lemma sstas_ind: ∀h,g,G,L,T. ∀R:predicate term.
R T → (
∀U1,U2,l. ⦃G, L⦄ ⊢ T •* [h, g] U1 → ⦃G, L⦄ ⊢ U1 •[h, g] ⦃l+1, U2⦄ →
R U1 → R U2
) →
∀U. ⦃G, L⦄ ⊢ T •*[h, g] U → R U.
-#h #g #L #T #R #IH1 #IH2 #U #H elim H -U //
+#h #g #G #L #T #R #IH1 #IH2 #U #H elim H -U //
#U1 #U2 #H * /2 width=5/
qed-.
-lemma sstas_ind_dx: ∀h,g,L,U2. ∀R:predicate term.
+lemma sstas_ind_dx: ∀h,g,G,L,U2. ∀R:predicate term.
R U2 → (
∀T,U1,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •* [h, g] U2 →
R U1 → R T
) →
∀T. ⦃G, L⦄ ⊢ T •*[h, g] U2 → R T.
-#h #g #L #U2 #R #IH1 #IH2 #T #H @(star_ind_l … T H) -T //
+#h #g #G #L #U2 #R #IH1 #IH2 #T #H @(star_ind_l … T H) -T //
#T #T0 * /2 width=5/
qed-.
(* Basic properties *********************************************************)
-lemma sstas_refl: ∀h,g,L. reflexive … (sstas h g L).
+lemma sstas_refl: ∀h,g,G,L. reflexive … (sstas h g G L).
// qed.
-lemma ssta_sstas: ∀h,g,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U⦄ → ⦃G, L⦄ ⊢ T •*[h, g] U.
+lemma ssta_sstas: ∀h,g,G,L,T,U,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l+1, U⦄ → ⦃G, L⦄ ⊢ T •*[h, g] U.
/3 width=2 by R_to_star, ex_intro/ qed. (**) (* auto fails without trace *)
-lemma sstas_strap1: ∀h,g,L,T1,T2,U2,l. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ →
+lemma sstas_strap1: ∀h,g,G,L,T1,T2,U2,l. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 → ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ →
⦃G, L⦄ ⊢ T1 •*[h, g] U2.
/3 width=4 by sstep, ex_intro/ (**) (* auto fails without trace *)
qed.
-lemma sstas_strap2: ∀h,g,L,T1,U1,U2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •*[h, g] U2 →
+lemma sstas_strap2: ∀h,g,G,L,T1,U1,U2,l. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l+1, U1⦄ → ⦃G, L⦄ ⊢ U1 •*[h, g] U2 →
⦃G, L⦄ ⊢ T1 •*[h, g] U2.
/3 width=3 by star_compl, ex_intro/ (**) (* auto fails without trace *)
qed.
(* Basic inversion lemmas ***************************************************)
-lemma sstas_inv_bind1: ∀h,g,a,I,L,Y,X,U. ⦃G, L⦄ ⊢ ⓑ{a,I}Y.X •*[h, g] U →
- ∃∃Z. ⦃h, L.ⓑ{I}Y⦄ ⊢ X •*[h, g] Z & U = ⓑ{a,I}Y.Z.
-#h #g #a #I #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
+lemma sstas_inv_bind1: ∀h,g,a,I,G,L,Y,X,U. ⦃G, L⦄ ⊢ ⓑ{a,I}Y.X •*[h, g] U →
+ ∃∃Z. ⦃G, L.ⓑ{I}Y⦄ ⊢ X •*[h, g] Z & U = ⓑ{a,I}Y.Z.
+#h #g #a #I #G #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
#T #U #l #_ #HTU * #Z #HXZ #H destruct
elim (ssta_inv_bind1 … HTU) -HTU #Z0 #HZ0 #H destruct /3 width=4/
qed-.
-lemma sstas_inv_appl1: ∀h,g,L,Y,X,U. ⦃G, L⦄ ⊢ ⓐY.X •*[h, g] U →
+lemma sstas_inv_appl1: ∀h,g,G,L,Y,X,U. ⦃G, L⦄ ⊢ ⓐY.X •*[h, g] U →
∃∃Z. ⦃G, L⦄ ⊢ X •*[h, g] Z & U = ⓐY.Z.
-#h #g #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
+#h #g #G #L #Y #X #U #H @(sstas_ind … H) -U /2 width=3/
#T #U #l #_ #HTU * #Z #HXZ #H destruct
elim (ssta_inv_appl1 … HTU) -HTU #Z0 #HZ0 #H destruct /3 width=4/
qed-.
(* Properties on atomic arity assignment for terms **************************)
-lemma sstas_aaa: ∀h,g,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
+lemma sstas_aaa: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
∀A. ⦃G, L⦄ ⊢ T ⁝ A → ⦃G, L⦄ ⊢ U ⁝ A.
-#h #g #L #T #U #H @(sstas_ind_dx … H) -T // /3 width=6/
+#h #g #G #L #T #U #H @(sstas_ind_dx … H) -T // /3 width=6/
qed.
(* Advanced forward lemmas **************************************************)
-lemma sstas_fwd_correct: ∀h,g,L,T1,U1,l1. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l1, U1⦄ →
+lemma sstas_fwd_correct: ∀h,g,G,L,T1,U1,l1. ⦃G, L⦄ ⊢ T1 •[h, g] ⦃l1, U1⦄ →
∀T2. ⦃G, L⦄ ⊢ T1 •*[h, g] T2 →
∃∃U2,l2. ⦃G, L⦄ ⊢ T2 •[h, g] ⦃l2, U2⦄.
-#h #g #L #T1 #U1 #l1 #HTU1 #T2 #H @(sstas_ind … H) -T2 [ /2 width=3/ ] -HTU1
+#h #g #G #L #T1 #U1 #l1 #HTU1 #T2 #H @(sstas_ind … H) -T2 [ /2 width=3/ ] -HTU1
#T #T2 #l #_ #HT2 * #U #l0 #_ -l0
elim (ssta_fwd_correct … HT2) -T /2 width=3/
qed-.
(* Properties on relocation *************************************************)
-lemma sstas_lift: ∀h,g,L1,T1,U1. ⦃h, L1⦄ ⊢ T1 •*[h, g] U1 →
+lemma sstas_lift: ∀h,g,G,L1,T1,U1. ⦃G, L1⦄ ⊢ T1 •*[h, g] U1 →
∀L2,d,e. ⇩[d, e] L2 ≡ L1 → ∀T2. ⇧[d, e] T1 ≡ T2 →
- ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃h, L2⦄ ⊢ T2 •*[h, g] U2.
-#h #g #L1 #T1 #U1 #H @(sstas_ind_dx … H) -T1
+ ∀U2. ⇧[d, e] U1 ≡ U2 → ⦃G, L2⦄ ⊢ T2 •*[h, g] U2.
+#h #g #G #L1 #T1 #U1 #H @(sstas_ind_dx … H) -T1
[ #L2 #d #e #HL21 #X #HX #U2 #HU12
>(lift_mono … HX … HU12) -X //
| #T0 #U0 #l0 #HTU0 #_ #IHU01 #L2 #d #e #HL21 #T2 #HT02 #U2 #HU12
(* Inversion lemmas on relocation *******************************************)
-lemma sstas_inv_lift1: ∀h,g,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 •*[h, g] U2 →
+lemma sstas_inv_lift1: ∀h,g,G,L2,T2,U2. ⦃G, L2⦄ ⊢ T2 •*[h, g] U2 →
∀L1,d,e. ⇩[d, e] L2 ≡ L1 → ∀T1. ⇧[d, e] T1 ≡ T2 →
- ∃∃U1. ⦃h, L1⦄ ⊢ T1 •*[h, g] U1 & ⇧[d, e] U1 ≡ U2.
-#h #g #L2 #T2 #U2 #H @(sstas_ind_dx … H) -T2 /2 width=3/
+ ∃∃U1. ⦃G, L1⦄ ⊢ T1 •*[h, g] U1 & ⇧[d, e] U1 ≡ U2.
+#h #g #G #L2 #T2 #U2 #H @(sstas_ind_dx … H) -T2 /2 width=3/
#T0 #U0 #l0 #HTU0 #_ #IHU01 #L1 #d #e #HL21 #U1 #HU12
elim (ssta_inv_lift1 … HTU0 … HL21 … HU12) -HTU0 -HU12 #U #HU1 #HU0
elim (IHU01 … HL21 … HU0) -IHU01 -HL21 -U0 /3 width=4/
(* Advanced inversion lemmas ************************************************)
-lemma sstas_inv_O: ∀h,g,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
+lemma sstas_inv_O: ∀h,g,G,L,T,U. ⦃G, L⦄ ⊢ T •*[h, g] U →
∀T0. ⦃G, L⦄ ⊢ T •[h, g] ⦃0, T0⦄ → U = T.
-#h #g #L #T #U #H @(sstas_ind_dx … H) -T //
+#h #g #G #L #T #U #H @(sstas_ind_dx … H) -T //
#T0 #U0 #l0 #HTU0 #_ #_ #T1 #HT01
elim (ssta_mono … HTU0 … HT01) <plus_n_Sm #H destruct
qed-.
(* Advanced properties ******************************************************)
-lemma sstas_strip: ∀h,g,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
+lemma sstas_strip: ∀h,g,G,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
∀U2,l. ⦃G, L⦄ ⊢ T •[h, g] ⦃l, U2⦄ →
T = U1 ∨ ⦃G, L⦄ ⊢ U2 •*[h, g] U1.
-#h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
+#h #g #G #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
#T #U #l0 #HTU #HU1 #_ #U2 #l #H2
elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/
qed-.
(* Main properties **********************************************************)
-theorem sstas_trans: ∀h,g,L,T1,U. ⦃G, L⦄ ⊢ T1 •*[h, g] U →
+theorem sstas_trans: ∀h,g,G,L,T1,U. ⦃G, L⦄ ⊢ T1 •*[h, g] U →
∀T2. ⦃G, L⦄ ⊢ U •*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*[h, g] T2.
/2 width=3/ qed-.
-theorem sstas_conf: ∀h,g,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
+theorem sstas_conf: ∀h,g,G,L,T,U1. ⦃G, L⦄ ⊢ T •*[h, g] U1 →
∀U2. ⦃G, L⦄ ⊢ T •*[h, g] U2 →
⦃G, L⦄ ⊢ U1 •*[h, g] U2 ∨ ⦃G, L⦄ ⊢ U2 •*[h, g] U1.
-#h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
+#h #g #G #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
#T #U #l #HTU #HU1 #IHU1 #U2 #H2
elim (sstas_strip … H2 … HTU) #H destruct
[ -H2 -IHU1 /3 width=4/
(* *)
(**************************************************************************)
-include "basic_2/notation/relations/unfold_3.ma".
+include "basic_2/notation/relations/unfold_4.ma".
+include "basic_2/grammar/genv.ma". (**) (* disambiguation error *)
include "basic_2/grammar/lenv_append.ma".
include "basic_2/relocation/ldrop.ma".
(* CONTEXT-SENSITIVE UNFOLD FOR TERMS ***************************************)
-inductive unfold: lenv → relation2 term lenv ≝
-| unfold_sort: ∀L,k. unfold L (⋆k) L
-| unfold_lref: ∀I,L1,L2,K1,K2,V,i. ⇩[0, i] L1 ≡ K1. ⓑ{I}V →
- unfold K1 V K2 → ⇩[|L2|, i] L2 ≡ K2 →
- unfold L1 (#i) (L1@@L2)
-| unfold_bind: ∀a,I,L1,L2,V,T.
- unfold (L1.ⓑ{I}V) T L2 → unfold L1 (ⓑ{a,I}V.T) L2
-| unfold_flat: ∀I,L1,L2,V,T.
- unfold L1 T L2 → unfold L1 (ⓕ{I}V.T) L2
+(* activate genv *)
+inductive unfold: relation4 genv lenv term lenv ≝
+| unfold_sort: ∀G,L,k. unfold G L (⋆k) L
+| unfold_lref: ∀I,G,L1,L2,K1,K2,V,i. ⇩[0, i] L1 ≡ K1. ⓑ{I}V →
+ unfold G K1 V K2 → ⇩[|L2|, i] L2 ≡ K2 →
+ unfold G L1 (#i) (L1@@L2)
+| unfold_bind: ∀a,I,G,L1,L2,V,T.
+ unfold G (L1.ⓑ{I}V) T L2 → unfold G L1 (ⓑ{a,I}V.T) L2
+| unfold_flat: ∀I,G,L1,L2,V,T.
+ unfold G L1 T L2 → unfold G L1 (ⓕ{I}V.T) L2
.
interpretation "context-sensitive unfold (term)"
- 'Unfold L1 T L2 = (unfold L1 T L2).
+ 'Unfold G L1 T L2 = (unfold G L1 T L2).
projects / helm.git / commitdiff