--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/btpredstarproper_8.ma".
+include "basic_2/reduction/ysc.ma".
+include "basic_2/computation/yprs.ma".
+
+(* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
+
+inductive ygt (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
+| ygt_inj : ∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+ ygt h g G1 L1 T1 G2 L2 T2
+| ygt_step: ∀G,L,L2,T. ygt h g G1 L1 T1 G L T → ⦃G, L⦄ ⊢ ➡ L2 → ygt h g G1 L1 T1 G L2 T
+.
+
+interpretation "'big tree' proper parallel computation (closure)"
+ 'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (ygt h g G1 L1 T1 G2 L2 T2).
+
+(* Basic forvard lemmas *****************************************************)
+
+lemma ygt_fwd_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
+/3 width=5 by yprs_strap1, ysc_ypr, ypr_lpr/
+qed-.
+
+(* Basic properties *********************************************************)
+
+lemma ysc_ygt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+/3 width=5 by ygt_inj, ygt_step/ qed.
+
+lemma ygt_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G, L, T⦄ →
+ ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
+lapply (ygt_fwd_yprs … H1) #H0
+elim (ypr_inv_ysc … H2) -H2 [| * #HG2 #HL2 #HT2 destruct ]
+/2 width=5 by ygt_inj, ygt_step/
+qed-.
+
+lemma ygt_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ →
+ ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim H2 -G2 -L2 -T2
+/3 width=5 by ygt_step, ygt_inj, yprs_strap2/
+qed-.
+
+lemma ygt_yprs_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G, L, T⦄ →
+ ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #HT1 #HT2 @(yprs_ind … HT2) -G2 -L2 -T2
+/2 width=5 by ygt_strap1/
+qed-.
+
+lemma yprs_ygt_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
+ ∀G2,L2,T2. ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #L1 #L #T1 #T #HT1 @(yprs_ind … HT1) -G -L -T
+/3 width=5 by ygt_strap2/
+qed-.
+
+lemma fsupp_ygt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -G2 -L2 -T2
+/3 width=5 by fsupp_yprs, ysc_fsup, ysc_ygt, ygt_inj/
+qed.
+
+lemma cprs_ygt: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
+ ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
+#h #g #G #L #T1 #T2 #H @(cprs_ind … H) -T2
+[ #H elim H //
+| #T #T2 #_ #HT2 #IHT1 #HT12
+ elim (term_eq_dec T1 T) #H destruct
+ [ -IHT1 /4 width=1/
+ | lapply (IHT1 … H) -IHT1 -H -HT12 #HT1
+ @(ygt_strap1 … HT1) -HT1 /2 width=1 by ypr_cpr/
+ ]
+]
+qed.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/unfold/lsstas_lift.ma".
+include "basic_2/computation/ygt.ma".
+
+(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
+
+(* Advanced properties ******************************************************)
+
+lemma lsstas_ygt: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
+ ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
+#h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2
+[ #H elim H //
+| #l2 #T #T2 #HT1 #HT2 #IHT1 #HT12 #l1 #Hl21
+ elim (term_eq_dec T1 T) #H destruct [ -IHT1 |]
+ [ elim (le_inv_plus_l … Hl21) -Hl21 #_ #Hl1
+ >(plus_minus_m_m … Hl1) -Hl1 /3 width=5 by ysc_ssta, ygt_inj/
+ | #Hl1 >commutative_plus in Hl21; #Hl21
+ elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
+ lapply (lsstas_da_conf … HT1 … Hl1) -HT1
+ >(plus_minus_m_m … Hl12) -Hl12
+ /4 width=5 by ypr_ssta, ygt_strap1/
+ ]
+]
+qed.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/computation/ygt.ma".
+
+(* "BIG TREE" ORDER FOR CLOSURES ********************************************)
+
+(* Main properties **********************************************************)
+
+theorem ygt_trans: ∀h,g. tri_transitive … (ygt h g).
+/3 width=5 by ygt_fwd_yprs, ygt_yprs_trans/ qed-.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/btpredstar_8.ma".
+include "basic_2/substitution/fsupp.ma".
+include "basic_2/reduction/ypr.ma".
+include "basic_2/computation/cprs.ma".
+include "basic_2/computation/lprs.ma".
+
+(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
+
+definition yprs: ∀h. sd h → tri_relation genv lenv term ≝
+ λh,g. tri_TC … (ypr h g).
+
+interpretation "'big tree' parallel computation (closure)"
+ 'BTPRedStar h g G1 L1 T1 G2 L2 T2 = (yprs h g G1 L1 T1 G2 L2 T2).
+
+(* Basic eliminators ********************************************************)
+
+lemma yprs_ind: ∀h,g,G1,L1,T1. ∀R:relation3 genv lenv term. R G1 L1 T1 →
+ (∀L,G2,G,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
+ ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
+/3 width=8 by tri_TC_star_ind/ qed-.
+
+lemma yprs_ind_dx: ∀h,g,G2,L2,T2. ∀R:relation3 genv lenv term. R G2 L2 T2 →
+ (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
+ ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
+/3 width=8 by tri_TC_star_ind_dx/ qed-.
+
+(* Basic properties *********************************************************)
+
+lemma yprs_refl: ∀h,g. tri_reflexive … (yprs h g).
+/2 width=1 by tri_inj/ qed.
+
+lemma ypr_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+/2 width=1 by tri_inj/ qed.
+
+lemma yprs_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
+ ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+/2 width=5 by tri_step/ qed-.
+
+lemma yprs_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ →
+ ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+/2 width=5 by tri_TC_strap/ qed-.
+
+(* Note: this is a general property of bi_TC *)
+lemma fsupp_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -G2 -L2 -T2
+/3 width=5 by ypr_fsup, tri_step, ypr_yprs/
+qed.
+
+lemma cprs_yprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
+#h #g #G #L #T1 #T2 #H @(cprs_ind … H) -T2
+/3 width=5 by ypr_cpr, yprs_strap1/
+qed.
+
+lemma lprs_yprs: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1, T⦄ ≥[h, g] ⦃G, L2, T⦄.
+#h #g #G #L1 #L2 #T #H @(lprs_ind … H) -L2
+/3 width=5 by ypr_lpr, yprs_strap1/
+qed.
+
+lemma cpr_lpr_yprs: ∀h,g,G,L1,L2,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
+ ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, T2⦄.
+/4 width=5 by yprs_strap1, ypr_lpr, ypr_cpr/ qed.
+
+lemma ssta_yprs: ∀h,g,G,L,T,U,l.
+ ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U →
+ ⦃G, L, T⦄ ≥[h, g] ⦃G, L, U⦄.
+/3 width=2 by ypr_yprs, ypr_ssta/ qed.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/unfold/lsstas_lift.ma".
+include "basic_2/computation/yprs.ma".
+
+(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
+
+(* Advanced properties ******************************************************)
+
+lemma lsstas_yprs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
+ ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
+#h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2 //
+#l2 #T #T2 #HT1 #HT2 #IHT1 #l1 >commutative_plus #Hl21 #Hl1
+elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
+lapply (lsstas_da_conf … HT1 … Hl1) -HT1
+>(plus_minus_m_m … Hl12) -Hl12
+/3 width=5 by ypr_ssta, yprs_strap1/
+qed.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/computation/yprs.ma".
+
+(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
+
+(* Main properties **********************************************************)
+
+theorem yprs_trans: ∀h,g. tri_transitive … (yprs h g).
+/2 width=5 by tri_TC_transitive/ qed-.
+
+(* Advanced properties ******************************************************)
+
+lemma cpr_lpr_ssta_yprs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
+ ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
+ ⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •[h, g] U2 →
+ ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.
+/3 width=5 by yprs_trans, cpr_lpr_yprs, ssta_yprs/ qed.
(**************************************************************************)
include "basic_2/unfold/lsstas_lsstas.ma".
+include "basic_2/computation/yprs_lift.ma".
+include "basic_2/computation/ygt.ma".
include "basic_2/equivalence/cpes_cpds.ma".
-include "basic_2/dynamic/yprs_lift.ma".
-include "basic_2/dynamic/ygt.ma".
+include "basic_2/dynamic/snv.ma".
(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
(* *)
(**************************************************************************)
+include "basic_2/computation/yprs_yprs.ma".
include "basic_2/dynamic/snv_lift.ma".
include "basic_2/dynamic/snv_cpcs.ma".
include "basic_2/dynamic/lsubsv_snv.ma".
-include "basic_2/dynamic/yprs_yprs.ma".
(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
(**************************************************************************)
include "basic_2/computation/cpds_cpds.ma".
+include "basic_2/computation/yprs_yprs.ma".
include "basic_2/dynamic/snv_aaa.ma".
include "basic_2/dynamic/snv_cpcs.ma".
include "basic_2/dynamic/lsubsv_lsstas.ma".
-include "basic_2/dynamic/yprs_yprs.ma".
(* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/btpredstarproper_8.ma".
-include "basic_2/dynamic/ysc.ma".
-include "basic_2/dynamic/yprs.ma".
-
-(* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
-
-inductive ygt (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| ygt_inj : ∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
- ygt h g G1 L1 T1 G2 L2 T2
-| ygt_step: ∀G,L,L2,T. ygt h g G1 L1 T1 G L T → ⦃G, L⦄ ⊢ ➡ L2 → ygt h g G1 L1 T1 G L2 T
-.
-
-interpretation "'big tree' proper parallel computation (closure)"
- 'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (ygt h g G1 L1 T1 G2 L2 T2).
-
-(* Basic forvard lemmas *****************************************************)
-
-lemma ygt_fwd_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
-/3 width=5 by yprs_strap1, ysc_ypr, ypr_lpr/
-qed-.
-
-(* Basic properties *********************************************************)
-
-lemma ysc_ygt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-/3 width=5/ qed.
-
-lemma ygt_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G, L, T⦄ →
- ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
-lapply (ygt_fwd_yprs … H1) #H0
-elim (ypr_inv_ysc … H2) -H2 [| * #HG2 #HL2 #HT2 destruct ] /2 width=5/
-qed-.
-
-lemma ygt_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ →
- ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim H2 -G2 -L2 -T2
-[ /3 width=5 by ygt_inj, yprs_strap2/ | /2 width=3/ ]
-qed-.
-
-lemma ygt_yprs_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G, L, T⦄ →
- ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #HT1 #HT2 @(yprs_ind … HT2) -G2 -L2 -T2 //
-/2 width=5 by ygt_strap1/
-qed-.
-
-lemma yprs_ygt_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
- ∀G2,L2,T2. ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T #HT1 @(yprs_ind … HT1) -G -L -T //
-/3 width=5 by ygt_strap2/
-qed-.
-
-lemma fsupp_ygt: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -G2 -L2 -T2 /3 width=1/ /3 width=5/
-qed.
-
-lemma cprs_ygt: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
- ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #H @(cprs_ind … H) -T2
-[ #H elim H //
-| #T #T2 #_ #HT2 #IHT1 #HT12
- elim (term_eq_dec T1 T) #H destruct
- [ -IHT1 /4 width=1/
- | lapply (IHT1 … H) -IHT1 -H -HT12 #HT1
- @(ygt_strap1 … HT1) -HT1 /2 width=1/
- ]
-]
-qed.
-
-lemma lsubsv_ygt: ∀h,g,G,L1,L2,T. G ⊢ L2 ¡⊑[h, g] L1 → (L1 = L2 → ⊥) →
- ⦃G, L1, T⦄ >[h, g] ⦃G, L2, T⦄.
-/4 width=1/ qed.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/unfold/lsstas_lift.ma".
-include "basic_2/dynamic/ygt.ma".
-
-(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
-
-(* Advanced properties ******************************************************)
-
-lemma lsstas_ygt: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 → (T1 = T2 → ⊥) →
- ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2
-[ #H elim H //
-| #l2 #T #T2 #HT1 #HT2 #IHT1 #HT12 #l1 #Hl21
- elim (term_eq_dec T1 T) #H destruct [ -IHT1 |]
- [ elim (le_inv_plus_l … Hl21) -Hl21 #_ #Hl1
- >(plus_minus_m_m … Hl1) -Hl1 /3 width=5 by ysc_ssta, ygt_inj/
- | #Hl1 >commutative_plus in Hl21; #Hl21
- elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
- lapply (lsstas_da_conf … HT1 … Hl1) -HT1
- >(plus_minus_m_m … Hl12) -Hl12
- /4 width=5 by ypr_ssta, ygt_strap1/
- ]
-]
-qed.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/dynamic/ygt.ma".
-
-(* "BIG TREE" ORDER FOR CLOSURES ********************************************)
-
-(* Main properties **********************************************************)
-
-theorem ygt_trans: ∀h,g. tri_transitive … (ygt h g).
-/3 width=5 by ygt_fwd_yprs, ygt_yprs_trans/ qed-.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/btpred_8.ma".
-include "basic_2/relocation/fsup.ma".
-include "basic_2/reduction/lpr.ma".
-include "basic_2/dynamic/lsubsv.ma".
-
-(* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
-
-inductive ypr (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| ypr_fsup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ypr h g G1 L1 T1 G2 L2 T2
-| ypr_lpr : ∀L2. ⦃G1, L1⦄ ⊢ ➡ L2 → ypr h g G1 L1 T1 G1 L2 T1
-| ypr_cpr : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → ypr h g G1 L1 T1 G1 L1 T2
-| ypr_ssta : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → ypr h g G1 L1 T1 G1 L1 T2
-| ypr_lsubsv: ∀L2. G1 ⊢ L2 ¡⊑[h, g] L1 → ypr h g G1 L1 T1 G1 L2 T1
-.
-
-interpretation
- "'big tree' parallel reduction (closure)"
- 'BTPRed h g G1 L1 T1 G2 L2 T2 = (ypr h g G1 L1 T1 G2 L2 T2).
-
-(* Basic properties *********************************************************)
-
-lemma ypr_refl: ∀h,g. tri_reflexive … (ypr h g).
-/2 width=1/ qed.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/btpredstar_8.ma".
-include "basic_2/substitution/fsupp.ma".
-include "basic_2/computation/lprs.ma".
-include "basic_2/dynamic/ypr.ma".
-
-(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
-
-definition yprs: ∀h. sd h → tri_relation genv lenv term ≝
- λh,g. tri_TC … (ypr h g).
-
-interpretation "'big tree' parallel computation (closure)"
- 'BTPRedStar h g G1 L1 T1 G2 L2 T2 = (yprs h g G1 L1 T1 G2 L2 T2).
-
-(* Basic eliminators ********************************************************)
-
-lemma yprs_ind: ∀h,g,G1,L1,T1. ∀R:relation3 genv lenv term. R G1 L1 T1 →
- (∀L,G2,G,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
-/3 width=8 by tri_TC_star_ind/ qed-.
-
-lemma yprs_ind_dx: ∀h,g,G2,L2,T2. ∀R:relation3 genv lenv term. R G2 L2 T2 →
- (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
- ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
-/3 width=8 by tri_TC_star_ind_dx/ qed-.
-
-(* Basic properties *********************************************************)
-
-lemma yprs_refl: ∀h,g. tri_reflexive … (yprs h g).
-/2 width=1/ qed.
-
-lemma ypr_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-/2 width=1/ qed.
-
-lemma yprs_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
- ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-/2 width=5/ qed-.
-
-lemma yprs_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ →
- ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-/2 width=5/ qed-.
-
-(* Note: this is a general property of bi_TC *)
-lemma fsupp_yprs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fsupp_ind … L2 T2 H) -G2 -L2 -T2 /3 width=1/ /3 width=5/
-qed.
-
-lemma cprs_yprs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #H @(cprs_ind … H) -T2 // /3 width=5 by ypr_cpr, yprs_strap1/
-qed.
-
-lemma lprs_yprs: ∀h,g,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1, T⦄ ≥[h, g] ⦃G, L2, T⦄.
-#h #g #G #L1 #L2 #T #H @(lprs_ind … H) -L2 // /3 width=5 by ypr_lpr, yprs_strap1/
-qed.
-
-lemma lsubsv_yprs: ∀h,g,G,L1,L2,T. G ⊢ L2 ¡⊑[h, g] L1 → ⦃G, L1, T⦄ ≥[h, g] ⦃G, L2, T⦄.
-/3 width=1/ qed.
-
-lemma cpr_lpr_yprs: ∀h,g,G,L1,L2,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
- ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, T2⦄.
-/4 width=5 by yprs_strap1, ypr_lpr, ypr_cpr/ qed.
-
-lemma ssta_yprs: ∀h,g,G,L,T,U,l.
- ⦃G, L⦄ ⊢ T ▪[h, g] l+1 → ⦃G, L⦄ ⊢ T •[h, g] U →
- ⦃G, L, T⦄ ≥[h, g] ⦃G, L, U⦄.
-/3 width=2 by ypr_yprs, ypr_ssta/ qed.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/unfold/lsstas_lift.ma".
-include "basic_2/dynamic/yprs.ma".
-
-(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
-
-(* Advanced properties ******************************************************)
-
-lemma lsstas_yprs: ∀h,g,G,L,T1,T2,l2. ⦃G, L⦄ ⊢ T1 •*[h, g, l2] T2 →
- ∀l1. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ⦃G, L, T1⦄ ≥[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #l2 #H @(lsstas_ind_dx … H) -l2 -T2 //
-#l2 #T #T2 #HT1 #HT2 #IHT1 #l1 >commutative_plus #Hl21 #Hl1
-elim (le_inv_plus_l … Hl21) -Hl21 #Hl12 #Hl21
-lapply (lsstas_da_conf … HT1 … Hl1) -HT1
->(plus_minus_m_m … Hl12) -Hl12
-/3 width=5 by ypr_ssta, yprs_strap1/
-qed.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/dynamic/yprs.ma".
-
-(* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
-
-(* Main properties **********************************************************)
-
-theorem yprs_trans: ∀h,g. tri_transitive … (yprs h g).
-/2 width=5/ qed-.
-
-(* Advanced properties ******************************************************)
-
-lemma cpr_lpr_ssta_yprs: ∀h,g,G,L1,L2,T1,T2,U2,l2.
- ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
- ⦃G, L2⦄ ⊢ T2 ▪[h, g] l2+1 → ⦃G, L2⦄ ⊢ T2 •[h, g] U2 →
- ⦃G, L1, T1⦄ ≥[h, g] ⦃G, L2, U2⦄.
-/3 width=5 by yprs_trans, cpr_lpr_yprs, ssta_yprs/ qed.
+++ /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 *)
-(* *)
-(**************************************************************************)
-
-include "basic_2/notation/relations/btpredproper_8.ma".
-include "basic_2/dynamic/ypr.ma".
-
-(* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
-
-inductive ysc (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| ysc_fsup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ysc h g G1 L1 T1 G2 L2 T2
-| ysc_cpr : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → ysc h g G1 L1 T1 G1 L1 T2
-| ysc_ssta : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → ysc h g G1 L1 T1 G1 L1 T2
-| ysc_lsubsv: ∀L2. G1 ⊢ L2 ¡⊑[h, g] L1 → (L1 = L2 → ⊥) → ysc h g G1 L1 T1 G1 L2 T1
-.
-
-interpretation
- "'big tree' proper parallel reduction (closure)"
- 'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (ysc h g G1 L1 T1 G2 L2 T2).
-
-(* Basic properties *********************************************************)
-
-lemma ysc_ypr: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1/ /2 width=2/
-qed.
-
-(* Inversion lemmas on "big tree" parallel reduction for closures ***********)
-
-lemma ypr_inv_ysc: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ ∨
- ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡ L2 & T1 = T2.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /3 width=1/ /3 width=2/
-[ #T2 #HT12 elim (term_eq_dec T1 T2) #H destruct /3 width=1/ /4 width=1/
-| #L2 #HL21 elim (lenv_eq_dec L1 L2) #H destruct /3 width=1/ /4 width=1/
-]
-qed-.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/btpred_8.ma".
+include "basic_2/relocation/fsup.ma".
+include "basic_2/static/ssta.ma".
+include "basic_2/reduction/lpr.ma".
+
+(* "BIG TREE" PARALLEL REDUCTION FOR CLOSURES *******************************)
+
+inductive ypr (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
+| ypr_fsup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ypr h g G1 L1 T1 G2 L2 T2
+| ypr_lpr : ∀L2. ⦃G1, L1⦄ ⊢ ➡ L2 → ypr h g G1 L1 T1 G1 L2 T1
+| ypr_cpr : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → ypr h g G1 L1 T1 G1 L1 T2
+| ypr_ssta : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → ypr h g G1 L1 T1 G1 L1 T2
+.
+
+interpretation
+ "'big tree' parallel reduction (closure)"
+ 'BTPRed h g G1 L1 T1 G2 L2 T2 = (ypr h g G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma ypr_refl: ∀h,g. tri_reflexive … (ypr h g).
+/2 width=1 by ypr_cpr/ qed.
--- /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 *)
+(* *)
+(**************************************************************************)
+
+include "basic_2/notation/relations/btpredproper_8.ma".
+include "basic_2/reduction/ypr.ma".
+
+(* "BIG TREE" PROPER PARALLEL REDUCTION FOR CLOSURES ************************)
+
+inductive ysc (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
+| ysc_fsup : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊃ ⦃G2, L2, T2⦄ → ysc h g G1 L1 T1 G2 L2 T2
+| ysc_cpr : ∀T2. ⦃G1, L1⦄ ⊢ T1 ➡ T2 → (T1 = T2 → ⊥) → ysc h g G1 L1 T1 G1 L1 T2
+| ysc_ssta : ∀T2,l. ⦃G1, L1⦄ ⊢ T1 ▪[h, g] l+1 → ⦃G1, L1⦄ ⊢ T1 •[h, g] T2 → ysc h g G1 L1 T1 G1 L1 T2
+.
+
+interpretation
+ "'big tree' proper parallel reduction (closure)"
+ 'BTPRedProper h g G1 L1 T1 G2 L2 T2 = (ysc h g G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+lemma ysc_ypr: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/2 width=2 by ypr_fsup, ypr_cpr, ypr_ssta/
+qed.
+
+(* Inversion lemmas on "big tree" parallel reduction for closures ***********)
+
+lemma ypr_inv_ysc: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ ∨
+ ∧∧ G1 = G2 & ⦃G1, L1⦄ ⊢ ➡ L2 & T1 = T2.
+#h #g #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+/3 width=2 by and3_intro, or_introl, or_intror, ysc_fsup, ysc_ssta/
+#T2 #HT12 elim (term_eq_dec T1 T2) #H destruct
+/4 width=1 by and3_intro, or_introl, or_intror, ysc_cpr/
+qed-.
}
]
*)
- [ { "\"big tree\" parallel computation" * } {
- [ "ygt ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "ygt_lift" + "ygt_ygt" * ]
- [ "yprs ( ? ⊢ ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "yprs_lift" + "yprs_yprs" * ]
- }
- ]
- [ { "\"big tree\" parallel reduction" * } {
- [ "ypr ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "ysc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" * ]
- }
- ]
[ { "local env. ref. for stratified native validity" * } {
[ "lsubsv ( ? ⊢ ? ¡⊑[?,?] ? )" "lsubsv_ldrop" + "lsubsv_lsubd" + "lsubsv_lsuba" + "lsubsv_lsstas" + "lsubsv_cpds" + "lsubsv_cpcs" + "lsubsv_snv" * ]
}
[ "csn ( ⦃?,?⦄ ⊢ ⬊*[?,?] ? )" "csn_alt ( ⦃?,?⦄ ⊢ ⬊⬊*[?,?] ? )" "csn_lift" + "csn_lpx" * ]
}
]
+ [ { "\"big tree\" parallel computation" * } {
+ [ "ygt ( ⦃?,?,?⦄ >[?,?] ⦃?,?,?⦄ )" "ygt_lift" + "ygt_ygt" * ]
+ [ "yprs ( ? ⊢ ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "yprs_lift" + "yprs_yprs" * ]
+ }
+ ]
[ { "decomposed extended computation" * } {
[ "cpds ( ⦃?,?⦄ ⊢ ? •*➡*[?,?] ? )" "cpds_lift" + "cpds_aaa" + "cpds_cpds" * ]
}
]
class "water"
[ { "reduction" * } {
+ [ { "\"big tree\" parallel reduction" * } {
+ [ "ypr ( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "ysc ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" * ]
+ }
+ ]
[ { "context-sensitive extended normal forms" * } {
[ "cnx ( ⦃?,?⦄ ⊢ 𝐍[?,?]⦃?⦄ )" "cnx_lift" + "cnx_crx" + "cnx_cix" * ]
}
projects / helm.git / commitdiff