--- /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/reduction/fpb_lift.ma".
+include "basic_2/computation/fpbg.ma".
+
+(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
+
+(* Advanced properties ******************************************************)
+
+lemma sta_fpbg: ∀h,o,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 ▪[h, o] d+1 →
+ ⦃G, L⦄ ⊢ T1 •*[h, 1] T2 → ⦃G, L, T1⦄ >≛[h, o] ⦃G, L, T2⦄.
+/4 width=2 by fpb_fpbg, sta_fpb/ qed.
--- /dev/null
+(* Properties on extended context-sensitive parallel computation for terms **)
+
+lemma fpbs_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
+ ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, o] U2 → (T2 = U2 → ⊥) →
+ ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ≥[h, o] ⦃G2, L2, U2⦄.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 #HnTU2 elim (fpbs_inv_alt … H) -H
+#L00 #L0 #T0 #HT10 #H10 #HL00 #HL02 lapply (lleq_cpx_trans … HTU2 … HL02) -HTU2
+#HTU2 lapply (cpx_lleq_conf_sn … HTU2 … HL02) -HL02
+#HL02 lapply (lpxs_cpx_trans … HTU2 … HL00) -HTU2
+#HTU2 elim (fqus_cpxs_trans_neq … H10 … HTU2 HnTU2) -H10 -HTU2 -HnTU2
+#U0 #HTU0 #HnTU0 #HU02 elim (eq_term_dec T1 T0) #HnT10 destruct
+[ -HT10 elim (cpxs_neq_inv_step_sn … HTU0 HnTU0) -HTU0 -HnTU0
+| -HnTU0 elim (cpxs_neq_inv_step_sn … HT10 HnT10) -HT10 -HnT10
+]
+/4 width=10 by fpbs_intro_alt, cpxs_trans, ex3_intro/
+qed-.
--- /dev/null
+(*
+lemma cprs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
+/3 width=1 by cprs_cpxs, cpxs_fpbs/ qed.
+
+lemma lprs_fpbs: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1, T⦄ ≥[h, o] ⦃G, L2, T⦄.
+/3 width=1 by lprs_lpxs, lpxs_fpbs/ qed.
+
+(* Note: this is used in the closure proof *)
+lemma cpr_lpr_fpbs: ∀h,o,G,L1,L2,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
+ ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, T2⦄.
+/4 width=5 by fpbs_strap1, fpbq_fpbs, lpr_fpbq, cpr_fpbq/
+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/static/ffdeq.ma".
+include "basic_2/rt_computation/csx_lfdeq.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Properties with degree-based equivalence for closures ********************)
+
+lemma csx_ffdeq_conf: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
+ ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
+#h #o #G1 #L1 #T1 #HT1 #G2 #L2 #T2 * -G2 -L2 -T2
+/3 width=3 by csx_lfdeq_conf, csx_tdeq_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/rt_transition/fpbq.ma".
+include "basic_2/rt_computation/csx_fqus.ma".
+include "basic_2/rt_computation/csx_ffdeq.ma".
+include "basic_2/rt_computation/csx_lfpx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Properties with parallel rst-transition for closures *********************)
+
+(* Basic_2A1: was: csx_fpb_conf *)
+lemma csx_fpbq_conf: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
+ ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
+#h #o #G1 #L1 #T1 #HT1 #G2 #L2 #T2 *
+/2 width=6 by csx_cpx_trans, csx_fquq_conf, csx_lfpx_conf, csx_ffdeq_conf/
+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/reduction/fpb_lift.ma".
-include "basic_2/computation/fpbg.ma".
-
-(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
-
-(* Advanced properties ******************************************************)
-
-lemma sta_fpbg: ∀h,o,G,L,T1,T2,d. ⦃G, L⦄ ⊢ T1 ▪[h, o] d+1 →
- ⦃G, L⦄ ⊢ T1 •*[h, 1] T2 → ⦃G, L, T1⦄ >≛[h, o] ⦃G, L, T2⦄.
-/4 width=2 by fpb_fpbg, sta_fpb/ qed.
(* *)
(**************************************************************************)
-include "basic_2/reduction/fpbq_aaa.ma".
-include "basic_2/computation/fpbs.ma".
+include "basic_2/rt_transition/fpbq_aaa.ma".
+include "basic_2/rt_computation/fpbs.ma".
-(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
-(* Properties on atomic arity assignment for terms **************************)
+(* Properties with atomic arity assignment for terms ************************)
lemma fpbs_aaa_conf: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
∀A1. ⦃G1, L1⦄ ⊢ T1 ⁝ A1 → ∃A2. ⦃G2, L2⦄ ⊢ T2 ⁝ A2.
(* *)
(**************************************************************************)
-include "basic_2/computation/fpbs.ma".
-include "basic_2/computation/csx_lleq.ma".
-include "basic_2/computation/csx_lpx.ma".
+include "basic_2/rt_computation/csx_fpbq.ma".
+include "basic_2/rt_computation/fpbs.ma".
-(* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
-(* Advanced properties ******************************************************)
+(* Properties with sn for uncounted parallel rt-transition for terms ********)
-lemma csx_fpb_conf: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
-#h #o #G1 #L1 #T1 #HT1 #G2 #L2 #T2 *
-/2 width=5 by csx_cpx_trans, csx_fquq_conf, csx_lpx_conf, csx_lleq_conf/
-qed-.
-
-lemma csx_fpbs_conf: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬊*[h, o] T1 →
- ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬊*[h, o] T2.
+(* Basic_2A1: was: csx_fpbs_conf *)
+lemma fpbs_csx_conf: ∀h,o,G1,L1,T1. ⦃G1, L1⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
+ ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G2, L2⦄ ⊢ ⬈*[h, o] 𝐒⦃T2⦄.
#h #o #G1 #L1 #T1 #HT1 #G2 #L2 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
-/2 width=5 by csx_fpb_conf/
+/2 width=5 by csx_fpbq_conf/
qed-.
(* *)
(**************************************************************************)
-include "basic_2/reduction/fpbq_alt.ma".
-include "basic_2/computation/fpbs_alt.ma".
+include "basic_2/rt_transition/fpbq_fpb.ma".
+include "basic_2/rt_computation/fpbs.ma".
-(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
-(* Properties on extended context-sensitive parallel computation for terms **)
-
-lemma fpbs_cpx_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
- ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡[h, o] U2 → (T2 = U2 → ⊥) →
- ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ≥[h, o] ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 #HnTU2 elim (fpbs_inv_alt … H) -H
-#L00 #L0 #T0 #HT10 #H10 #HL00 #HL02 lapply (lleq_cpx_trans … HTU2 … HL02) -HTU2
-#HTU2 lapply (cpx_lleq_conf_sn … HTU2 … HL02) -HL02
-#HL02 lapply (lpxs_cpx_trans … HTU2 … HL00) -HTU2
-#HTU2 elim (fqus_cpxs_trans_neq … H10 … HTU2 HnTU2) -H10 -HTU2 -HnTU2
-#U0 #HTU0 #HnTU0 #HU02 elim (eq_term_dec T1 T0) #HnT10 destruct
-[ -HT10 elim (cpxs_neq_inv_step_sn … HTU0 HnTU0) -HTU0 -HnTU0
-| -HnTU0 elim (cpxs_neq_inv_step_sn … HT10 HnT10) -HT10 -HnT10
-]
-/4 width=10 by fpbs_intro_alt, cpxs_trans, ex3_intro/
-qed-.
-
-(* Properties on "rst" proper parallel reduction on closures ****************)
+(* Properties with proper parallel rst-reduction on closures ****************)
lemma fpb_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
(* *)
(**************************************************************************)
-include "basic_2/computation/fpbs.ma".
+include "basic_2/rt_computation/fpbs.ma".
-(* "QRST" PARALLEL COMPUTATION FOR CLOSURES *********************************)
+(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
(* Main properties **********************************************************)
+++ /dev/null
-(*
-lemma cprs_fpbs: ∀h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h] T2 → ⦃G, L, T1⦄ ≥[h, o] ⦃G, L, T2⦄.
-/3 width=1 by cprs_cpxs, cpxs_fpbs/ qed.
-
-lemma lprs_fpbs: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1, T⦄ ≥[h, o] ⦃G, L2, T⦄.
-/3 width=1 by lprs_lpxs, lpxs_fpbs/ qed.
-
-(* Note: this is used in the closure proof *)
-lemma cpr_lpr_fpbs: ∀h,o,G,L1,L2,T1,T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ⦃G, L1⦄ ⊢ ➡ L2 →
- ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, T2⦄.
-/4 width=5 by fpbs_strap1, fpbq_fpbs, lpr_fpbq, cpr_fpbq/
-qed.
-*)
cpxs_ext.ma
lpxs.ma lpxs_length.ma lpxs_lpx.ma lpxs_cpxs.ma
lfpxs.ma lfpxs_length.ma lfpxs_drops.ma lfpxs_fqup.ma lfpxs_lfdeq.ma lfpxs_ffdeq.ma lfpxs_aaa.ma lfpxs_cpxs.ma lfpxs_lpxs.ma lfpxs_lfpxs.ma
-csx.ma csx_simple.ma csx_simple_theq.ma csx_drops.ma csx_fqus.ma csx_lsubr.ma csx_lfdeq.ma csx_aaa.ma csx_gcp.ma csx_gcr.ma csx_lfpx.ma csx_cnx.ma csx_cpxs.ma csx_lfpxs.ma csx_csx.ma
+csx.ma csx_simple.ma csx_simple_theq.ma csx_drops.ma csx_fqus.ma csx_lsubr.ma csx_lfdeq.ma csx_ffdeq.ma csx_aaa.ma csx_gcp.ma csx_gcr.ma csx_lfpx.ma csx_cnx.ma csx_fpbq.ma csx_cpxs.ma csx_lfpxs.ma csx_csx.ma
csx_vector.ma csx_cnx_vector.ma csx_csx_vector.ma
lfsx.ma lfsx_drops.ma lfsx_fqup.ma lfsx_lpx.ma lfsx_lpxs.ma lfsx_lfpxs.ma lfsx_csx.ma lfsx_lfsx.ma
lsubsx.ma lsubsx_lfsx.ma lsubsx_lsubsx.ma
-fpbs.ma fpbs_fqus.ma fpbs_fqup.ma fpbs_cpxs.ma fpbs_lfpxs.ma
+fpbs.ma fpbs_fqup.ma fpbs_fqus.ma fpbs_aaa.ma fpbs_fpb.ma fpbs_cpxs.ma fpbs_lfpxs.ma fpbs_csx.ma fpbs_fpbs.ma
[ [ "" ] "fsb ( ⦥[?,?] ⦃?,?,?⦄ )" "fsb_alt ( ⦥⦥[?,?] ⦃?,?,?⦄ )" "fsb_aaa" + "fsb_csx" * ]
}
]
- [ { "strongly normalizing rt-computation" * } {
- [ [ "" ] "llsx_csx" * ]
- [ [ "" ] "csx_fpbs" * ]
- }
- ]
[ { "parallel qrst-computation" * } {
[ [ "" ] "fpbg ( ⦃?,?,?⦄ >≛[?,?] ⦃?,?,?⦄ )" "fpbg_lift" + "fpbg_fleq" + "fpbg_fpbs" + "fpbg_fpbg" * ]
- [ [ "" ] "fpbs_alt" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_fpbs" * ]
}
]
[ { "decomposed rt-computation" * } {
]
*)
[ { "uncounted context-sensitive parallel rst-computation" * } {
- [ [ "for closures" ] "fpbs" + "( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_fqup" + "fpbs_fqus" + "fpbs_cpxs" + "fpbs_lfpxs" * ]
+ [ [ "for closures" ] "fpbs" + "( ⦃?,?,?⦄ ≥[?,?] ⦃?,?,?⦄ )" "fpbs_fqup" + "fpbs_fqus" + "fpbs_aaa" + "fpbs_fpb" + "fpbs_cpxs" + "fpbs_lfpxs" + "fpbs_csx" + "fpbs_fpbs" * ]
}
]
[ { "uncounted context-sensitive parallel rt-computation" * } {
[ [ "refinement for lenvs on selected entries" ] "lsubsx" + "( ? ⊢ ? ⊆ⓧ[?,?,?] ? )" "lsubsx_lfsx" + "lsubsx_lsubsx" * ]
[ [ "strongly normalizing for lenvs on referred entries" ] "lfsx" + "( ? ⊢ ⬈*[?,?,?] 𝐒⦃?⦄ )" "lfsx_drops" + "lfsx_fqup" + "lfsx_cpx" + "lfsx_cpxs" + "lfsx_lfpxs" + "lfsx_lfsx" * ]
[ [ "strongly normalizing for term vectors" ] "csx_vector" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_cnx_vector" + "csx_csx_vector" * ]
- [ [ "strongly normalizing for terms" ] "csx" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_theq" + "csx_drops" + "csx_fqus" + "csx_lsubr" + "csx_lfdeq" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lfpx" + "csx_cnx" + "csx_cpxs" + "csx_lfpxs" + "csx_csx" * ]
+ [ [ "strongly normalizing for terms" ] "csx" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_theq" + "csx_drops" + "csx_fqus" + "csx_lsubr" + "csx_lfdeq" + "csx_ffdeq" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lfpx" + "csx_cnx" + "csx_fpbq" + "csx_cpxs" + "csx_lfpxs" + "csx_csx" * ]
[ [ "for lenvs on referred entries" ] "lfpxs" + "( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_drops" + "lfpxs_fqup" + "lfpxs_lfdeq" + "lfpxs_ffdeq" + "lfpxs_aaa" + "lfpxs_cpxs" + "lfpxs_lpxs" + "lfpxs_lfpxs" * ]
[ [ "for lenvs on all entries" ] "lpxs" + "( ⦃?,?⦄ ⊢ ⬈*[?] ? )" "lpxs_length" + "lpxs_lpx" + "lpxs_cpxs" * ]
[ [ "for binders" ] "cpxs_ext" + "( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" * ]
projects / helm.git / commitdiff