advances on fpb to be continued ...
"F. Guidi:" +
@@("download/ld_talk_10s.pdf"
"Adding Schematic Abstraction to λP") +
- "(revised <span class=\"emph gamma\">2018-02</span>)." +
+ "(<span class=\"emph alpha\">2018-02</span>)." +
"Presentation at University of Bologna (slides)."
* }
]
+++ /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/multiple/fleq.ma".
-include "basic_2/reduction/fpb_lleq.ma".
-
-(* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
-
-(* Properties on lazy equivalence for closures ******************************)
-
-lemma fleq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≡[0] ⦃F2, K2, T2⦄ →
- ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
- ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≡[0] ⦃G2, L2, U2⦄.
-#h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
-#K2 #HK12 #G2 #L2 #U2 #H12 elim (lleq_fpb_trans … HK12 … H12) -K2
-/3 width=5 by fleq_intro, ex2_3_intro/
-qed-.
-
-(* Inversion lemmas on lazy equivalence for closures ************************)
-
-lemma fpb_inv_fleq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
- ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
-[ #G2 #L2 #T2 #H12 #H elim (fleq_inv_gen … H) -H
- /3 width=8 by lleq_fwd_length, fqu_inv_eq/
-| #T2 #_ #HnT #H elim (fleq_inv_gen … H) -H /2 width=1 by/
-| #L2 #_ #HnL #H elim (fleq_inv_gen … H) -H /2 width=1 by/
-]
-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_transition/fpb_lfdeq.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with degree-based equivalence for closures ********************)
+
+(* Basic_2A1: uses: fleq_fpb_trans *)
+lemma ffdeq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≛[h, o] ⦃F2, K2, T2⦄ →
+ ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
+ ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄.
+#h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
+#K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
+elim (tdeq_fpb_trans … HT12 … H12) -T2 #K0 #T0 #H #HT0 #HK0
+elim (lfdeq_fpb_trans … HK12 … H) -K2 #L0 #U0 #H #HUT0 #HLK0
+@(ex2_3_intro … H) -H (**) (* full auto too slow *)
+/4 width=3 by ffdeq_intro_dx, lfdeq_trans, tdeq_lfdeq_conf, tdeq_trans/
+qed-.
+
+(* Inversion lemmas with degree-based equivalence for closures **************)
+(*
+(* Basic_2A1: uses: fpb_inv_fleq *)
+lemma fpb_inv_ffdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
+ ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+[ #G2 #L2 #T2 #H12 #H elim (ffdeq_inv_gen_sn … H) -H
+ #_ #H1 #H2
+(*
+
+ /3 width=8 by lfdeq_fwd_length, fqu_inv_eq/
+*)
+| #T2 #_ #HnT #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
+| #L2 #_ #HnL #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
+]
+qed-.
+*)
\ No newline at end of file
(* Properties with degree-based equivalence for local environments **********)
+lemma tdeq_fpb_trans: ∀h,o,U2,U1. U2 ≛[h, o] U1 →
+ ∀G1,G2,L1,L2,T1. ⦃G1, L1, U1⦄ ≻[h, o] ⦃G2, L2, T1⦄ →
+ ∃∃L,T2. ⦃G1, L1, U2⦄ ≻[h, o] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
+#h #o #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
+[ #G2 #L2 #T1 #H
+ elim (tdeq_fqu_trans … H … HU21) -H
+ /3 width=5 by fpb_fqu, ex3_2_intro/
+| #T1 #HUT1 #HnUT1
+ elim (tdeq_cpx_trans … HU21 … HUT1) -HUT1
+ /6 width=5 by fpb_cpx, tdeq_canc_sn, tdeq_trans, ex3_2_intro/
+| /6 width=5 by fpb_lfpx, lfpx_tdeq_div, tdeq_lfdeq_conf, ex3_2_intro/
+]
+qed-.
+
(* Basic_2A1: was just: lleq_fpb_trans *)
lemma lfdeq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≛[h, o, T] K2 →
∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
∃∃K2. ⦃G, K1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] K2 & K2.ⓧ ≛[h, o, T] L2.
/3 width=5 by lfpx_fsge_comp, lfxs_bind_dx_split_void/ qed-.
+lemma lfpx_tdeq_conf: ∀h,o,G. s_r_confluent1 … (cdeq h o) (lfpx h G).
+/2 width=5 by tdeq_lfxs_conf/ qed-.
+
+lemma lfpx_tdeq_div: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
+ ∀G,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, T2] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T1] L2.
+/2 width=5 by tdeq_lfxs_div/ qed-.
+
lemma cpx_tdeq_conf_lexs: ∀h,o,G. R_confluent2_lfxs … (cpx h G) (cdeq h o) (cpx h G) (cdeq h o).
#h #o #G #L0 #T0 #T1 #H @(cpx_ind … H) -G -L0 -T0 -T1 /2 width=3 by ex2_intro/
[ #G #L0 #s0 #X0 #H0 #L1 #HL01 #L2 #HL02
∀L2. L1 ≛[h, o, f] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
/2 width=7 by frees_tdeq_conf_lfdeq, tdeq_refl/ qed-.
-lemma tdeq_lfdeq_conf: ∀h,o. s_r_confluent1 … (cdeq h o) (lfdeq h o).
-#h #o #L1 #T1 #T2 #HT12 #L2 *
+lemma tdeq_lfxs_conf: ∀R,h,o. s_r_confluent1 … (cdeq h o) (lfxs R).
+#R #h #o #L1 #T1 #T2 #HT12 #L2 *
/3 width=5 by frees_tdeq_conf, ex2_intro/
qed-.
+lemma tdeq_lfxs_div: ∀R,h,o,T1,T2. T1 ≛[h, o] T2 →
+ ∀L1,L2. L1 ⪤*[R, T2] L2 → L1 ⪤*[R, T1] L2.
+/3 width=5 by tdeq_lfxs_conf, tdeq_sym/ qed-.
+
+lemma tdeq_lfdeq_conf: ∀h,o. s_r_confluent1 … (cdeq h o) (lfdeq h o).
+/2 width=5 by tdeq_lfxs_conf/ qed-.
+
lemma tdeq_lfdeq_div: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
∀L1,L2. L1 ≛[h, o, T2] L2 → L1 ≛[h, o, T1] L2.
-/3 width=3 by tdeq_lfdeq_conf, tdeq_sym/ qed-.
+/2 width=5 by tdeq_lfxs_div/ qed-.
lemma lfdeq_atom: ∀h,o,I. ⋆ ≛[h, o, ⓪{I}] ⋆.
/2 width=1 by lfxs_atom/ qed.
<subsection name="A2">Stage "A2": "Extending the Applicability Condition"</subsection>
+ <news class="alpha" date="2018 March 9.">
+ Support for rt-computation completed.
+ </news>
<news class="alpha" date="2017 October 17.">
Exclusion binder in local environments.
Syntactic component updated:
(anniversary milestone).
</news>
<news class="alpha" date="2017 March 16.">
- First behavioral component reconstructed:
+ First behavioral component completed:
rt_transition.
</news>
<news class="alpha" date="2017 February 19.">
Confluence for context-sensitive parallel r-transition on terms.
</news>
<news class="alpha" date="2016 April 16.">
- Syntactic component reconstructed:
+ Syntactic component completed:
syntax, relocation, s_transition, s_computation, static
(anniversary milestone).
</news>
[ { "rt-transition" * } {
[ { "uncounted parallel rst-transition" * } {
[ [ "for closures" ] "fpbq" + "( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_aaa" * ]
- [ [ "proper for closures" ] "fpb" + "( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" * ]
+ [ [ "proper for closures" ] "fpb" + "( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" + "fpb_ffdeq" * ]
}
]
[ { "context-sensitive parallel r-transition" * } {
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