1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 include "basic_2/rt_computation/cpms_cpms.ma".
16 include "basic_2/rt_computation/cprs_cpr.ma".
18 (* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
20 (* Main properties **********************************************************)
22 (* Basic_1: was: pr3_t *)
23 (* Basic_1: includes: pr1_t *)
24 theorem cprs_trans (h) (G) (L): Transitive … (cpms h G L 0).
25 /2 width=3 by cpms_trans/ qed-.
27 (* Basic_1: was: pr3_confluence *)
28 (* Basic_1: includes: pr1_confluence *)
29 theorem cprs_conf (h) (G) (L): confluent2 … (cpms h G L 0) (cpms h G L 0).
30 #h #G #L #T0 #T1 #HT01 #T2 #HT02
31 elim (TC_confluent2 … T0 T1 … T2)
32 [ /3 width=3 by cprs_CTC, ex2_intro/ |5,6: skip
33 | /2 width=1 by cprs_inv_CTC/
34 | /2 width=1 by cprs_inv_CTC/
35 | /2 width=3 by cpr_conf/
39 (* Basic_1: was: pr3_flat *)
40 theorem cprs_flat (h) (G) (L):
41 ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
42 ∀V1,V2. ⦃G,L⦄ ⊢ V1 ➡*[h] V2 →
43 ∀I. ⦃G,L⦄ ⊢ ⓕ{I}V1.T1 ➡*[h] ⓕ{I}V2.T2.
44 #h #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind_dx … H) -V2
45 [ /2 width=3 by cprs_flat_dx/
46 | /3 width=3 by cpr_pair_sn, cprs_step_dx/
50 (* Advanced inversion lemmas ************************************************)
52 (* Basic_1: was pr3_gen_appl *)
53 (* Basic_2A1: was: cprs_inv_appl1 *)
54 lemma cprs_inv_appl_sn (h) (G) (L):
55 ∀V1,T1,X2. ⦃G,L⦄ ⊢ ⓐV1.T1 ➡*[h] X2 →
56 ∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ➡*[h] V2 &
59 | ∃∃p,W,T. ⦃G,L⦄ ⊢ T1 ➡*[h] ⓛ{p}W.T &
60 ⦃G,L⦄ ⊢ ⓓ{p}ⓝW.V1.T ➡*[h] X2
61 | ∃∃p,V0,V2,V,T. ⦃G,L⦄ ⊢ V1 ➡*[h] V0 & ⬆*[1] V0 ≘ V2 &
62 ⦃G,L⦄ ⊢ T1 ➡*[h] ⓓ{p}V.T &
63 ⦃G,L⦄ ⊢ ⓓ{p}V.ⓐV2.T ➡*[h] X2.
64 #h #G #L #V1 #T1 #X2 #H elim (cpms_inv_appl_sn … H) -H *
65 [ /3 width=5 by or3_intro0, ex3_2_intro/
66 | #n1 #n2 #p #V2 #T2 #HT12 #HTX2 #H
67 elim (plus_inv_O3 … H) -H #H1 #H2 destruct
68 /3 width=5 by or3_intro1, ex2_3_intro/
69 | #n1 #n2 #p #V2 #W2 #V #T2 #HV12 #HVW2 #HT12 #HTX2 #H
70 elim (plus_inv_O3 … H) -H #H1 #H2 destruct
71 /3 width=9 by or3_intro2, ex4_5_intro/