+(*
+ ||M|| This file is part of HELM, an Hypertextual, Electronic
+ ||A|| Library of Mathematics, developed at the Computer Science
+ ||T|| Department of the University of Bologna, Italy.
+ ||I||
+ ||T||
+ ||A||
+ \ / This file is distributed under the terms of the
+ \ / GNU General Public License Version 2
+ V_____________________________________________________________*)
+
+
+include "turing/universal/trans_to_tuples.ma".
+
+check TM
+
+(* definition zero : ∀n.initN n ≝ λn.mk_Sig ?? 0 (le_O_n n). *)
+
+definition normalTM ≝ λn,t,h.
+ λk:0<n.mk_TM FinBool (initN n) t (mk_Sig ?? 0 k) h.
+
+definition low_config: ∀n,h,t.config FinBool (initN n) → tape STape ≝
+λn,h.λtrans:trans_source n →trans_target n.λc.
+ let q ≝ cstate … c in
+ let q_low ≝ m_bits_of_state n h q in
+ let current_low ≝
+ match current … (ctape … c) with
+ [ None ⇒ 〈null,false〉
+ | Some b ⇒ 〈bit b,false〉] in
+ let low_left ≝ map … (λb.〈bit b,false〉) (left … (ctape …c)) in
+ let low_right ≝ map … (λb.〈bit b,false〉) (right … (ctape …c)) in
+ let table ≝ flatten ? (tuples_of_pairs n h (graph_enum ?? trans)) in
+ mk_tape STape low_left (Some ? 〈grid,false〉)
+ (q_low@current_low::〈grid,false〉::table@〈grid,false〉::low_right).
+
+(*
+definition R_uni_step_true ≝ λt1,t2.
+ ∀n,t0,table,s0,s1,c0,c1,ls,rs,curconfig,newconfig,mv.
+ table_TM (S n) (〈t0,false〉::table) →
+ match_in_table (S n) (〈s0,false〉::curconfig) 〈c0,false〉
+ (〈s1,false〉::newconfig) 〈c1,false〉 〈mv,false〉 (〈t0,false〉::table) →
+ legal_tape ls 〈c0,false〉 rs →
+ t1 = midtape STape (〈grid,false〉::ls) 〈s0,false〉
+ (curconfig@〈c0,false〉::〈grid,false〉::〈t0,false〉::table@〈grid,false〉::rs) →
+ ∀t1'.t1' = lift_tape ls 〈c0,false〉 rs →
+ s0 = bit false ∧
+ ∃ls1,rs1,c2.
+ (t2 = midtape STape (〈grid,false〉::ls1) 〈s1,false〉
+ (newconfig@〈c2,false〉::〈grid,false〉::〈t0,false〉::table@〈grid,false〉::rs1) ∧
+ lift_tape ls1 〈c2,false〉 rs1 =
+ tape_move STape t1' (map_move c1 mv) ∧ legal_tape ls1 〈c2,false〉 rs1).
+ *)
\ No newline at end of file