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[helm.git] / matita / matita / lib / turing / mono.ma

diff --git a/matita/matita/lib/turing/mono.ma b/matita/matita/lib/turing/mono.ma
index a192f608ec46475fbbe7c48090f6c04a07bbc8aa..e559c88dbc7970375f6a6b41bfe50ac62e2d825b 100644 (file)
--- a/matita/matita/lib/turing/mono.ma
+++ b/matita/matita/lib/turing/mono.ma
@@ -183,6 +183,11 @@ lemma loop_eq : ∀sig,f,q,i,j,a,x,y.
 ]
 qed.
 
+lemma loop_p_true : 
+  ∀A,k,f,p,a.p a = true → loop A (S k) f p a = Some ? a.
+#A #k #f #p #a #Ha normalize >Ha %
+qed.
+
 lemma loop_Some : 
   ∀A,k,f,p,a,b.loop A k f p a = Some ? b → p b = true.
 #A #k #f #p elim k 
@@ -209,6 +214,10 @@ qed.
 definition loopM ≝ λsig,M,i,cin.
   loop ? i (step sig M) (λc.halt sig M (cstate ?? c)) cin.
 
+lemma loopM_unfold : ∀sig,M,i,cin.
+  loopM sig M i cin = loop ? i (step sig M) (λc.halt sig M (cstate ?? c)) cin.
+// qed.
+
 definition initc ≝ λsig.λM:TM sig.λt.
   mk_config sig (states sig M) (start sig M) t.
 
@@ -248,6 +257,9 @@ definition accRealize ≝ λsig.λM:TM sig.λacc:states sig M.λRtrue,Rfalse.
   loopM sig M i (initc sig M t) = Some ? outc ∧
     (cstate ?? outc = acc → Rtrue t (ctape ?? outc)) ∧ 
     (cstate ?? outc ≠ acc → Rfalse t (ctape ?? outc)).
+    
+notation "M ⊨ [q: R1,R2]" non associative with precedence 45 for @{ 'cmodels $M $q $R1 $R2}.
+interpretation "conditional realizability" 'cmodels M q R1 R2 = (accRealize ? M q R1 R2).
 
 (******************************** NOP Machine *********************************)
 
@@ -270,6 +282,12 @@ lemma sem_nop :
 @(ex_intro … (mk_config ?? start_nop intape)) % % 
 qed.
 
+lemma nop_single_state: ∀sig.∀q1,q2:states ? (nop sig). q1 = q2.
+normalize #sig * #n #ltn1 * #m #ltm1 
+generalize in match ltn1; generalize in match ltm1;
+<(le_n_O_to_eq … (le_S_S_to_le … ltn1)) <(le_n_O_to_eq … (le_S_S_to_le … ltm1)) 
+// qed.
+
 (************************** Sequential Composition ****************************)
 
 definition seq_trans ≝ λsig. λM1,M2 : TM sig. 
@@ -292,11 +310,6 @@ definition seq ≝ λsig. λM1,M2 : TM sig.
 notation "a · b" non associative with precedence 65 for @{ 'middot $a $b}.
 interpretation "sequential composition" 'middot a b = (seq ? a b).
 
-definition Rcomp ≝ λA.λR1,R2:relation A.λa1,a2.
-  ∃am.R1 a1 am ∧ R2 am a2.
-  
-interpretation "relation composition" 'compose R1 R2 = (Rcomp ? R1 R2).
-
 definition lift_confL ≝ 
   λsig,S1,S2,c.match c with 
   [ mk_config s t ⇒ mk_config sig (FinSum S1 S2) (inl … s) t ].