--- a/src/HOL/ex/Comb.ML Wed Apr 23 11:05:18 1997 +0200
+++ b/src/HOL/ex/Comb.ML Wed Apr 23 11:05:52 1997 +0200
@@ -28,8 +28,8 @@
"!!r. [| diamond(r); (x,y):r^* |] ==> \
\ ALL y'. (x,y'):r --> (EX z. (y',z): r^* & (y,z): r)";
by (etac rtrancl_induct 1);
-by (Fast_tac 1);
-by (slow_best_tac (!claset addIs [r_into_rtrancl RSN (2, rtrancl_trans)]
+by (Blast_tac 1);
+by (slow_best_tac (set_cs addIs [r_into_rtrancl RSN (2, rtrancl_trans)]
addSDs [spec_mp]) 1);
val diamond_strip_lemmaE = result() RS spec RS mp RS exE;
@@ -37,44 +37,43 @@
by (rewtac diamond_def); (*unfold only in goal, not in premise!*)
by (rtac (impI RS allI RS allI) 1);
by (etac rtrancl_induct 1);
-by (Fast_tac 1);
-by (ALLGOALS (*Seems to be a brittle, undirected search*)
- (slow_best_tac ((claset_of "Fun") addIs [r_into_rtrancl, rtrancl_trans]
- addEs [major RS diamond_strip_lemmaE])));
+by (Blast_tac 1);
+by (slow_best_tac (*Seems to be a brittle, undirected search*)
+ (set_cs addIs [r_into_rtrancl RSN (2, rtrancl_trans)]
+ addEs [major RS diamond_strip_lemmaE]) 1);
qed "diamond_rtrancl";
(*** Results about Contraction ***)
-(** Non-contraction results **)
-
(*Derive a case for each combinator constructor*)
val K_contractE = contract.mk_cases comb.simps "K -1-> z";
val S_contractE = contract.mk_cases comb.simps "S -1-> z";
val Ap_contractE = contract.mk_cases comb.simps "x#y -1-> z";
-AddIs contract.intrs;
+AddSIs [contract.K, contract.S];
+AddIs [contract.Ap1, contract.Ap2];
AddSEs [K_contractE, S_contractE, Ap_contractE];
Unsafe_Addss (!simpset);
goalw Comb.thy [I_def] "!!z. I -1-> z ==> P";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "I_contract_E";
AddSEs [I_contract_E];
goal Comb.thy "!!x z. K#x -1-> z ==> (EX x'. z = K#x' & x -1-> x')";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "K1_contractD";
AddSEs [K1_contractD];
goal Comb.thy "!!x z. x ---> y ==> x#z ---> y#z";
by (etac rtrancl_induct 1);
-by (ALLGOALS (best_tac (!claset addIs [r_into_rtrancl, rtrancl_trans])));
+by (ALLGOALS (blast_tac (!claset addIs [r_into_rtrancl, rtrancl_trans])));
qed "Ap_reduce1";
goal Comb.thy "!!x z. x ---> y ==> z#x ---> z#y";
by (etac rtrancl_induct 1);
-by (ALLGOALS (best_tac (!claset addIs [r_into_rtrancl, rtrancl_trans])));
+by (ALLGOALS (blast_tac (!claset addIs [r_into_rtrancl, rtrancl_trans])));
qed "Ap_reduce2";
(** Counterexample to the diamond property for -1-> **)
@@ -84,15 +83,15 @@
qed "KIII_contract1";
goalw Comb.thy [I_def] "K#I#(I#I) -1-> K#I#((K#I)#(K#I))";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "KIII_contract2";
goal Comb.thy "K#I#((K#I)#(K#I)) -1-> I";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "KIII_contract3";
goalw Comb.thy [diamond_def] "~ diamond(contract)";
-by (fast_tac (!claset addIs [KIII_contract1,KIII_contract2,KIII_contract3]) 1);
+by (blast_tac (!claset addIs [KIII_contract1,KIII_contract2,KIII_contract3]) 1);
qed "not_diamond_contract";
@@ -111,18 +110,18 @@
(*** Basic properties of parallel contraction ***)
goal Comb.thy "!!x z. K#x =1=> z ==> (EX x'. z = K#x' & x =1=> x')";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "K1_parcontractD";
AddSDs [K1_parcontractD];
goal Comb.thy "!!x z. S#x =1=> z ==> (EX x'. z = S#x' & x =1=> x')";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "S1_parcontractD";
AddSDs [S1_parcontractD];
goal Comb.thy
"!!x y z. S#x#y =1=> z ==> (EX x' y'. z = S#x'#y' & x =1=> x' & y =1=> y')";
-by (Fast_tac 1);
+by (Blast_tac 1);
qed "S2_parcontractD";
AddSDs [S2_parcontractD];
@@ -133,7 +132,8 @@
goalw Comb.thy [diamond_def] "diamond parcontract";
by (rtac (impI RS allI RS allI) 1);
by (etac parcontract.induct 1 THEN prune_params_tac);
-by (ALLGOALS Fast_tac);
+by (Step_tac 1);
+by (ALLGOALS Blast_tac);
qed "diamond_parcontract";
@@ -143,25 +143,24 @@
by (rtac subsetI 1);
by (split_all_tac 1);
by (etac contract.induct 1);
-by (ALLGOALS Fast_tac);
+by (ALLGOALS Blast_tac);
qed "contract_subset_parcontract";
(*Reductions: simply throw together reflexivity, transitivity and
the one-step reductions*)
-AddSIs [contract.K, contract.S];
AddIs [Ap_reduce1, Ap_reduce2, r_into_rtrancl, rtrancl_trans];
(*Example only: not used*)
goalw Comb.thy [I_def] "I#x ---> x";
-by (Deepen_tac 0 1);
+by (Blast_tac 1);
qed "reduce_I";
goal Comb.thy "parcontract <= contract^*";
by (rtac subsetI 1);
by (split_all_tac 1);
by (etac parcontract.induct 1 THEN prune_params_tac);
-by (ALLGOALS (Deepen_tac 0));
+by (ALLGOALS Blast_tac);
qed "parcontract_subset_reduce";
goal Comb.thy "contract^* = parcontract^*";