src/HOL/BCV/DFAimpl.ML

--- a/src/HOL/BCV/DFAimpl.ML	Thu Oct 28 14:00:25 1999 +0200
+++ b/src/HOL/BCV/DFAimpl.ML	Thu Oct 28 14:55:23 1999 +0200
@@ -7,40 +7,40 @@
 (** merges **)
 
 Goal "!sos. size(merges t ps sos) = size sos";
-by(induct_tac "ps" 1);
-by(Auto_tac);
+by (induct_tac "ps" 1);
+by (Auto_tac);
 qed_spec_mp "length_merges";
 Addsimps [length_merges];
 
 Goal
  "!xs. xs : listsn n (option A) --> x : A --> (!p : set ps. p<n) --> \
 \      semilat A --> merges x ps xs : listsn n (option A)";
-by(induct_tac "ps" 1);
-by(Auto_tac);
+by (induct_tac "ps" 1);
+by (Auto_tac);
 qed_spec_mp "merges_preserves_type";
 Addsimps [merges_preserves_type];
 (*AddSIs [merges_preserves_type];*)
 
 Goal "semilat A ==> !xs. xs : listsn n (option A) --> x:A --> (!p:set ps. p<n) \
 \ --> xs <= merges x ps xs";
-by(induct_tac "ps" 1);
- by(Simp_tac 1);
-by(Simp_tac 1);
-by(Clarify_tac 1);
-br order_trans 1;
- be list_update_incr 1;
-   by(Blast_tac 2);
-  ba 2;
- be (Some_in_option RS iffD2) 1;
-by(blast_tac (claset() addSIs [listsnE_set]
+by (induct_tac "ps" 1);
+ by (Simp_tac 1);
+by (Simp_tac 1);
+by (Clarify_tac 1);
+by (rtac order_trans 1);
+ by (etac list_update_incr 1);
+   by (Blast_tac 2);
+  by (assume_tac 2);
+ by (etac (Some_in_option RS iffD2) 1);
+by (blast_tac (claset() addSIs [listsnE_set]
           addIs [semilat_plus,listsnE_length RS nth_in]) 1);
 qed_spec_mp "merges_incr";
 
 (* is redundant but useful *)
 Goal "[| xs!i = Some x; xs : listsn n (option A); i < n |] ==> x:A";
-bd listsnE_nth_in 1;
-ba 1;
-by(Asm_full_simp_tac 1);
+by (dtac listsnE_nth_in 1);
+by (assume_tac 1);
+by (Asm_full_simp_tac 1);
 qed "listsn_optionE_in";
 (*Addsimps [listsn_optionE_in];*)
 
@@ -48,29 +48,29 @@
  "[| semilat L |] ==> \
 \ (!xs. xs : listsn n (option L) --> x:L --> (!p:set ps. p<n) --> \
 \      (merges x ps xs = xs) = (!p:set ps. Some x <= xs!p))";
-by(induct_tac "ps" 1);
- by(Asm_simp_tac 1);
-by(Clarsimp_tac 1);
-by(rename_tac "p ps xs" 1);
-br iffI 1;
- br context_conjI 1;
-  by(subgoal_tac "xs[p := Some x + xs!p] <= xs" 1);
-   by(EVERY[etac subst 2, rtac merges_incr 2]);
-      ba 2;
-     by(Force_tac 2);
-    ba 2;
-   ba 2;
-  by(exhaust_tac "xs!p" 1);
-   by(asm_full_simp_tac (simpset() addsimps [list_update_le_conv]) 1);
-  by(asm_full_simp_tac (simpset() addsimps
+by (induct_tac "ps" 1);
+ by (Asm_simp_tac 1);
+by (Clarsimp_tac 1);
+by (rename_tac "p ps xs" 1);
+by (rtac iffI 1);
+ by (rtac context_conjI 1);
+  by (subgoal_tac "xs[p := Some x + xs!p] <= xs" 1);
+   by (EVERY[etac subst 2, rtac merges_incr 2]);
+      by (assume_tac 2);
+     by (Force_tac 2);
+    by (assume_tac 2);
+   by (assume_tac 2);
+  by (exhaust_tac "xs!p" 1);
+   by (asm_full_simp_tac (simpset() addsimps [list_update_le_conv]) 1);
+  by (asm_full_simp_tac (simpset() addsimps
       [list_update_le_conv,listsn_optionE_in]) 1);
- by(Clarify_tac 1);
- by(rotate_tac ~3 1);
- by(asm_full_simp_tac (simpset() addsimps
+ by (Clarify_tac 1);
+ by (rotate_tac ~3 1);
+ by (asm_full_simp_tac (simpset() addsimps
       [le_iff_plus_unchanged RS iffD1,listsn_optionE_in,
        list_update_same_conv RS iffD2]) 1);
-by(Clarify_tac 1);
-by(asm_simp_tac (simpset() addsimps
+by (Clarify_tac 1);
+by (asm_simp_tac (simpset() addsimps
       [le_iff_plus_unchanged RS iffD1,listsn_optionE_in,
        list_update_same_conv RS iffD2]) 1);
 qed_spec_mp "merges_same_conv";
@@ -80,11 +80,11 @@
  "xs <= ys --> xs : listsn n (option L) --> ys : listsn n (option L) --> \
 \ p < n --> ys!p = Some y --> x <= y --> x : L --> semilat L --> \
 \ xs[p := Some x + xs!p] <= ys";
-by(simp_tac (simpset()  addsimps [nth_list_update]
+by (simp_tac (simpset()  addsimps [nth_list_update]
                         addsplits [option.split]) 1);
-by(Clarify_tac 1);
-by(rotate_tac 3 1);
-by(force_tac (claset() addEs [listsn_optionE_in] addIs [semilat_lub],
+by (Clarify_tac 1);
+by (rotate_tac 3 1);
+by (force_tac (claset() addEs [listsn_optionE_in] addIs [semilat_lub],
               simpset()) 1);
 qed_spec_mp "list_update_le_listI";
 
@@ -94,9 +94,9 @@
 \    !p. p:set ps --> p<n |] ==> \
 \ set qs <= set ps  --> \
 \ (!sos. sos : listsn n (option L) & sos <= tos --> merges t qs sos <= tos)";
-by(induct_tac "qs" 1);
- by(Asm_simp_tac 1);
-by(force_tac (claset(),simpset() addsimps [list_update_le_listI]) 1);
+by (induct_tac "qs" 1);
+ by (Asm_simp_tac 1);
+by (force_tac (claset(),simpset() addsimps [list_update_le_listI]) 1);
 val lemma = result();
 
 Goal
@@ -105,7 +105,7 @@
 \    !p. p:set ps --> p<n; \
 \    sos <= tos; sos : listsn n (option L); tos : listsn n (option L) |] \
 \ ==> merges t ps sos <= tos";
-by(blast_tac (claset() addDs [lemma]) 1);
+by (blast_tac (claset() addDs [lemma]) 1);
 qed "merges_pres_le_ub";
 
 
@@ -115,9 +115,9 @@
  "[| is_next next; next step succs sos = None; succs_bounded succs n; \
 \    sos : listsn n S |] ==> \
 \ ? p<n. ? s. sos!p = Some s & step p s = None";
-by(subgoal_tac "n=size sos" 1);
-by(Blast_tac 1);
-by(Asm_simp_tac 1);
+by (subgoal_tac "n=size sos" 1);
+by (Blast_tac 1);
+by (Asm_simp_tac 1);
 qed "next_None";
 
 Goalw [is_next_def]
@@ -125,9 +125,9 @@
 \ next step succs sos = Some sos --> \
 \ (!p<n. !s. sos!p = Some s --> (? t. \
 \         step p s = Some(t) & merges t (succs p) sos = sos))";
-by(subgoal_tac "n=size sos" 1);
-by(Blast_tac 1);
-by(Asm_simp_tac 1);
+by (subgoal_tac "n=size sos" 1);
+by (Blast_tac 1);
+by (Asm_simp_tac 1);
 qed "next_Some1";
 
 Goalw [is_next_def]
@@ -135,9 +135,9 @@
 \    succs_bounded succs n; sos : listsn n S |] ==> \
 \ ? p<n. ? s. sos!p = Some s & (? t. \
 \     step p s = Some(t) & merges t (succs p) sos = sos')";
-by(subgoal_tac "n=size sos" 1);
-by(Blast_tac 1);
-by(Asm_simp_tac 1);
+by (subgoal_tac "n=size sos" 1);
+by (Blast_tac 1);
+by (Asm_simp_tac 1);
 qed "next_Some2";
 
 Goal
@@ -145,26 +145,26 @@
 \ (next step succs sos = Some sos) = \
 \ (!p<n. !s. sos!p = Some s --> (? t. \
 \         step p s = Some(t) & merges t (succs p) sos = sos))";
-br iffI 1;
- by(asm_simp_tac (simpset() addsimps [next_Some1]) 1);
-by(exhaust_tac "next step succs sos" 1);
- by(best_tac (claset() addSDs [next_None] addss simpset()) 1);
-by(rename_tac "sos'" 1);
-by(case_tac "sos' = sos" 1);
- by(Blast_tac 1);
-by(best_tac (claset() addSDs [next_Some2] addss simpset()) 1);
+by (rtac iffI 1);
+ by (asm_simp_tac (simpset() addsimps [next_Some1]) 1);
+by (exhaust_tac "next step succs sos" 1);
+ by (best_tac (claset() addSDs [next_None] addss simpset()) 1);
+by (rename_tac "sos'" 1);
+by (case_tac "sos' = sos" 1);
+ by (Blast_tac 1);
+by (best_tac (claset() addSDs [next_Some2] addss simpset()) 1);
 qed "next_Some1_eq";
 
 Addsimps [next_Some1_eq];
 
 Goalw [step_pres_type_def]
  "[| step_pres_type step n L; s:L; p<n; step p s = Some(t) |] ==> t:L";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "step_pres_typeD";
 
 Goalw [succs_bounded_def]
  "[| succs_bounded succs n; p < n; q : set(succs p) |] ==> q < n";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "succs_boundedD";
 
 Goal
@@ -172,21 +172,21 @@
 \    step_pres_type step n A; succs_bounded succs n;\
 \    sos : listsn n (option A) |] ==> \
 \ next step succs sos : option (listsn n (option A))";
-by(exhaust_tac "next step succs sos" 1);
- by(ALLGOALS Asm_simp_tac);
-by(rename_tac "sos'" 1);
-by(case_tac "sos' = sos" 1);
- by(Asm_simp_tac 1);
-by(blast_tac (claset() addIs [step_pres_typeD,succs_boundedD,listsn_optionE_in] addSIs [merges_preserves_type] addDs [next_Some2]) 1);
+by (exhaust_tac "next step succs sos" 1);
+ by (ALLGOALS Asm_simp_tac);
+by (rename_tac "sos'" 1);
+by (case_tac "sos' = sos" 1);
+ by (Asm_simp_tac 1);
+by (blast_tac (claset() addIs [step_pres_typeD,succs_boundedD,listsn_optionE_in] addSIs [merges_preserves_type] addDs [next_Some2]) 1);
 qed_spec_mp "next_preserves_type";
 
 Goal
  "[| is_next next; semilat A; \
 \    step_pres_type step n A; succs_bounded succs n; \
 \    next step succs xs = Some ys; xs : listsn n (option A) |] ==> xs <= ys";
-by(case_tac "ys = xs" 1);
- by(Asm_full_simp_tac 1);
-by(blast_tac (claset() addSIs [merges_incr] addIs [listsn_optionE_in]
+by (case_tac "ys = xs" 1);
+ by (Asm_full_simp_tac 1);
+by (blast_tac (claset() addSIs [merges_incr] addIs [listsn_optionE_in]
        addDs [step_pres_typeD,succs_boundedD,next_Some2]) 1);
 qed_spec_mp "next_incr";
 
@@ -196,13 +196,13 @@
 
 Goalw [is_next_def]
  "is_next (%step succs sos. itnext (size sos) step succs sos)";
-by(Clarify_tac 1);
-by(etac thin_rl 1);
-by(res_inst_tac [("n","length sos")] nat_induct 1);
- by(Asm_full_simp_tac 1);
-by(asm_full_simp_tac (simpset() addsimps [less_Suc_eq,Let_def]
+by (Clarify_tac 1);
+by (etac thin_rl 1);
+by (res_inst_tac [("n","length sos")] nat_induct 1);
+ by (Asm_full_simp_tac 1);
+by (asm_full_simp_tac (simpset() addsimps [less_Suc_eq,Let_def]
                                 addsplits [option.split])1);
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "is_next_itnext";
 
 Unify.trace_bound := !(fst lemma);
@@ -213,37 +213,37 @@
 Goalw [step_mono_None_def]
  "[| step_mono_None step n L; s : L; p < n; s <= t; step p s = None |] ==> \
 \ step p t = None";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "step_mono_NoneD";
 
 Goalw [step_mono_def]
  "[| step_mono step n L; s : L; p < n; s <= t; step p s = Some(u) |] ==> \
 \ !v. step p t = Some(v) --> u <= v";
-by(Blast_tac 1);
+by (Blast_tac 1);
 qed "step_monoD";
 
 Goalw [stable_def]
 "[| is_next next; semilat L; sos : listsn n (option L); \
 \   step_pres_type step n L; succs_bounded succs n |] \
 \ ==> (next step succs sos = Some sos) = (!p<n. stable step succs p sos)";
-by(Asm_simp_tac 1);
-br iffI 1;
- by(Clarify_tac 1);
- by(etac allE 1 THEN mp_tac 1);
- by(etac allE 1 THEN mp_tac 1);
- by(Clarify_tac 1);
+by (Asm_simp_tac 1);
+by (rtac iffI 1);
+ by (Clarify_tac 1);
+ by (etac allE 1 THEN mp_tac 1);
+ by (etac allE 1 THEN mp_tac 1);
+ by (Clarify_tac 1);
  bd(merges_same_conv RS iffD1)1;
-     ba 4;
-    ba 1;
-   by(blast_tac (claset() addIs [step_pres_typeD,listsn_optionE_in]) 1);
-  by(blast_tac (claset() addIs [succs_boundedD,listsn_optionE_in]) 1);
- by(Blast_tac 1);
-by(Clarify_tac 1);
-by(etac allE 1 THEN mp_tac 1);
-by(Asm_full_simp_tac 1);
-by(Clarify_tac 1);
-by(Asm_simp_tac 1);
-by(blast_tac (claset() addSIs [merges_same_conv RS iffD2]
+     by (assume_tac 4);
+    by (assume_tac 1);
+   by (blast_tac (claset() addIs [step_pres_typeD,listsn_optionE_in]) 1);
+  by (blast_tac (claset() addIs [succs_boundedD,listsn_optionE_in]) 1);
+ by (Blast_tac 1);
+by (Clarify_tac 1);
+by (etac allE 1 THEN mp_tac 1);
+by (Asm_full_simp_tac 1);
+by (Clarify_tac 1);
+by (Asm_simp_tac 1);
+by (blast_tac (claset() addSIs [merges_same_conv RS iffD2]
      addIs [step_pres_typeD,succs_boundedD,listsn_optionE_in]) 1);
 qed "fixpoint_next_iff_stable";
 
@@ -253,60 +253,60 @@
 \    tos:listsn n (option L); next step succs tos = Some tos; \
 \    sos:listsn n (option L); sos <= tos |] \
 \ ==> ? sos'. next step succs sos = Some sos' & sos' <= tos";
-by(subgoal_tac
+by (subgoal_tac
    "!p<n. !s. sos!p = Some s --> (? u. \
 \             step p s = Some(u) & (!q:set(succs p). Some u<=tos!q))" 1);
- by(exhaust_tac "next step succs sos" 1);
-  bd next_None 1;
-     ba 1;
-    ba 1;
-   ba 1;
-  by(Force_tac 1);
- by(rename_tac "sos'" 1);
- by(case_tac "sos' = sos" 1);
-  by(Blast_tac 1);
- bd next_Some2 1;
-    by(EVERY1[atac, atac, atac, atac]);
- by(Clarify_tac 1);
- by(etac allE 1 THEN mp_tac 1);
- by(etac allE 1 THEN mp_tac 1);
- by(Clarify_tac 1);
- by(EVERY1[rtac exI, rtac conjI, atac]);
- br merges_pres_le_ub 1;
-       ba 1;
-      by(blast_tac (claset() addIs [step_pres_typeD,listsn_optionE_in]) 1);
-     by(Asm_full_simp_tac 1);
-    by(blast_tac (claset() addIs [succs_boundedD,listsn_optionE_in]) 1);
-   by(REPEAT(atac 1));
-by(Clarify_tac 1);
-by(exhaust_tac "tos!p" 1);
- by(force_tac (claset() addDs [le_listD],simpset()) 1);
-by(rename_tac "t" 1);
-by(subgoal_tac "s <= t" 1);
- by(force_tac (claset() addDs [le_listD],simpset()) 2);
-by(exhaust_tac "step p s" 1);
- bd step_mono_NoneD 1;
-     ba 4;
-    by(blast_tac (claset() addIs [listsn_optionE_in]) 1);
-   ba 1;
-  ba 1;
- by(Force_tac 1);
-bd step_monoD 1;
-    ba 4;
-   by(blast_tac (claset() addIs [listsn_optionE_in]) 1);
-  ba 1;
- ba 1;
-by(Asm_full_simp_tac 1);
-by(etac allE 1 THEN mp_tac 1);
-by(etac allE 1 THEN mp_tac 1);
-by(Clarify_tac 1);
-by(Asm_full_simp_tac 1);
-by(forward_tac[merges_same_conv RS iffD1]1);
-    ba 4;
-   ba 1;
-  by(blast_tac (claset() addIs [step_pres_typeD,listsn_optionE_in]) 1);
- by(blast_tac (claset() addIs [succs_boundedD,listsn_optionE_in]) 1);
-by(blast_tac (claset() addIs [order_trans]) 1);
+ by (exhaust_tac "next step succs sos" 1);
+  by (dtac next_None 1);
+     by (assume_tac 1);
+    by (assume_tac 1);
+   by (assume_tac 1);
+  by (Force_tac 1);
+ by (rename_tac "sos'" 1);
+ by (case_tac "sos' = sos" 1);
+  by (Blast_tac 1);
+ by (dtac next_Some2 1);
+    by (EVERY1[atac, atac, atac, atac]);
+ by (Clarify_tac 1);
+ by (etac allE 1 THEN mp_tac 1);
+ by (etac allE 1 THEN mp_tac 1);
+ by (Clarify_tac 1);
+ by (EVERY1[rtac exI, rtac conjI, atac]);
+ by (rtac merges_pres_le_ub 1);
+       by (assume_tac 1);
+      by (blast_tac (claset() addIs [step_pres_typeD,listsn_optionE_in]) 1);
+     by (Asm_full_simp_tac 1);
+    by (blast_tac (claset() addIs [succs_boundedD,listsn_optionE_in]) 1);
+   by (REPEAT(atac 1));
+by (Clarify_tac 1);
+by (exhaust_tac "tos!p" 1);
+ by (force_tac (claset() addDs [le_listD],simpset()) 1);
+by (rename_tac "t" 1);
+by (subgoal_tac "s <= t" 1);
+ by (force_tac (claset() addDs [le_listD],simpset()) 2);
+by (exhaust_tac "step p s" 1);
+ by (dtac step_mono_NoneD 1);
+     by (assume_tac 4);
+    by (blast_tac (claset() addIs [listsn_optionE_in]) 1);
+   by (assume_tac 1);
+  by (assume_tac 1);
+ by (Force_tac 1);
+by (dtac step_monoD 1);
+    by (assume_tac 4);
+   by (blast_tac (claset() addIs [listsn_optionE_in]) 1);
+  by (assume_tac 1);
+ by (assume_tac 1);
+by (Asm_full_simp_tac 1);
+by (etac allE 1 THEN mp_tac 1);
+by (etac allE 1 THEN mp_tac 1);
+by (Clarify_tac 1);
+by (Asm_full_simp_tac 1);
+by (forward_tac[merges_same_conv RS iffD1]1);
+    by (assume_tac 4);
+   by (assume_tac 1);
+  by (blast_tac (claset() addIs [step_pres_typeD,listsn_optionE_in]) 1);
+ by (blast_tac (claset() addIs [succs_boundedD,listsn_optionE_in]) 1);
+by (blast_tac (claset() addIs [order_trans]) 1);
 val lemma = result();
 
 Goalw [is_dfa_def]
@@ -314,14 +314,14 @@
 \    step_pres_type step n L; succs_bounded succs n; \
 \    step_mono_None step n L; step_mono step n L |] ==> \
 \ is_dfa (%sos. fix(next step succs, sos)) step succs n L";
-by(Clarify_tac 1);
-by(stac fix_iff_has_fixpoint 1);
-     by(etac (acc_option RS acc_listsn) 1);
-    by(blast_tac (claset() addIs [lemma]) 1);
-   by(blast_tac (claset() addIs [next_preserves_type]) 1);
-  by(blast_tac (claset() addIs [next_incr]) 1);
- ba 1;
-by(asm_simp_tac (simpset() delsimps [next_Some1_eq] addsimps [fixpoint_next_iff_stable]) 1);
+by (Clarify_tac 1);
+by (stac fix_iff_has_fixpoint 1);
+     by (etac (acc_option RS acc_listsn) 1);
+    by (blast_tac (claset() addIs [lemma]) 1);
+   by (blast_tac (claset() addIs [next_preserves_type]) 1);
+  by (blast_tac (claset() addIs [next_incr]) 1);
+ by (assume_tac 1);
+by (asm_simp_tac (simpset() delsimps [next_Some1_eq] addsimps [fixpoint_next_iff_stable]) 1);
 qed "is_dfa_fix_next";
 
 Goal
@@ -332,5 +332,5 @@
 \    sos : listsn n (option L) |] ==> \
 \ fix(next step succs, sos) = \
 \ (? tos:listsn n (option L). sos<=tos & welltyping wti tos)";
-by(blast_tac (claset() addSDs [dfa_iff_welltyping] addSIs [is_dfa_fix_next]) 1);
+by (blast_tac (claset() addSDs [dfa_iff_welltyping] addSIs [is_dfa_fix_next]) 1);
 qed "fix_next_iff_welltyping";