diff -r f493a20feeb3 -r 04b5e904a220 thys3/FBound.thy
--- a/thys3/FBound.thy	Sat Apr 30 00:50:08 2022 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,180 +0,0 @@
-
-theory FBound
-  imports "BlexerSimp" "ClosedFormsBounds"
-begin
-
-fun distinctBy :: "'a list \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'b set \<Rightarrow> 'a list"
-  where
-  "distinctBy [] f acc = []"
-| "distinctBy (x#xs) f acc = 
-     (if (f x) \<in> acc then distinctBy xs f acc 
-      else x # (distinctBy xs f ({f x} \<union> acc)))"
-
-fun rerase :: "arexp \<Rightarrow> rrexp"
-where
-  "rerase AZERO = RZERO"
-| "rerase (AONE _) = RONE"
-| "rerase (ACHAR _ c) = RCHAR c"
-| "rerase (AALTs bs rs) = RALTS (map rerase rs)"
-| "rerase (ASEQ _ r1 r2) = RSEQ (rerase r1) (rerase r2)"
-| "rerase (ASTAR _ r) = RSTAR (rerase r)"
-
-lemma eq1_rerase:
-  shows "x ~1 y \<longleftrightarrow> (rerase x) = (rerase y)"
-  apply(induct x y rule: eq1.induct)
-  apply(auto)
-  done
-
-
-lemma distinctBy_distinctWith:
-  shows "distinctBy xs f (f ` acc) = distinctWith xs (\<lambda>x y. f x = f y) acc"
-  apply(induct xs arbitrary: acc)
-  apply(auto)
-  by (metis image_insert)
-
-lemma distinctBy_distinctWith2:
-  shows "distinctBy xs rerase {} = distinctWith xs eq1 {}"
-  apply(subst distinctBy_distinctWith[of _ _ "{}", simplified])
-  using eq1_rerase by presburger
-  
-lemma asize_rsize:
-  shows "rsize (rerase r) = asize r"
-  apply(induct r rule: rerase.induct)
-  apply(auto)
-  apply (metis (mono_tags, lifting) comp_apply map_eq_conv)
-  done
-
-lemma rerase_fuse:
-  shows "rerase (fuse bs r) = rerase r"
-  apply(induct r)
-       apply simp+
-  done
-
-lemma rerase_bsimp_ASEQ:
-  shows "rerase (bsimp_ASEQ x1 a1 a2) = rsimp_SEQ (rerase a1) (rerase a2)"
-  apply(induct x1 a1 a2 rule: bsimp_ASEQ.induct)
-  apply(auto)
-  done
-
-lemma rerase_bsimp_AALTs:
-  shows "rerase (bsimp_AALTs bs rs) = rsimp_ALTs (map rerase rs)"
-  apply(induct bs rs rule: bsimp_AALTs.induct)
-  apply(auto simp add: rerase_fuse)
-  done
-
-fun anonalt :: "arexp \<Rightarrow> bool"
-  where
-  "anonalt (AALTs bs2 rs) = False"
-| "anonalt r = True"
-
-
-fun agood :: "arexp \<Rightarrow> bool" where
-  "agood AZERO = False"
-| "agood (AONE cs) = True" 
-| "agood (ACHAR cs c) = True"
-| "agood (AALTs cs []) = False"
-| "agood (AALTs cs [r]) = False"
-| "agood (AALTs cs (r1#r2#rs)) = (distinct (map rerase (r1 # r2 # rs)) \<and>(\<forall>r' \<in> set (r1#r2#rs). agood r' \<and> anonalt r'))"
-| "agood (ASEQ _ AZERO _) = False"
-| "agood (ASEQ _ (AONE _) _) = False"
-| "agood (ASEQ _ _ AZERO) = False"
-| "agood (ASEQ cs r1 r2) = (agood r1 \<and> agood r2)"
-| "agood (ASTAR cs r) = True"
-
-
-fun anonnested :: "arexp \<Rightarrow> bool"
-  where
-  "anonnested (AALTs bs2 []) = True"
-| "anonnested (AALTs bs2 ((AALTs bs1 rs1) # rs2)) = False"
-| "anonnested (AALTs bs2 (r # rs2)) = anonnested (AALTs bs2 rs2)"
-| "anonnested r = True"
-
-
-lemma asize0:
-  shows "0 < asize r"
-  apply(induct  r)
-  apply(auto)
-  done
-
-lemma rnullable:
-  shows "rnullable (rerase r) = bnullable r"
-  apply(induct r rule: rerase.induct)
-  apply(auto)
-  done
-
-lemma rder_bder_rerase:
-  shows "rder c (rerase r ) = rerase (bder c r)"
-  apply (induct r)
-  apply (auto)
-  using rerase_fuse apply presburger
-  using rnullable apply blast
-  using rnullable by blast
-
-lemma rerase_map_bsimp:
-  assumes "\<And> r. r \<in> set rs \<Longrightarrow> rerase (bsimp r) = (rsimp \<circ> rerase) r"
-  shows "map rerase (map bsimp rs) =  map (rsimp \<circ> rerase) rs"
-  using assms
-  apply(induct rs)
-  by simp_all
-
-
-lemma rerase_flts:
-  shows "map rerase (flts rs) = rflts (map rerase rs)"
-  apply(induct rs rule: flts.induct)
-  apply(auto simp add: rerase_fuse)
-  done
-
-lemma rerase_dB:
-  shows "map rerase (distinctBy rs rerase acc) = rdistinct (map rerase rs) acc"
-  apply(induct rs arbitrary: acc)
-  apply simp+
-  done
-  
-lemma rerase_earlier_later_same:
-  assumes " \<And>r. r \<in> set rs \<Longrightarrow> rerase (bsimp r) = rsimp (rerase r)"
-  shows " (map rerase (distinctBy (flts (map bsimp rs)) rerase {})) =
-          (rdistinct (rflts (map (rsimp \<circ> rerase) rs)) {})"
-  apply(subst rerase_dB)
-  apply(subst rerase_flts)
-  apply(subst rerase_map_bsimp)
-  apply auto
-  using assms
-  apply simp
-  done
-
-lemma bsimp_rerase:
-  shows "rerase (bsimp a) = rsimp (rerase a)"
-  apply(induct a rule: bsimp.induct)
-  apply(auto)
-  using rerase_bsimp_ASEQ apply presburger
-  using distinctBy_distinctWith2 rerase_bsimp_AALTs rerase_earlier_later_same by fastforce
-
-lemma rders_simp_size:
-  shows "rders_simp (rerase r) s  = rerase (bders_simp r s)"
-  apply(induct s rule: rev_induct)
-  apply simp
-  by (simp add: bders_simp_append rder_bder_rerase rders_simp_append bsimp_rerase)
-
-
-corollary aders_simp_finiteness:
-  assumes "\<exists>N. \<forall>s. rsize (rders_simp (rerase r) s) \<le> N"
-  shows " \<exists>N. \<forall>s. asize (bders_simp r s) \<le> N"
-proof - 
-  from assms obtain N where "\<forall>s. rsize (rders_simp (rerase r) s) \<le> N"
-    by blast
-  then have "\<forall>s. rsize (rerase (bders_simp r s)) \<le> N"
-    by (simp add: rders_simp_size) 
-  then have "\<forall>s. asize (bders_simp r s) \<le> N"
-    by (simp add: asize_rsize) 
-  then show "\<exists>N. \<forall>s. asize (bders_simp r s) \<le> N" by blast
-qed
-  
-theorem annotated_size_bound:
-  shows "\<exists>N. \<forall>s. asize (bders_simp r s) \<le> N"
-  apply(insert aders_simp_finiteness)
-  by (simp add: rders_simp_bounded)
-
-
-unused_thms
-
-end