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Quot/Examples/IntEx.thy
changeset 618 8dfae5d97387
parent 617 ca37f4b6457c
parent 612 ec37a279ca55
child 619 faab2540f13e
equal deleted inserted replaced
617:ca37f4b6457c 618:8dfae5d97387 
   134 
   134 
   135 lemma plus_rsp[quotient_rsp]:
 
   135 lemma plus_rsp[quotient_rsp]:
 
   136   shows "(intrel ===> intrel ===> intrel) my_plus my_plus"
 
   136   shows "(intrel ===> intrel ===> intrel) my_plus my_plus"
 
   137 by (simp)
 
   137 by (simp)
 
   138 
   138 
   139 ML {* val qty = @{typ "my_int"} *}
 
       
   140 ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
 
       
   141 ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "my_int"; *}
 
       
   142 
       
   143 ML {* fun lift_tac_intex lthy t = lift_tac lthy t *}
 
       
   144 
       
   145 ML {* fun inj_repabs_tac_intex lthy = inj_repabs_tac lthy [rel_refl] [trans2] *}
 
       
   146 ML {* fun all_inj_repabs_tac_intex lthy = all_inj_repabs_tac lthy [rel_refl] [trans2] *}
 
       
   147 
       
   148 lemma test1: "my_plus a b = my_plus a b"
 
   139 lemma test1: "my_plus a b = my_plus a b"
 
   149 apply(rule refl)
 
   140 apply(rule refl)
 
   150 done
 
   141 done
 
   151 
   142 
   152 lemma "PLUS a b = PLUS a b"
 
   143 lemma "PLUS a b = PLUS a b"
 
   153 apply(tactic {* procedure_tac @{context} @{thm test1} 1 *})
 
   144 apply(tactic {* procedure_tac @{context} @{thm test1} 1 *})
 
   154 apply(tactic {* regularize_tac @{context} 1 *})
 
   145 apply(tactic {* regularize_tac @{context} 1 *})
 
   155 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   146 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   156 apply(tactic {* clean_tac @{context} 1 *}) 
   147 apply(tactic {* clean_tac @{context} 1 *}) 
   157 done
 
   148 done
 
   158 
   149 
   159 thm lambda_prs
 
   150 thm lambda_prs
 
   160 
   151 
   166 apply(tactic {* procedure_tac @{context} @{thm test2} 1 *})
 
   157 apply(tactic {* procedure_tac @{context} @{thm test2} 1 *})
 
   167 apply(rule impI)
 
   158 apply(rule impI)
 
   168 apply(rule ballI)
 
   159 apply(rule ballI)
 
   169 apply(rule apply_rsp[OF Quotient_my_int plus_rsp])
 
   160 apply(rule apply_rsp[OF Quotient_my_int plus_rsp])
 
   170 apply(simp only: in_respects)
 
   161 apply(simp only: in_respects)
 
   171 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   162 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   172 apply(tactic {* clean_tac @{context} 1 *})
 
   163 apply(tactic {* clean_tac @{context} 1 *})
 
   173 done
 
   164 done
 
   174 
   165 
   175 lemma test3: "my_plus = my_plus"
 
   166 lemma test3: "my_plus = my_plus"
 
   176 apply(rule refl)
 
   167 apply(rule refl)
 
   178 
   169 
   179 lemma "PLUS = PLUS"
 
   170 lemma "PLUS = PLUS"
 
   180 apply(tactic {* procedure_tac @{context} @{thm test3} 1 *})
 
   171 apply(tactic {* procedure_tac @{context} @{thm test3} 1 *})
 
   181 apply(rule impI)
 
   172 apply(rule impI)
 
   182 apply(rule plus_rsp)
 
   173 apply(rule plus_rsp)
 
   183 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   174 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   184 apply(tactic {* clean_tac @{context} 1 *})
 
   175 apply(tactic {* clean_tac @{context} 1 *})
 
   185 done
 
   176 done
 
   186 
   177 
   187 
   178 
   188 lemma "PLUS a b = PLUS b a"
 
   179 lemma "PLUS a b = PLUS b a"
 
   189 apply(tactic {* procedure_tac @{context} @{thm plus_sym_pre} 1 *})
 
   180 apply(tactic {* procedure_tac @{context} @{thm plus_sym_pre} 1 *})
 
   190 apply(tactic {* regularize_tac @{context} 1 *})
 
   181 apply(tactic {* regularize_tac @{context} 1 *})
 
   191 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   182 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   192 apply(tactic {* clean_tac @{context} 1 *})
 
   183 apply(tactic {* clean_tac @{context} 1 *})
 
   193 done
 
   184 done
 
   194 
   185 
   195 lemma plus_assoc_pre:
 
   186 lemma plus_assoc_pre:
 
   196   shows "my_plus (my_plus i j) k \<approx> my_plus i (my_plus j k)"
 
   187   shows "my_plus (my_plus i j) k \<approx> my_plus i (my_plus j k)"
 
   201   done
 
   192   done
 
   202 
   193 
   203 lemma plus_assoc: "PLUS (PLUS x xa) xb = PLUS x (PLUS xa xb)"
 
   194 lemma plus_assoc: "PLUS (PLUS x xa) xb = PLUS x (PLUS xa xb)"
 
   204 apply(tactic {* procedure_tac @{context} @{thm plus_assoc_pre} 1 *})
 
   195 apply(tactic {* procedure_tac @{context} @{thm plus_assoc_pre} 1 *})
 
   205 apply(tactic {* regularize_tac @{context} 1 *})
 
   196 apply(tactic {* regularize_tac @{context} 1 *})
 
   206 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   197 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   207 apply(tactic {* clean_tac @{context} 1 *})
 
   198 apply(tactic {* clean_tac @{context} 1 *})
 
   208 done
 
   199 done
 
   209 
   200 
   210 lemma ho_tst: "foldl my_plus x [] = x"
 
   201 lemma ho_tst: "foldl my_plus x [] = x"
 
   211 apply simp
 
   202 apply simp
 
   212 done
 
   203 done
 
   213 
   204 
   214 lemma "foldl PLUS x [] = x"
 
   205 lemma "foldl PLUS x [] = x"
 
   215 apply(tactic {* procedure_tac @{context} @{thm ho_tst} 1 *})
 
   206 apply(tactic {* procedure_tac @{context} @{thm ho_tst} 1 *})
 
   216 apply(tactic {* regularize_tac @{context} 1 *})
 
   207 apply(tactic {* regularize_tac @{context} 1 *})
 
   217 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   208 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   218 apply(tactic {* clean_tac @{context} 1 *})
 
   209 apply(tactic {* clean_tac @{context} 1 *})
 
   219 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int] nil_prs[OF Quotient_my_int])
 
   210 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int] nil_prs[OF Quotient_my_int])
 
   220 done
 
   211 done
 
   221 
   212 
   222 lemma ho_tst2: "foldl my_plus x (h # t) \<approx> my_plus h (foldl my_plus x t)"
 
   213 lemma ho_tst2: "foldl my_plus x (h # t) \<approx> my_plus h (foldl my_plus x t)"
 
   223 sorry
 
   214 sorry
 
   224 
   215 
   225 lemma "foldl PLUS x (h # t) = PLUS h (foldl PLUS x t)"
 
   216 lemma "foldl PLUS x (h # t) = PLUS h (foldl PLUS x t)"
 
   226 apply(tactic {* procedure_tac @{context} @{thm ho_tst2} 1 *})
 
   217 apply(tactic {* procedure_tac @{context} @{thm ho_tst2} 1 *})
 
   227 apply(tactic {* regularize_tac @{context} 1 *})
 
   218 apply(tactic {* regularize_tac @{context} 1 *})
 
   228 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   219 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   229 apply(tactic {* clean_tac @{context} 1 *})
 
   220 apply(tactic {* clean_tac @{context} 1 *})
 
   230 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int] cons_prs[OF Quotient_my_int])
 
   221 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int] cons_prs[OF Quotient_my_int])
 
   231 done
 
   222 done
 
   232 
   223 
   233 lemma ho_tst3: "foldl f (s::nat \<times> nat) ([]::(nat \<times> nat) list) = s"
 
   224 lemma ho_tst3: "foldl f (s::nat \<times> nat) ([]::(nat \<times> nat) list) = s"
 
   234 by simp
 
   225 by simp
 
   235 
   226 
   236 lemma "foldl f (x::my_int) ([]::my_int list) = x"
 
   227 lemma "foldl f (x::my_int) ([]::my_int list) = x"
 
   237 apply(tactic {* procedure_tac @{context} @{thm ho_tst3} 1 *})
 
   228 apply(tactic {* procedure_tac @{context} @{thm ho_tst3} 1 *})
 
   238 apply(tactic {* regularize_tac @{context} 1 *})
 
   229 apply(tactic {* regularize_tac @{context} 1 *})
 
   239 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   230 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   240 (* TODO: does not work when this is added *)
 
   231 (* TODO: does not work when this is added *)
 
   241 (* apply(tactic {* lambda_prs_tac @{context} 1 *})*)
 
   232 (* apply(tactic {* lambda_prs_tac @{context} 1 *})*)
 
   242 apply(tactic {* clean_tac @{context} 1 *})
 
   233 apply(tactic {* clean_tac @{context} 1 *})
 
   243 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int] nil_prs[OF Quotient_my_int])
 
   234 apply(simp only: foldl_prs[OF Quotient_my_int Quotient_my_int] nil_prs[OF Quotient_my_int])
 
   244 done
 
   235 done
 
   247 by simp
 
   238 by simp
 
   248 
   239 
   249 lemma "(\<lambda>x. (x, x)) (y::my_int) = (y, y)"
 
   240 lemma "(\<lambda>x. (x, x)) (y::my_int) = (y, y)"
 
   250 apply(tactic {* procedure_tac @{context} @{thm lam_tst} 1 *})
 
   241 apply(tactic {* procedure_tac @{context} @{thm lam_tst} 1 *})
 
   251 apply(tactic {* regularize_tac @{context} 1 *})
 
   242 apply(tactic {* regularize_tac @{context} 1 *})
 
   252 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   243 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   253 apply(tactic {* clean_tac @{context} 1 *})
 
   244 apply(tactic {* clean_tac @{context} 1 *})
 
   254 apply(simp add: pair_prs)
 
   245 apply(simp add: pair_prs)
 
   255 done
 
   246 done
 
   256 
   247 
   257 lemma lam_tst2: "(\<lambda>(y :: nat \<times> nat). y) = (\<lambda>(x :: nat \<times> nat). x)"
 
   248 lemma lam_tst2: "(\<lambda>(y :: nat \<times> nat). y) = (\<lambda>(x :: nat \<times> nat). x)"
 
   323 done
 
   314 done
 
   324 
   315 
   325 lemma "(\<lambda>(y :: my_int). y) = (\<lambda>(x :: my_int). x)"
 
   316 lemma "(\<lambda>(y :: my_int). y) = (\<lambda>(x :: my_int). x)"
 
   326 apply(tactic {* procedure_tac @{context} @{thm lam_tst3a} 1 *})
 
   317 apply(tactic {* procedure_tac @{context} @{thm lam_tst3a} 1 *})
 
   327 defer
 
   318 defer
 
   328 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   319 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   329 apply(tactic {* clean_tac  @{context} 1 *})
 
   320 apply(tactic {* clean_tac  @{context} 1 *})
 
   330 apply(subst babs_rsp)
 
   321 apply(subst babs_rsp)
 
   331 apply(tactic {* clean_tac  @{context} 1 *})
 
   322 apply(tactic {* clean_tac  @{context} 1 *})
 
   332 apply(simp)
 
   323 apply(simp)
 
   333 apply(tactic {* regularize_tac @{context} 1*})?
 
   324 apply(tactic {* regularize_tac @{context} 1*})?
 
   341 by auto
 
   332 by auto
 
   342 
   333 
   343 lemma "(\<lambda>(y :: my_int => my_int). y) = (\<lambda>(x :: my_int => my_int). x)"
 
   334 lemma "(\<lambda>(y :: my_int => my_int). y) = (\<lambda>(x :: my_int => my_int). x)"
 
   344 apply(tactic {* procedure_tac @{context} @{thm lam_tst3b} 1 *})
 
   335 apply(tactic {* procedure_tac @{context} @{thm lam_tst3b} 1 *})
 
   345 defer
 
   336 defer
 
   346 apply(tactic {* all_inj_repabs_tac_intex @{context} 1*})
 
   337 apply(tactic {* all_inj_repabs_tac @{context} 1*})
 
   347 apply(tactic {* clean_tac  @{context} 1 *})
 
   338 apply(tactic {* clean_tac  @{context} 1 *})
 
   348 apply(subst babs_rsp)
 
   339 apply(subst babs_rsp)
 
   349 apply(tactic {* clean_tac  @{context} 1 *})
 
   340 apply(tactic {* clean_tac  @{context} 1 *})
 
   350 apply(simp)
 
   341 apply(simp)
 
   351 apply(tactic {* regularize_tac @{context} 1*})?
 
   342 apply(tactic {* regularize_tac @{context} 1*})?
nominal2