106 val dc_rep = %%(dname^"_rep"); |
106 val dc_rep = %%(dname^"_rep"); |
107 val dc_copy = %%(dname^"_copy"); |
107 val dc_copy = %%(dname^"_copy"); |
108 val x_name = "x"; |
108 val x_name = "x"; |
109 |
109 |
110 val (rep_strict, abs_strict) = let |
110 val (rep_strict, abs_strict) = let |
111 val r = ax_rep_iso RS (ax_abs_iso RS (allI RSN(2,allI RS iso_strict))) |
111 val r = ax_rep_iso RS (ax_abs_iso RS (allI RSN(2,allI RS iso_strict))) |
112 in (r RS conjunct1, r RS conjunct2) end; |
112 in (r RS conjunct1, r RS conjunct2) end; |
113 val abs_defin' = pg [] ((dc_abs`%x_name === UU) ==> (%x_name === UU)) [ |
113 val abs_defin' = pg [] ((dc_abs`%x_name === UU) ==> (%x_name === UU)) [ |
114 res_inst_tac [("t",x_name)] (ax_abs_iso RS subst) 1, |
114 res_inst_tac [("t",x_name)] (ax_abs_iso RS subst) 1, |
115 etac ssubst 1, |
115 etac ssubst 1, |
116 rtac rep_strict 1]; |
116 rtac rep_strict 1]; |
117 val rep_defin' = pg [] ((dc_rep`%x_name === UU) ==> (%x_name === UU)) [ |
117 val rep_defin' = pg [] ((dc_rep`%x_name === UU) ==> (%x_name === UU)) [ |
118 res_inst_tac [("t",x_name)] (ax_rep_iso RS subst) 1, |
118 res_inst_tac [("t",x_name)] (ax_rep_iso RS subst) 1, |
119 etac ssubst 1, |
119 etac ssubst 1, |
120 rtac abs_strict 1]; |
120 rtac abs_strict 1]; |
121 val iso_rews = [ax_abs_iso,ax_rep_iso,abs_strict,rep_strict]; |
121 val iso_rews = [ax_abs_iso,ax_rep_iso,abs_strict,rep_strict]; |
122 |
122 |
123 local |
123 local |
124 val iso_swap = pg [] (dc_rep`%"x" === %"y" ==> %"x" === dc_abs`%"y") [ |
124 val iso_swap = pg [] (dc_rep`%"x" === %"y" ==> %"x" === dc_abs`%"y") [ |
125 dres_inst_tac [("f",dname^"_abs")] cfun_arg_cong 1, |
125 dres_inst_tac [("f",dname^"_abs")] cfun_arg_cong 1, |
126 etac (ax_rep_iso RS subst) 1]; |
126 etac (ax_rep_iso RS subst) 1]; |
127 fun exh foldr1 cn quant foldr2 var = let |
127 fun exh foldr1 cn quant foldr2 var = let |
128 fun one_con (con,args) = let val vns = map vname args in |
128 fun one_con (con,args) = let val vns = map vname args in |
129 foldr quant (vns, foldr2 ((%x_name === con_app2 con (var vns) vns):: |
129 foldr quant (vns, foldr2 ((%x_name === con_app2 con (var vns) vns):: |
130 map (defined o (var vns)) (nonlazy args))) end |
130 map (defined o (var vns)) (nonlazy args))) end |
131 in foldr1 ((cn(%x_name===UU))::map one_con cons) end; |
131 in foldr1 ((cn(%x_name===UU))::map one_con cons) end; |
132 in |
132 in |
133 val cases = let |
133 val cases = let |
134 fun common_tac thm = rtac thm 1 THEN contr_tac 1; |
134 fun common_tac thm = rtac thm 1 THEN contr_tac 1; |
135 fun unit_tac true = common_tac liftE1 |
135 fun unit_tac true = common_tac liftE1 |
136 | unit_tac _ = all_tac; |
136 | unit_tac _ = all_tac; |
137 fun prod_tac [] = common_tac oneE |
137 fun prod_tac [] = common_tac oneE |
138 | prod_tac [arg] = unit_tac (is_lazy arg) |
138 | prod_tac [arg] = unit_tac (is_lazy arg) |
139 | prod_tac (arg::args) = |
139 | prod_tac (arg::args) = |
140 common_tac sprodE THEN |
140 common_tac sprodE THEN |
141 kill_neq_tac 1 THEN |
141 kill_neq_tac 1 THEN |
142 unit_tac (is_lazy arg) THEN |
142 unit_tac (is_lazy arg) THEN |
143 prod_tac args; |
143 prod_tac args; |
144 fun sum_one_tac p = SELECT_GOAL(EVERY[ |
144 fun sum_one_tac p = SELECT_GOAL(EVERY[ |
145 rtac p 1, |
145 rtac p 1, |
146 rewrite_goals_tac axs_con_def, |
146 rewrite_goals_tac axs_con_def, |
147 dtac iso_swap 1, |
147 dtac iso_swap 1, |
148 simp_tac HOLCF_ss 1, |
148 simp_tac HOLCF_ss 1, |
149 UNTIL_SOLVED(fast_tac HOL_cs 1)]) 1; |
149 UNTIL_SOLVED(fast_tac HOL_cs 1)]) 1; |
150 fun sum_tac [(_,args)] [p] = |
150 fun sum_tac [(_,args)] [p] = |
151 prod_tac args THEN sum_one_tac p |
151 prod_tac args THEN sum_one_tac p |
152 | sum_tac ((_,args)::cons') (p::prems) = DETERM( |
152 | sum_tac ((_,args)::cons') (p::prems) = DETERM( |
153 common_tac ssumE THEN |
153 common_tac ssumE THEN |
154 kill_neq_tac 1 THEN kill_neq_tac 2 THEN |
154 kill_neq_tac 1 THEN kill_neq_tac 2 THEN |
155 prod_tac args THEN sum_one_tac p) THEN |
155 prod_tac args THEN sum_one_tac p) THEN |
156 sum_tac cons' prems |
156 sum_tac cons' prems |
157 | sum_tac _ _ = Imposs "theorems:sum_tac"; |
157 | sum_tac _ _ = Imposs "theorems:sum_tac"; |
158 in pg'' thy [] (exh (fn l => foldr (op ===>) (l,mk_trp(%"P"))) |
158 in pg'' thy [] (exh (fn l => foldr (op ===>) (l,mk_trp(%"P"))) |
159 (fn T => T ==> %"P") mk_All |
159 (fn T => T ==> %"P") mk_All |
160 (fn l => foldr (op ===>) (map mk_trp l,mk_trp(%"P"))) |
160 (fn l => foldr (op ===>) (map mk_trp l,mk_trp(%"P"))) |
161 bound_arg) |
161 bound_arg) |
162 (fn prems => [ |
162 (fn prems => [ |
163 cut_facts_tac [excluded_middle] 1, |
163 cut_facts_tac [excluded_middle] 1, |
164 etac disjE 1, |
164 etac disjE 1, |
165 rtac (hd prems) 2, |
165 rtac (hd prems) 2, |
166 etac rep_defin' 2, |
166 etac rep_defin' 2, |
167 if is_one_con_one_arg (not o is_lazy) cons |
167 if is_one_con_one_arg (not o is_lazy) cons |
168 then rtac (hd (tl prems)) 1 THEN atac 2 THEN |
168 then rtac (hd (tl prems)) 1 THEN atac 2 THEN |
169 rewrite_goals_tac axs_con_def THEN |
169 rewrite_goals_tac axs_con_def THEN |
170 simp_tac (HOLCF_ss addsimps [ax_rep_iso]) 1 |
170 simp_tac (HOLCF_ss addsimps [ax_rep_iso]) 1 |
171 else sum_tac cons (tl prems)])end; |
171 else sum_tac cons (tl prems)])end; |
172 val exhaust = pg [] (mk_trp(exh (foldr' mk_disj) Id mk_ex (foldr' mk_conj) (K %))) [ |
172 val exhaust = pg [] (mk_trp(exh (foldr' mk_disj) Id mk_ex (foldr' mk_conj) (K %))) [ |
173 rtac cases 1, |
173 rtac cases 1, |
174 UNTIL_SOLVED(fast_tac HOL_cs 1)]; |
174 UNTIL_SOLVED(fast_tac HOL_cs 1)]; |
175 end; |
175 end; |
176 |
176 |
177 local |
177 local |
178 val when_app = foldl (op `) (%%(dname^"_when"), map % (when_funs cons)); |
178 val when_app = foldl (op `) (%%(dname^"_when"), map % (when_funs cons)); |
179 val when_appl = pg [ax_when_def] (mk_trp(when_app`%x_name===when_body cons |
179 val when_appl = pg [ax_when_def] (mk_trp(when_app`%x_name===when_body cons |
180 (fn (_,n) => %(nth_elem(n-1,when_funs cons)))`(dc_rep`%x_name))) [ |
180 (fn (_,n) => %(nth_elem(n-1,when_funs cons)))`(dc_rep`%x_name))) [ |
181 simp_tac HOLCF_ss 1]; |
181 simp_tac HOLCF_ss 1]; |
182 in |
182 in |
183 val when_strict = pg [] ((if is_one_con_one_arg (K true) cons |
183 val when_strict = pg [] ((if is_one_con_one_arg (K true) cons |
184 then fn t => mk_trp(strict(%"f")) ===> t else Id)(mk_trp(strict when_app))) [ |
184 then fn t => mk_trp(strict(%"f")) ===> t else Id)(mk_trp(strict when_app))) [ |
185 simp_tac(HOLCF_ss addsimps [when_appl,rep_strict]) 1]; |
185 simp_tac(HOLCF_ss addsimps [when_appl,rep_strict]) 1]; |
186 val when_apps = let fun one_when n (con,args) = pg axs_con_def |
186 val when_apps = let fun one_when n (con,args) = pg axs_con_def |
187 (lift_defined % (nonlazy args, mk_trp(when_app`(con_app con args) === |
187 (lift_defined % (nonlazy args, mk_trp(when_app`(con_app con args) === |
188 mk_cfapp(%(nth_elem(n,when_funs cons)),map %# args))))[ |
188 mk_cfapp(%(nth_elem(n,when_funs cons)),map %# args))))[ |
189 asm_simp_tac (HOLCF_ss addsimps [when_appl,ax_abs_iso]) 1]; |
189 asm_simp_tac (HOLCF_ss addsimps [when_appl,ax_abs_iso]) 1]; |
190 in mapn one_when 0 cons end; |
190 in mapn one_when 0 cons end; |
191 end; |
191 end; |
192 val when_rews = when_strict::when_apps; |
192 val when_rews = when_strict::when_apps; |
193 |
193 |
194 (* ----- theorems concerning the constructors, discriminators and selectors ------- *) |
194 (* ----- theorems concerning the constructors, discriminators and selectors ------- *) |
195 |
195 |
196 val dis_stricts = map (fn (con,_) => pg axs_dis_def (mk_trp( |
196 val dis_stricts = map (fn (con,_) => pg axs_dis_def (mk_trp( |
197 (if is_one_con_one_arg (K true) cons then mk_not else Id) |
197 (if is_one_con_one_arg (K true) cons then mk_not else Id) |
198 (strict(%%(dis_name con))))) [ |
198 (strict(%%(dis_name con))))) [ |
199 simp_tac (HOLCF_ss addsimps (if is_one_con_one_arg (K true) cons |
199 simp_tac (HOLCF_ss addsimps (if is_one_con_one_arg (K true) cons |
200 then [ax_when_def] else when_rews)) 1]) cons; |
200 then [ax_when_def] else when_rews)) 1]) cons; |
201 val dis_apps = let fun one_dis c (con,args)= pg (axs_dis_def) |
201 val dis_apps = let fun one_dis c (con,args)= pg (axs_dis_def) |
202 (lift_defined % (nonlazy args, (*(if is_one_con_one_arg is_lazy cons |
202 (lift_defined % (nonlazy args, (*(if is_one_con_one_arg is_lazy cons |
203 then curry (lift_defined %#) args else Id) |
203 then curry (lift_defined %#) args else Id) |
204 #################*) |
204 #################*) |
205 (mk_trp((%%(dis_name c))`(con_app con args) === |
205 (mk_trp((%%(dis_name c))`(con_app con args) === |
206 %%(if con=c then "TT" else "FF"))))) [ |
206 %%(if con=c then "TT" else "FF"))))) [ |
207 asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
207 asm_simp_tac (HOLCF_ss addsimps when_rews) 1]; |
208 in flat(map (fn (c,_) => map (one_dis c) cons) cons) end; |
208 in flat(map (fn (c,_) => map (one_dis c) cons) cons) end; |
209 val dis_defins = map (fn (con,args) => pg [] (defined(%x_name)==> |
209 val dis_defins = map (fn (con,args) => pg [] (defined(%x_name)==> |
210 defined(%%(dis_name con)`%x_name)) [ |
210 defined(%%(dis_name con)`%x_name)) [ |
211 rtac cases 1, |
211 rtac cases 1, |
212 contr_tac 1, |
212 contr_tac 1, |
213 UNTIL_SOLVED (CHANGED(asm_simp_tac |
213 UNTIL_SOLVED (CHANGED(asm_simp_tac |
214 (HOLCF_ss addsimps dis_apps) 1))]) cons; |
214 (HOLCF_ss addsimps dis_apps) 1))]) cons; |
215 val dis_rews = dis_stricts @ dis_defins @ dis_apps; |
215 val dis_rews = dis_stricts @ dis_defins @ dis_apps; |
216 |
216 |
217 val con_stricts = flat(map (fn (con,args) => map (fn vn => |
217 val con_stricts = flat(map (fn (con,args) => map (fn vn => |
218 pg (axs_con_def) |
218 pg (axs_con_def) |
219 (mk_trp(con_app2 con (fn arg => if vname arg = vn |
219 (mk_trp(con_app2 con (fn arg => if vname arg = vn |
220 then UU else %# arg) args === UU))[ |
220 then UU else %# arg) args === UU))[ |
221 asm_simp_tac (HOLCF_ss addsimps [abs_strict]) 1] |
221 asm_simp_tac (HOLCF_ss addsimps [abs_strict]) 1] |
222 ) (nonlazy args)) cons); |
222 ) (nonlazy args)) cons); |
223 val con_defins = map (fn (con,args) => pg [] |
223 val con_defins = map (fn (con,args) => pg [] |
224 (lift_defined % (nonlazy args, |
224 (lift_defined % (nonlazy args, |
225 mk_trp(defined(con_app con args)))) ([ |
225 mk_trp(defined(con_app con args)))) ([ |
226 rtac swap3 1] @ (if is_one_con_one_arg (K true) cons |
226 rtac swap3 1] @ (if is_one_con_one_arg (K true) cons |
227 then [ |
227 then [ |
228 if is_lazy (hd args) then rtac defined_up 2 |
228 if is_lazy (hd args) then rtac defined_up 2 |
229 else atac 2, |
229 else atac 2, |
230 rtac abs_defin' 1, |
230 rtac abs_defin' 1, |
231 asm_full_simp_tac (HOLCF_ss addsimps axs_con_def) 1] |
231 asm_full_simp_tac (HOLCF_ss addsimps axs_con_def) 1] |
232 else [ |
232 else [ |
233 eres_inst_tac [("f",dis_name con)] cfun_arg_cong 1, |
233 eres_inst_tac [("f",dis_name con)] cfun_arg_cong 1, |
234 asm_simp_tac (HOLCF_ss addsimps dis_rews) 1])))cons; |
234 asm_simp_tac (HOLCF_ss addsimps dis_rews) 1])))cons; |
235 val con_rews = con_stricts @ con_defins; |
235 val con_rews = con_stricts @ con_defins; |
236 |
236 |
237 val sel_stricts = let fun one_sel sel = pg axs_sel_def (mk_trp(strict(%%sel))) [ |
237 val sel_stricts = let fun one_sel sel = pg axs_sel_def (mk_trp(strict(%%sel))) [ |
238 simp_tac (HOLCF_ss addsimps when_rews) 1]; |
238 simp_tac (HOLCF_ss addsimps when_rews) 1]; |
239 in flat(map (fn (_,args) => map (fn arg => one_sel (sel_of arg)) args) cons) end; |
239 in flat(map (fn (_,args) => map (fn arg => one_sel (sel_of arg)) args) cons) end; |
240 val sel_apps = let fun one_sel c n sel = map (fn (con,args) => |
240 val sel_apps = let fun one_sel c n sel = map (fn (con,args) => |
241 let val nlas = nonlazy args; |
241 let val nlas = nonlazy args; |
242 val vns = map vname args; |
242 val vns = map vname args; |
243 in pg axs_sel_def (lift_defined % |
243 in pg axs_sel_def (lift_defined % |
244 (filter (fn v => con=c andalso (v<>nth_elem(n,vns))) nlas, |
244 (filter (fn v => con=c andalso (v<>nth_elem(n,vns))) nlas, |
245 mk_trp((%%sel)`(con_app con args) === (if con=c then %(nth_elem(n,vns)) else UU)))) |
245 mk_trp((%%sel)`(con_app con args) === (if con=c then %(nth_elem(n,vns)) else UU)))) |
246 ( (if con=c then [] |
246 ( (if con=c then [] |
247 else map(case_UU_tac(when_rews@con_stricts)1) nlas) |
247 else map(case_UU_tac(when_rews@con_stricts)1) nlas) |
248 @(if con=c andalso ((nth_elem(n,vns)) mem nlas) |
248 @(if con=c andalso ((nth_elem(n,vns)) mem nlas) |
249 then[case_UU_tac (when_rews @ con_stricts) 1 |
249 then[case_UU_tac (when_rews @ con_stricts) 1 |
250 (nth_elem(n,vns))] else []) |
250 (nth_elem(n,vns))] else []) |
251 @ [asm_simp_tac(HOLCF_ss addsimps when_rews)1])end) cons; |
251 @ [asm_simp_tac(HOLCF_ss addsimps when_rews)1])end) cons; |
252 in flat(map (fn (c,args) => |
252 in flat(map (fn (c,args) => |
253 flat(mapn (fn n => fn arg => one_sel c n (sel_of arg)) 0 args)) cons) end; |
253 flat(mapn (fn n => fn arg => one_sel c n (sel_of arg)) 0 args)) cons) end; |
254 val sel_defins = if length cons = 1 then map (fn arg => pg [] (defined(%x_name) ==> |
254 val sel_defins = if length cons = 1 then map (fn arg => pg [] (defined(%x_name) ==> |
255 defined(%%(sel_of arg)`%x_name)) [ |
255 defined(%%(sel_of arg)`%x_name)) [ |
256 rtac cases 1, |
256 rtac cases 1, |
257 contr_tac 1, |
257 contr_tac 1, |
258 UNTIL_SOLVED (CHANGED(asm_simp_tac |
258 UNTIL_SOLVED (CHANGED(asm_simp_tac |
259 (HOLCF_ss addsimps sel_apps) 1))]) |
259 (HOLCF_ss addsimps sel_apps) 1))]) |
260 (filter_out is_lazy (snd(hd cons))) else []; |
260 (filter_out is_lazy (snd(hd cons))) else []; |
261 val sel_rews = sel_stricts @ sel_defins @ sel_apps; |
261 val sel_rews = sel_stricts @ sel_defins @ sel_apps; |
262 |
262 |
263 val distincts_le = let |
263 val distincts_le = let |
264 fun dist (con1, args1) (con2, args2) = pg [] |
264 fun dist (con1, args1) (con2, args2) = pg [] |
265 (lift_defined % ((nonlazy args1), |
265 (lift_defined % ((nonlazy args1), |
266 (mk_trp (con_app con1 args1 ~<< con_app con2 args2))))([ |
266 (mk_trp (con_app con1 args1 ~<< con_app con2 args2))))([ |
267 rtac swap3 1, |
267 rtac swap3 1, |
268 eres_inst_tac [("fo5",dis_name con1)] monofun_cfun_arg 1] |
268 eres_inst_tac [("fo5",dis_name con1)] monofun_cfun_arg 1] |
269 @ map (case_UU_tac (con_stricts @ dis_rews) 1) (nonlazy args2) |
269 @ map (case_UU_tac (con_stricts @ dis_rews) 1) (nonlazy args2) |
270 @[asm_simp_tac (HOLCF_ss addsimps dis_rews) 1]); |
270 @[asm_simp_tac (HOLCF_ss addsimps dis_rews) 1]); |
271 fun distinct (con1,args1) (con2,args2) = |
271 fun distinct (con1,args1) (con2,args2) = |
272 let val arg1 = (con1, args1); |
272 let val arg1 = (con1, args1); |
273 val arg2 = (con2, (map (fn (arg,vn) => upd_vname (K vn) arg) |
273 val arg2 = (con2, (map (fn (arg,vn) => upd_vname (K vn) arg) |
274 (args2~~variantlist(map vname args2,map vname args1)))); |
274 (args2~~variantlist(map vname args2,map vname args1)))); |
275 in [dist arg1 arg2, dist arg2 arg1] end; |
275 in [dist arg1 arg2, dist arg2 arg1] end; |
276 fun distincts [] = [] |
276 fun distincts [] = [] |
277 | distincts (c::cs) = (map (distinct c) cs) :: distincts cs; |
277 | distincts (c::cs) = (map (distinct c) cs) :: distincts cs; |
278 in distincts cons end; |
278 in distincts cons end; |
279 val dists_le = flat (flat distincts_le); |
279 val dists_le = flat (flat distincts_le); |
280 val dists_eq = let |
280 val dists_eq = let |
281 fun distinct (_,args1) ((_,args2),leqs) = let |
281 fun distinct (_,args1) ((_,args2),leqs) = let |
282 val (le1,le2) = (hd leqs, hd(tl leqs)); |
282 val (le1,le2) = (hd leqs, hd(tl leqs)); |
283 val (eq1,eq2) = (le1 RS dist_eqI, le2 RS dist_eqI) in |
283 val (eq1,eq2) = (le1 RS dist_eqI, le2 RS dist_eqI) in |
284 if nonlazy args1 = [] then [eq1, eq1 RS not_sym] else |
284 if nonlazy args1 = [] then [eq1, eq1 RS not_sym] else |
285 if nonlazy args2 = [] then [eq2, eq2 RS not_sym] else |
285 if nonlazy args2 = [] then [eq2, eq2 RS not_sym] else |
286 [eq1, eq2] end; |
286 [eq1, eq2] end; |
287 fun distincts [] = [] |
287 fun distincts [] = [] |
288 | distincts ((c,leqs)::cs) = flat(map (distinct c) ((map fst cs)~~leqs)) @ |
288 | distincts ((c,leqs)::cs) = flat(map (distinct c) ((map fst cs)~~leqs)) @ |
289 distincts cs; |
289 distincts cs; |
290 in distincts (cons~~distincts_le) end; |
290 in distincts (cons~~distincts_le) end; |
291 |
291 |
292 local |
292 local |
293 fun pgterm rel con args = let |
293 fun pgterm rel con args = let |
294 fun append s = upd_vname(fn v => v^s); |
294 fun append s = upd_vname(fn v => v^s); |
295 val (largs,rargs) = (args, map (append "'") args); |
295 val (largs,rargs) = (args, map (append "'") args); |
296 in pg [] (mk_trp (rel(con_app con largs,con_app con rargs)) ===> |
296 in pg [] (mk_trp (rel(con_app con largs,con_app con rargs)) ===> |
297 lift_defined % ((nonlazy largs),lift_defined % ((nonlazy rargs), |
297 lift_defined % ((nonlazy largs),lift_defined % ((nonlazy rargs), |
298 mk_trp (foldr' mk_conj |
298 mk_trp (foldr' mk_conj |
299 (map rel (map %# largs ~~ map %# rargs)))))) end; |
299 (map rel (map %# largs ~~ map %# rargs)))))) end; |
300 val cons' = filter (fn (_,args) => args<>[]) cons; |
300 val cons' = filter (fn (_,args) => args<>[]) cons; |
301 in |
301 in |
302 val inverts = map (fn (con,args) => |
302 val inverts = map (fn (con,args) => |
303 pgterm (op <<) con args (flat(map (fn arg => [ |
303 pgterm (op <<) con args (flat(map (fn arg => [ |
304 TRY(rtac conjI 1), |
304 TRY(rtac conjI 1), |
305 dres_inst_tac [("fo5",sel_of arg)] monofun_cfun_arg 1, |
305 dres_inst_tac [("fo5",sel_of arg)] monofun_cfun_arg 1, |
306 asm_full_simp_tac (HOLCF_ss addsimps sel_apps) 1] |
306 asm_full_simp_tac (HOLCF_ss addsimps sel_apps) 1] |
307 ) args))) cons'; |
307 ) args))) cons'; |
308 val injects = map (fn ((con,args),inv_thm) => |
308 val injects = map (fn ((con,args),inv_thm) => |
309 pgterm (op ===) con args [ |
309 pgterm (op ===) con args [ |
310 etac (antisym_less_inverse RS conjE) 1, |
310 etac (antisym_less_inverse RS conjE) 1, |
311 dtac inv_thm 1, REPEAT(atac 1), |
311 dtac inv_thm 1, REPEAT(atac 1), |
312 dtac inv_thm 1, REPEAT(atac 1), |
312 dtac inv_thm 1, REPEAT(atac 1), |
313 TRY(safe_tac HOL_cs), |
313 TRY(safe_tac HOL_cs), |
314 REPEAT(rtac antisym_less 1 ORELSE atac 1)] ) |
314 REPEAT(rtac antisym_less 1 ORELSE atac 1)] ) |
315 (cons'~~inverts); |
315 (cons'~~inverts); |
316 end; |
316 end; |
317 |
317 |
318 (* ----- theorems concerning one induction step ----------------------------------- *) |
318 (* ----- theorems concerning one induction step ----------------------------------- *) |
319 |
319 |
320 val copy_strict = pg [ax_copy_def] ((if is_one_con_one_arg (K true) cons then fn t => |
320 val copy_strict = pg [ax_copy_def] ((if is_one_con_one_arg (K true) cons then fn t => |
321 mk_trp(strict(cproj (%"f") eqs (rec_of (hd(snd(hd cons)))))) ===> t |
321 mk_trp(strict(cproj (%"f") eqs (rec_of (hd(snd(hd cons)))))) ===> t |
322 else Id) (mk_trp(strict(dc_copy`%"f")))) [ |
322 else Id) (mk_trp(strict(dc_copy`%"f")))) [ |
323 asm_simp_tac(HOLCF_ss addsimps [abs_strict,rep_strict, |
323 asm_simp_tac(HOLCF_ss addsimps [abs_strict,rep_strict, |
324 cfst_strict,csnd_strict]) 1]; |
324 cfst_strict,csnd_strict]) 1]; |
325 val copy_apps = map (fn (con,args) => pg (ax_copy_def::axs_con_def) |
325 val copy_apps = map (fn (con,args) => pg (ax_copy_def::axs_con_def) |
326 (lift_defined %# (filter is_nonlazy_rec args, |
326 (lift_defined %# (filter is_nonlazy_rec args, |
327 mk_trp(dc_copy`%"f"`(con_app con args) === |
327 mk_trp(dc_copy`%"f"`(con_app con args) === |
328 (con_app2 con (app_rec_arg (cproj (%"f") eqs)) args)))) |
328 (con_app2 con (app_rec_arg (cproj (%"f") eqs)) args)))) |
329 (map (case_UU_tac [ax_abs_iso] 1 o vname) |
329 (map (case_UU_tac [ax_abs_iso] 1 o vname) |
330 (filter(fn a=>not(is_rec a orelse is_lazy a))args)@ |
330 (filter(fn a=>not(is_rec a orelse is_lazy a))args)@ |
331 [asm_simp_tac (HOLCF_ss addsimps [ax_abs_iso]) 1]) |
331 [asm_simp_tac (HOLCF_ss addsimps [ax_abs_iso]) 1]) |
332 )cons; |
332 )cons; |
333 val copy_stricts = map(fn(con,args)=>pg[](mk_trp(dc_copy`UU`(con_app con args) ===UU)) |
333 val copy_stricts = map(fn(con,args)=>pg[](mk_trp(dc_copy`UU`(con_app con args) ===UU)) |
334 (let val rews = cfst_strict::csnd_strict::copy_strict::copy_apps@con_rews |
334 (let val rews = cfst_strict::csnd_strict::copy_strict::copy_apps@con_rews |
335 in map (case_UU_tac rews 1) (nonlazy args) @ [ |
335 in map (case_UU_tac rews 1) (nonlazy args) @ [ |
336 asm_simp_tac (HOLCF_ss addsimps rews) 1] end)) |
336 asm_simp_tac (HOLCF_ss addsimps rews) 1] end)) |
337 (filter (fn (_,args)=>exists is_nonlazy_rec args) cons); |
337 (filter (fn (_,args)=>exists is_nonlazy_rec args) cons); |
338 val copy_rews = copy_strict::copy_apps @ copy_stricts; |
338 val copy_rews = copy_strict::copy_apps @ copy_stricts; |
339 |
339 |
340 in (iso_rews, exhaust, cases, when_rews, |
340 in (iso_rews, exhaust, cases, when_rews, |
341 con_rews, sel_rews, dis_rews, dists_eq, dists_le, inverts, injects, |
341 con_rews, sel_rews, dis_rews, dists_eq, dists_le, inverts, injects, |
342 copy_rews) |
342 copy_rews) |
343 end; (* let *) |
343 end; (* let *) |
344 |
344 |
345 |
345 |
346 fun comp_theorems thy (comp_dname, eqs: eq list, casess, con_rews, copy_rews) = |
346 fun comp_theorems thy (comp_dname, eqs: eq list, casess, con_rews, copy_rews) = |
347 let |
347 let |
367 fun dc_take dn = %%(dn^"_take"); |
367 fun dc_take dn = %%(dn^"_take"); |
368 val x_name = idx_name dnames "x"; |
368 val x_name = idx_name dnames "x"; |
369 val P_name = idx_name dnames "P"; |
369 val P_name = idx_name dnames "P"; |
370 |
370 |
371 local |
371 local |
372 val iterate_ss = simpset_of "Fix"; |
372 val iterate_ss = simpset_of "Fix"; |
373 val iterate_Cprod_strict_ss = iterate_ss addsimps [cfst_strict, csnd_strict]; |
373 val iterate_Cprod_strict_ss = iterate_ss addsimps [cfst_strict, csnd_strict]; |
374 val iterate_Cprod_ss = iterate_ss addsimps [cfst2,csnd2,csplit2]; |
374 val iterate_Cprod_ss = iterate_ss addsimps [cfst2,csnd2,csplit2]; |
375 val copy_con_rews = copy_rews @ con_rews; |
375 val copy_con_rews = copy_rews @ con_rews; |
376 val copy_take_defs = (if length dnames=1 then [] else [ax_copy2_def]) @axs_take_def; |
376 val copy_take_defs = (if length dnames=1 then [] else [ax_copy2_def]) @axs_take_def; |
377 val take_stricts = pg copy_take_defs (mk_trp(foldr' mk_conj (map (fn ((dn,args),_)=> |
377 val take_stricts = pg copy_take_defs (mk_trp(foldr' mk_conj (map (fn ((dn,args),_)=> |
378 (dc_take dn $ %"n")`UU === mk_constrain(Type(dn,args),UU)) eqs)))([ |
378 (dc_take dn $ %"n")`UU === mk_constrain(Type(dn,args),UU)) eqs)))([ |
379 nat_ind_tac "n" 1, |
379 nat_ind_tac "n" 1, |
380 simp_tac iterate_ss 1, |
380 simp_tac iterate_ss 1, |
381 simp_tac iterate_Cprod_strict_ss 1, |
381 simp_tac iterate_Cprod_strict_ss 1, |
382 asm_simp_tac iterate_Cprod_ss 1, |
382 asm_simp_tac iterate_Cprod_ss 1, |
383 TRY(safe_tac HOL_cs)] @ |
383 TRY(safe_tac HOL_cs)] @ |
384 map(K(asm_simp_tac (HOL_ss addsimps copy_rews)1))dnames); |
384 map(K(asm_simp_tac (HOL_ss addsimps copy_rews)1))dnames); |
385 val take_stricts' = rewrite_rule copy_take_defs take_stricts; |
385 val take_stricts' = rewrite_rule copy_take_defs take_stricts; |
386 val take_0s = mapn (fn n => fn dn => pg axs_take_def(mk_trp((dc_take dn $ %%"0") |
386 val take_0s = mapn (fn n => fn dn => pg axs_take_def(mk_trp((dc_take dn $ %%"0") |
387 `%x_name n === UU))[ |
387 `%x_name n === UU))[ |
388 simp_tac iterate_Cprod_strict_ss 1]) 1 dnames; |
388 simp_tac iterate_Cprod_strict_ss 1]) 1 dnames; |
389 val take_apps = pg copy_take_defs (mk_trp(foldr' mk_conj |
389 val take_apps = pg copy_take_defs (mk_trp(foldr' mk_conj |
390 (flat(map (fn ((dn,_),cons) => map (fn (con,args) => foldr mk_all |
390 (flat(map (fn ((dn,_),cons) => map (fn (con,args) => foldr mk_all |
391 (map vname args,(dc_take dn $ (%%"Suc" $ %"n"))`(con_app con args) === |
391 (map vname args,(dc_take dn $ (%%"Suc" $ %"n"))`(con_app con args) === |
392 con_app2 con (app_rec_arg (fn n=>dc_take (nth_elem(n,dnames))$ %"n")) |
392 con_app2 con (app_rec_arg (fn n=>dc_take (nth_elem(n,dnames))$ %"n")) |
393 args)) cons) eqs)))) ([ |
393 args)) cons) eqs)))) ([ |
394 nat_ind_tac "n" 1, |
394 nat_ind_tac "n" 1, |
395 simp_tac iterate_Cprod_strict_ss 1, |
395 simp_tac iterate_Cprod_strict_ss 1, |
396 simp_tac (HOLCF_ss addsimps copy_con_rews) 1, |
396 simp_tac (HOLCF_ss addsimps copy_con_rews) 1, |
397 TRY(safe_tac HOL_cs)] @ |
397 TRY(safe_tac HOL_cs)] @ |
398 (flat(map (fn ((dn,_),cons) => map (fn (con,args) => EVERY ( |
398 (flat(map (fn ((dn,_),cons) => map (fn (con,args) => EVERY ( |
399 asm_full_simp_tac iterate_Cprod_ss 1:: |
399 asm_full_simp_tac iterate_Cprod_ss 1:: |
400 map (case_UU_tac (take_stricts'::copy_con_rews) 1) |
400 map (case_UU_tac (take_stricts'::copy_con_rews) 1) |
401 (nonlazy args) @[ |
401 (nonlazy args) @[ |
402 asm_full_simp_tac (HOLCF_ss addsimps copy_rews) 1]) |
402 asm_full_simp_tac (HOLCF_ss addsimps copy_rews) 1]) |
403 ) cons) eqs))); |
403 ) cons) eqs))); |
404 in |
404 in |
405 val take_rews = atomize take_stricts @ take_0s @ atomize take_apps; |
405 val take_rews = atomize take_stricts @ take_0s @ atomize take_apps; |
406 end; (* local *) |
406 end; (* local *) |
407 |
407 |
408 val take_lemmas = mapn (fn n => fn(dn,ax_reach) => pg'' thy axs_take_def (mk_All("n", |
408 val take_lemmas = mapn (fn n => fn(dn,ax_reach) => pg'' thy axs_take_def (mk_All("n", |
409 mk_trp(dc_take dn $ Bound 0 `%(x_name n) === |
409 mk_trp(dc_take dn $ Bound 0 `%(x_name n) === |
410 dc_take dn $ Bound 0 `%(x_name n^"'"))) |
410 dc_take dn $ Bound 0 `%(x_name n^"'"))) |
411 ===> mk_trp(%(x_name n) === %(x_name n^"'"))) (fn prems => [ |
411 ===> mk_trp(%(x_name n) === %(x_name n^"'"))) (fn prems => [ |
412 res_inst_tac[("t",x_name n )](ax_reach RS subst) 1, |
412 res_inst_tac[("t",x_name n )](ax_reach RS subst) 1, |
413 res_inst_tac[("t",x_name n^"'")](ax_reach RS subst) 1, |
413 res_inst_tac[("t",x_name n^"'")](ax_reach RS subst) 1, |
414 rtac (fix_def2 RS ssubst) 1, |
414 rtac (fix_def2 RS ssubst) 1, |
415 REPEAT(CHANGED(rtac (contlub_cfun_arg RS ssubst) 1 |
415 REPEAT(CHANGED(rtac (contlub_cfun_arg RS ssubst) 1 |
416 THEN chain_tac 1)), |
416 THEN chain_tac 1)), |
417 rtac (contlub_cfun_fun RS ssubst) 1, |
417 rtac (contlub_cfun_fun RS ssubst) 1, |
418 rtac (contlub_cfun_fun RS ssubst) 2, |
418 rtac (contlub_cfun_fun RS ssubst) 2, |
419 rtac lub_equal 3, |
419 rtac lub_equal 3, |
420 chain_tac 1, |
420 chain_tac 1, |
421 rtac allI 1, |
421 rtac allI 1, |
422 resolve_tac prems 1])) 1 (dnames~~axs_reach); |
422 resolve_tac prems 1])) 1 (dnames~~axs_reach); |
423 |
423 |
424 local |
424 local |
425 fun one_con p (con,args) = foldr mk_All (map vname args, |
425 fun one_con p (con,args) = foldr mk_All (map vname args, |
426 lift_defined (bound_arg (map vname args)) (nonlazy args, |
426 lift_defined (bound_arg (map vname args)) (nonlazy args, |
427 lift (fn arg => %(P_name (1+rec_of arg)) $ bound_arg args arg) |
427 lift (fn arg => %(P_name (1+rec_of arg)) $ bound_arg args arg) |
428 (filter is_rec args,mk_trp(%p $ con_app2 con (bound_arg args) args)))); |
428 (filter is_rec args,mk_trp(%p $ con_app2 con (bound_arg args) args)))); |
429 fun one_eq ((p,cons),concl) = (mk_trp(%p $ UU) ===> |
429 fun one_eq ((p,cons),concl) = (mk_trp(%p $ UU) ===> |
430 foldr (op ===>) (map (one_con p) cons,concl)); |
430 foldr (op ===>) (map (one_con p) cons,concl)); |
431 fun ind_term concf = foldr one_eq (mapn (fn n => fn x => (P_name n, x)) 1 conss, |
431 fun ind_term concf = foldr one_eq (mapn (fn n => fn x => (P_name n, x)) 1 conss, |
432 mk_trp(foldr' mk_conj (mapn (fn n => concf (P_name n,x_name n)) 1 dnames))); |
432 mk_trp(foldr' mk_conj (mapn (fn n => concf (P_name n,x_name n)) 1 dnames))); |
433 val take_ss = HOL_ss addsimps take_rews; |
433 val take_ss = HOL_ss addsimps take_rews; |
434 fun ind_tacs tacsf thms1 thms2 prems = TRY(safe_tac HOL_cs):: |
434 fun ind_tacs tacsf thms1 thms2 prems = TRY(safe_tac HOL_cs):: |
435 flat (mapn (fn n => fn (thm1,thm2) => |
435 flat (mapn (fn n => fn (thm1,thm2) => |
436 tacsf (n,prems) (thm1,thm2) @ |
436 tacsf (n,prems) (thm1,thm2) @ |
437 flat (map (fn cons => |
437 flat (map (fn cons => |
438 (resolve_tac prems 1 :: |
438 (resolve_tac prems 1 :: |
439 flat (map (fn (_,args) => |
439 flat (map (fn (_,args) => |
440 resolve_tac prems 1:: |
440 resolve_tac prems 1:: |
441 map (K(atac 1)) (nonlazy args) @ |
441 map (K(atac 1)) (nonlazy args) @ |
442 map (K(atac 1)) (filter is_rec args)) |
442 map (K(atac 1)) (filter is_rec args)) |
443 cons))) |
443 cons))) |
444 conss)) |
444 conss)) |
445 0 (thms1~~thms2)); |
445 0 (thms1~~thms2)); |
446 local |
446 local |
447 fun all_rec_to ns lazy_rec (n,cons) = forall (exists (fn arg => |
447 fun all_rec_to ns lazy_rec (n,cons) = forall (exists (fn arg => |
448 is_rec arg andalso not(rec_of arg mem ns) andalso |
448 is_rec arg andalso not(rec_of arg mem ns) andalso |
449 ((rec_of arg = n andalso not(lazy_rec orelse is_lazy arg)) orelse |
449 ((rec_of arg = n andalso not(lazy_rec orelse is_lazy arg)) orelse |
450 rec_of arg <> n andalso all_rec_to (rec_of arg::ns) |
450 rec_of arg <> n andalso all_rec_to (rec_of arg::ns) |
451 (lazy_rec orelse is_lazy arg) (n, (nth_elem(rec_of arg,conss)))) |
451 (lazy_rec orelse is_lazy arg) (n, (nth_elem(rec_of arg,conss)))) |
452 ) o snd) cons; |
452 ) o snd) cons; |
453 fun warn (n,cons) = if all_rec_to [] false (n,cons) then (writeln |
453 fun warn (n,cons) = if all_rec_to [] false (n,cons) then (writeln |
454 ("WARNING: domain "^nth_elem(n,dnames)^" is empty!"); true) |
454 ("WARNING: domain "^nth_elem(n,dnames)^" is empty!"); true) |
455 else false; |
455 else false; |
456 fun lazy_rec_to ns lazy_rec (n,cons) = exists (exists (fn arg => |
456 fun lazy_rec_to ns lazy_rec (n,cons) = exists (exists (fn arg => |
457 is_rec arg andalso not(rec_of arg mem ns) andalso |
457 is_rec arg andalso not(rec_of arg mem ns) andalso |
458 ((rec_of arg = n andalso (lazy_rec orelse is_lazy arg)) orelse |
458 ((rec_of arg = n andalso (lazy_rec orelse is_lazy arg)) orelse |
459 rec_of arg <> n andalso lazy_rec_to (rec_of arg::ns) |
459 rec_of arg <> n andalso lazy_rec_to (rec_of arg::ns) |
460 (lazy_rec orelse is_lazy arg) (n, (nth_elem(rec_of arg,conss)))) |
460 (lazy_rec orelse is_lazy arg) (n, (nth_elem(rec_of arg,conss)))) |
461 ) o snd) cons; |
461 ) o snd) cons; |
462 in val is_emptys = map warn (mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs); |
462 in val is_emptys = map warn (mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs); |
463 val is_finite = forall (not o lazy_rec_to [] false) |
463 val is_finite = forall (not o lazy_rec_to [] false) |
464 (mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs) |
464 (mapn (fn n => fn (_,cons) => (n,cons)) 0 eqs) |
465 end; |
465 end; |
466 in |
466 in |
467 val finite_ind = pg'' thy [] (ind_term (fn (P,x) => fn dn => |
467 val finite_ind = pg'' thy [] (ind_term (fn (P,x) => fn dn => |
468 mk_all(x,%P $ (dc_take dn $ %"n" `Bound 0)))) (fn prems=> [ |
468 mk_all(x,%P $ (dc_take dn $ %"n" `Bound 0)))) (fn prems=> [ |
469 nat_ind_tac "n" 1, |
469 nat_ind_tac "n" 1, |
470 simp_tac (take_ss addsimps prems) 1, |
470 simp_tac (take_ss addsimps prems) 1, |
471 TRY(safe_tac HOL_cs)] |
471 TRY(safe_tac HOL_cs)] |
472 @ flat(mapn (fn n => fn (cons,cases) => [ |
472 @ flat(mapn (fn n => fn (cons,cases) => [ |
473 res_inst_tac [("x",x_name n)] cases 1, |
473 res_inst_tac [("x",x_name n)] cases 1, |
474 asm_simp_tac (take_ss addsimps prems) 1] |
474 asm_simp_tac (take_ss addsimps prems) 1] |
475 @ flat(map (fn (con,args) => |
475 @ flat(map (fn (con,args) => |
476 asm_simp_tac take_ss 1 :: |
476 asm_simp_tac take_ss 1 :: |
477 map (fn arg => |
477 map (fn arg => |
478 case_UU_tac (prems@con_rews) 1 ( |
478 case_UU_tac (prems@con_rews) 1 ( |
479 nth_elem(rec_of arg,dnames)^"_take n1`"^vname arg)) |
479 nth_elem(rec_of arg,dnames)^"_take n1`"^vname arg)) |
480 (filter is_nonlazy_rec args) @ [ |
480 (filter is_nonlazy_rec args) @ [ |
481 resolve_tac prems 1] @ |
481 resolve_tac prems 1] @ |
482 map (K (atac 1)) (nonlazy args) @ |
482 map (K (atac 1)) (nonlazy args) @ |
483 map (K (etac spec 1)) (filter is_rec args)) |
483 map (K (etac spec 1)) (filter is_rec args)) |
484 cons)) |
484 cons)) |
485 1 (conss~~casess))); |
485 1 (conss~~casess))); |
486 |
486 |
487 val (finites,ind) = if is_finite then |
487 val (finites,ind) = if is_finite then |
488 let |
488 let |
489 fun take_enough dn = mk_ex ("n",dc_take dn $ Bound 0 ` %"x" === %"x"); |
489 fun take_enough dn = mk_ex ("n",dc_take dn $ Bound 0 ` %"x" === %"x"); |
490 val finite_lemmas1a = map (fn dn => pg [] (mk_trp(defined (%"x")) ===> |
490 val finite_lemmas1a = map (fn dn => pg [] (mk_trp(defined (%"x")) ===> |
491 mk_trp(mk_disj(mk_all("n",dc_take dn $ Bound 0 ` %"x" === UU), |
491 mk_trp(mk_disj(mk_all("n",dc_take dn $ Bound 0 ` %"x" === UU), |
492 take_enough dn)) ===> mk_trp(take_enough dn)) [ |
492 take_enough dn)) ===> mk_trp(take_enough dn)) [ |
493 etac disjE 1, |
493 etac disjE 1, |
494 etac notE 1, |
494 etac notE 1, |
495 resolve_tac take_lemmas 1, |
495 resolve_tac take_lemmas 1, |
496 asm_simp_tac take_ss 1, |
496 asm_simp_tac take_ss 1, |
497 atac 1]) dnames; |
497 atac 1]) dnames; |
498 val finite_lemma1b = pg [] (mk_trp (mk_all("n",foldr' mk_conj (mapn |
498 val finite_lemma1b = pg [] (mk_trp (mk_all("n",foldr' mk_conj (mapn |
499 (fn n => fn ((dn,args),_) => mk_constrainall(x_name n,Type(dn,args), |
499 (fn n => fn ((dn,args),_) => mk_constrainall(x_name n,Type(dn,args), |
500 mk_disj(dc_take dn $ Bound 1 ` Bound 0 === UU, |
500 mk_disj(dc_take dn $ Bound 1 ` Bound 0 === UU, |
501 dc_take dn $ Bound 1 ` Bound 0 === Bound 0))) 1 eqs)))) ([ |
501 dc_take dn $ Bound 1 ` Bound 0 === Bound 0))) 1 eqs)))) ([ |
502 rtac allI 1, |
502 rtac allI 1, |
503 nat_ind_tac "n" 1, |
503 nat_ind_tac "n" 1, |
504 simp_tac take_ss 1, |
504 simp_tac take_ss 1, |
505 TRY(safe_tac(empty_cs addSEs[conjE] addSIs[conjI]))] @ |
505 TRY(safe_tac(empty_cs addSEs[conjE] addSIs[conjI]))] @ |
506 flat(mapn (fn n => fn (cons,cases) => [ |
506 flat(mapn (fn n => fn (cons,cases) => [ |
507 simp_tac take_ss 1, |
507 simp_tac take_ss 1, |
508 rtac allI 1, |
508 rtac allI 1, |
509 res_inst_tac [("x",x_name n)] cases 1, |
509 res_inst_tac [("x",x_name n)] cases 1, |
510 asm_simp_tac take_ss 1] @ |
510 asm_simp_tac take_ss 1] @ |
511 flat(map (fn (con,args) => |
511 flat(map (fn (con,args) => |
512 asm_simp_tac take_ss 1 :: |
512 asm_simp_tac take_ss 1 :: |
513 flat(map (fn arg => [ |
513 flat(map (fn arg => [ |
514 eres_inst_tac [("x",vname arg)] all_dupE 1, |
514 eres_inst_tac [("x",vname arg)] all_dupE 1, |
515 etac disjE 1, |
515 etac disjE 1, |
516 asm_simp_tac (HOL_ss addsimps con_rews) 1, |
516 asm_simp_tac (HOL_ss addsimps con_rews) 1, |
517 asm_simp_tac take_ss 1]) |
517 asm_simp_tac take_ss 1]) |
518 (filter is_nonlazy_rec args))) |
518 (filter is_nonlazy_rec args))) |
519 cons)) |
519 cons)) |
520 1 (conss~~casess))) handle ERROR => raise ERROR; |
520 1 (conss~~casess))) handle ERROR => raise ERROR; |
521 val all_finite=map (fn(dn,l1b)=>pg axs_finite_def (mk_trp(%%(dn^"_finite") $ %"x"))[ |
521 val all_finite=map (fn(dn,l1b)=>pg axs_finite_def (mk_trp(%%(dn^"_finite") $ %"x"))[ |
522 case_UU_tac take_rews 1 "x", |
522 case_UU_tac take_rews 1 "x", |
523 eresolve_tac finite_lemmas1a 1, |
523 eresolve_tac finite_lemmas1a 1, |
524 step_tac HOL_cs 1, |
524 step_tac HOL_cs 1, |
525 step_tac HOL_cs 1, |
525 step_tac HOL_cs 1, |
526 cut_facts_tac [l1b] 1, |
526 cut_facts_tac [l1b] 1, |
527 fast_tac HOL_cs 1]) (dnames~~atomize finite_lemma1b); |
527 fast_tac HOL_cs 1]) (dnames~~atomize finite_lemma1b); |
528 in |
528 in |
529 (all_finite, |
529 (all_finite, |
530 pg'' thy [] (ind_term (fn (P,x) => fn dn => %P $ %x)) |
530 pg'' thy [] (ind_term (fn (P,x) => fn dn => %P $ %x)) |
531 (ind_tacs (fn _ => fn (all_fin,finite_ind) => [ |
531 (ind_tacs (fn _ => fn (all_fin,finite_ind) => [ |
532 rtac (rewrite_rule axs_finite_def all_fin RS exE) 1, |
532 rtac (rewrite_rule axs_finite_def all_fin RS exE) 1, |
533 etac subst 1, |
533 etac subst 1, |
534 rtac finite_ind 1]) all_finite (atomize finite_ind)) |
534 rtac finite_ind 1]) all_finite (atomize finite_ind)) |
535 ) end (* let *) else |
535 ) end (* let *) else |
536 (mapn (fn n => fn dn => read_instantiate_sg (sign_of thy) |
536 (mapn (fn n => fn dn => read_instantiate_sg (sign_of thy) |
537 [("P",dn^"_finite "^x_name n)] excluded_middle) 1 dnames, |
537 [("P",dn^"_finite "^x_name n)] excluded_middle) 1 dnames, |
538 pg'' thy [] (foldr (op ===>) (mapn (fn n =>K(mk_trp(%%"adm" $ %(P_name n))))1 |
538 pg'' thy [] (foldr (op ===>) (mapn (fn n =>K(mk_trp(%%"adm" $ %(P_name n))))1 |
539 dnames,ind_term (fn(P,x)=>fn dn=> %P $ %x))) |
539 dnames,ind_term (fn(P,x)=>fn dn=> %P $ %x))) |
540 (ind_tacs (fn (n,prems) => fn (ax_reach,finite_ind) =>[ |
540 (ind_tacs (fn (n,prems) => fn (ax_reach,finite_ind) =>[ |
541 rtac (ax_reach RS subst) 1, |
541 rtac (ax_reach RS subst) 1, |
542 res_inst_tac [("x",x_name n)] spec 1, |
542 res_inst_tac [("x",x_name n)] spec 1, |
543 rtac wfix_ind 1, |
543 rtac wfix_ind 1, |
544 rtac adm_impl_admw 1, |
544 rtac adm_impl_admw 1, |
545 resolve_tac adm_thms 1, |
545 resolve_tac adm_thms 1, |
546 rtac adm_subst 1, |
546 rtac adm_subst 1, |
547 cont_tacR 1, |
547 cont_tacR 1, |
548 resolve_tac prems 1, |
548 resolve_tac prems 1, |
549 strip_tac 1, |
549 strip_tac 1, |
550 rtac(rewrite_rule axs_take_def finite_ind) 1]) |
550 rtac(rewrite_rule axs_take_def finite_ind) 1]) |
551 axs_reach (atomize finite_ind)) |
551 axs_reach (atomize finite_ind)) |
552 ) |
552 ) |
553 end; (* local *) |
553 end; (* local *) |
554 |
554 |
555 local |
555 local |
556 val xs = mapn (fn n => K (x_name n)) 1 dnames; |
556 val xs = mapn (fn n => K (x_name n)) 1 dnames; |
557 fun bnd_arg n i = Bound(2*(length dnames - n)-i-1); |
557 fun bnd_arg n i = Bound(2*(length dnames - n)-i-1); |
558 val take_ss = HOL_ss addsimps take_rews; |
558 val take_ss = HOL_ss addsimps take_rews; |
559 val sproj = bin_branchr (fn s => "fst("^s^")") (fn s => "snd("^s^")"); |
559 val sproj = bin_branchr (fn s => "fst("^s^")") (fn s => "snd("^s^")"); |
560 val coind_lemma = pg [ax_bisim_def] (mk_trp(mk_imp(%%(comp_dname^"_bisim") $ %"R", |
560 val coind_lemma = pg [ax_bisim_def] (mk_trp(mk_imp(%%(comp_dname^"_bisim") $ %"R", |
561 foldr (fn (x,t)=> mk_all(x,mk_all(x^"'",t))) (xs, |
561 foldr (fn (x,t)=> mk_all(x,mk_all(x^"'",t))) (xs, |
562 foldr mk_imp (mapn (fn n => K(proj (%"R") dnames n $ |
562 foldr mk_imp (mapn (fn n => K(proj (%"R") dnames n $ |
563 bnd_arg n 0 $ bnd_arg n 1)) 0 dnames, |
563 bnd_arg n 0 $ bnd_arg n 1)) 0 dnames, |
564 foldr' mk_conj (mapn (fn n => fn dn => |
564 foldr' mk_conj (mapn (fn n => fn dn => |
565 (dc_take dn $ %"n" `bnd_arg n 0 === |
565 (dc_take dn $ %"n" `bnd_arg n 0 === |
566 (dc_take dn $ %"n" `bnd_arg n 1))) 0 dnames)))))) ([ |
566 (dc_take dn $ %"n" `bnd_arg n 1))) 0 dnames)))))) ([ |
567 rtac impI 1, |
567 rtac impI 1, |
568 nat_ind_tac "n" 1, |
568 nat_ind_tac "n" 1, |
569 simp_tac take_ss 1, |
569 simp_tac take_ss 1, |
570 safe_tac HOL_cs] @ |
570 safe_tac HOL_cs] @ |
571 flat(mapn (fn n => fn x => [ |
571 flat(mapn (fn n => fn x => [ |
572 etac allE 1, etac allE 1, |
572 etac allE 1, etac allE 1, |
573 eres_inst_tac [("P1",sproj "R" dnames n^ |
573 eres_inst_tac [("P1",sproj "R" dnames n^ |
574 " "^x^" "^x^"'")](mp RS disjE) 1, |
574 " "^x^" "^x^"'")](mp RS disjE) 1, |
575 TRY(safe_tac HOL_cs), |
575 TRY(safe_tac HOL_cs), |
576 REPEAT(CHANGED(asm_simp_tac take_ss 1))]) |
576 REPEAT(CHANGED(asm_simp_tac take_ss 1))]) |
577 0 xs)); |
577 0 xs)); |
578 in |
578 in |
579 val coind = pg [] (mk_trp(%%(comp_dname^"_bisim") $ %"R") ===> |
579 val coind = pg [] (mk_trp(%%(comp_dname^"_bisim") $ %"R") ===> |
580 foldr (op ===>) (mapn (fn n => fn x => |
580 foldr (op ===>) (mapn (fn n => fn x => |
581 mk_trp(proj (%"R") dnames n $ %x $ %(x^"'"))) 0 xs, |
581 mk_trp(proj (%"R") dnames n $ %x $ %(x^"'"))) 0 xs, |
582 mk_trp(foldr' mk_conj (map (fn x => %x === %(x^"'")) xs)))) ([ |
582 mk_trp(foldr' mk_conj (map (fn x => %x === %(x^"'")) xs)))) ([ |
583 TRY(safe_tac HOL_cs)] @ |
583 TRY(safe_tac HOL_cs)] @ |
584 flat(map (fn take_lemma => [ |
584 flat(map (fn take_lemma => [ |
585 rtac take_lemma 1, |
585 rtac take_lemma 1, |
586 cut_facts_tac [coind_lemma] 1, |
586 cut_facts_tac [coind_lemma] 1, |
587 fast_tac HOL_cs 1]) |
587 fast_tac HOL_cs 1]) |
588 take_lemmas)); |
588 take_lemmas)); |
589 end; (* local *) |
589 end; (* local *) |
590 |
590 |
591 |
591 |
592 in (take_rews, take_lemmas, finites, finite_ind, ind, coind) |
592 in (take_rews, take_lemmas, finites, finite_ind, ind, coind) |
593 |
593 |