1 (* Title: Pure/Isar/obtain.ML
2 Author: Markus Wenzel, TU Muenchen
4 The 'obtain' and 'guess' language elements -- generalized existence at
5 the level of proof texts: 'obtain' involves a proof that certain
6 fixes/assumes may be introduced into the present context; 'guess' is
7 similar, but derives these elements from the course of reasoning!
10 obtain x where "A x" <proof> ==
12 have "!!thesis. (!!x. A x ==> thesis) ==> thesis"
15 assume that [intro?]: "!!x. A x ==> thesis"
21 fix x assm <<obtain_export>> "A x"
25 guess x <proof body> <proof end> ==
29 <chain_facts> have "PROP ?guess"
30 apply magic -- {* turns goal into "thesis ==> #thesis" *}
32 apply_end magic -- {* turns final "(!!x. P x ==> thesis) ==> #thesis" into
33 "#((!!x. A x ==> thesis) ==> thesis)" which is a finished goal state *}
36 fix x assm <<obtain_export>> "A x"
42 val obtain: string -> (binding * typ option * mixfix) list ->
43 (Thm.binding * (term * term list) list) list -> bool -> Proof.state -> Proof.state
44 val obtain_cmd: string -> (binding * string option * mixfix) list ->
45 (Attrib.binding * (string * string list) list) list -> bool -> Proof.state -> Proof.state
46 val result: (Proof.context -> tactic) -> thm list -> Proof.context ->
47 ((string * cterm) list * thm list) * Proof.context
48 val guess: (binding * typ option * mixfix) list -> bool -> Proof.state -> Proof.state
49 val guess_cmd: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state
52 structure Obtain: OBTAIN =
64 fun eliminate_term ctxt xs tm =
66 val vs = map (dest_Free o Thm.term_of) xs;
67 val bads = Term.fold_aterms (fn t as Free v =>
68 if member (op =) vs v then insert (op aconv) t else I | _ => I) tm [];
69 val _ = null bads orelse
70 error ("Result contains obtained parameters: " ^
71 space_implode " " (map (Syntax.string_of_term ctxt) bads));
74 fun eliminate fix_ctxt rule xs As thm =
76 val thy = Proof_Context.theory_of fix_ctxt;
78 val _ = eliminate_term fix_ctxt xs (Thm.full_prop_of thm);
79 val _ = Object_Logic.is_judgment thy (Thm.concl_of thm) orelse
80 error "Conclusion in obtained context must be object-logic judgment";
82 val ((_, [thm']), ctxt') = Variable.import true [thm] fix_ctxt;
83 val prems = Drule.strip_imp_prems (#prop (Thm.crep_thm thm'));
85 ((Drule.implies_elim_list thm' (map Thm.assume prems)
86 |> Drule.implies_intr_list (map Drule.norm_hhf_cterm As)
87 |> Drule.forall_intr_list xs)
89 |> Drule.implies_intr_list prems
90 |> singleton (Variable.export ctxt' fix_ctxt)
93 fun obtain_export ctxt rule xs _ As =
94 (eliminate ctxt rule xs As, eliminate_term ctxt xs);
100 fun bind_judgment ctxt name =
102 val (bind, ctxt') = Proof_Context.bind_fixes [name] ctxt;
103 val (t as _ $ Free v) = bind (Object_Logic.fixed_judgment (Proof_Context.theory_of ctxt) name);
104 in ((v, t), ctxt') end;
110 fun gen_obtain prep_att prep_vars prep_propp
111 name raw_vars raw_asms int state =
113 val _ = Proof.assert_forward_or_chain state;
114 val thy = Proof.theory_of state;
115 val cert = Thm.cterm_of thy;
116 val ctxt = Proof.context_of state;
117 val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
120 val (vars, vars_ctxt) = prep_vars raw_vars ctxt;
121 val (_, fix_ctxt) = vars_ctxt |> Proof_Context.add_fixes vars;
122 val xs = map (Variable.name o #1) vars;
125 val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
126 val asm_props = maps (map fst) proppss;
127 val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;
129 val _ = Variable.warn_extra_tfrees fix_ctxt asms_ctxt;
131 (*obtain statements*)
132 val thesisN = Name.variant xs Auto_Bind.thesisN;
133 val (thesis_var, thesis) = #1 (bind_judgment fix_ctxt thesisN);
135 val asm_frees = fold Term.add_frees asm_props [];
136 val parms = xs |> map (fn x =>
137 let val x' = Proof_Context.get_skolem fix_ctxt x
138 in (x', the_default propT (AList.lookup (op =) asm_frees x')) end);
140 val that_name = if name = "" then thatN else name;
142 Term.list_all_free (parms, Logic.list_implies (asm_props, thesis))
143 |> Library.curry Logic.list_rename_params xs;
145 Logic.list_rename_params ([Auto_Bind.thesisN],
146 Term.list_all_free ([thesis_var], Logic.mk_implies (that_prop, thesis)));
149 Proof.local_qed (NONE, false)
150 #> `Proof.the_fact #-> (fn rule =>
152 #> Proof.assm (obtain_export fix_ctxt rule (map (cert o Free) parms)) asms);
155 |> Proof.enter_forward
156 |> Proof.have NONE (K I) [(Thm.empty_binding, [(obtain_prop, [])])] int
157 |> Proof.proof (SOME Method.succeed_text) |> Seq.hd
158 |> Proof.fix [(Binding.name thesisN, NONE, NoSyn)]
160 [((Binding.name that_name, [Context_Rules.intro_query NONE]), [(that_prop, [])])]
162 ||> Proof.chain_facts chain_facts
163 ||> Proof.show NONE after_qed [(Thm.empty_binding, [(thesis, [])])] false
164 |-> Proof.refine_insert
169 val obtain = gen_obtain (K I) Proof_Context.cert_vars Proof_Context.cert_propp;
170 val obtain_cmd = gen_obtain Attrib.attribute Proof_Context.read_vars Proof_Context.read_propp;
176 (** tactical result **)
178 fun check_result ctxt thesis th =
179 (case Thm.prems_of th of
181 if Thm.concl_of th aconv thesis andalso
182 Logic.strip_assums_concl prem aconv thesis then th
183 else error ("Guessed a different clause:\n" ^ Display.string_of_thm ctxt th)
184 | [] => error "Goal solved -- nothing guessed"
185 | _ => error ("Guess split into several cases:\n" ^ Display.string_of_thm ctxt th));
187 fun result tac facts ctxt =
189 val thy = Proof_Context.theory_of ctxt;
190 val cert = Thm.cterm_of thy;
192 val ((thesis_var, thesis), thesis_ctxt) = bind_judgment ctxt Auto_Bind.thesisN;
194 (case SINGLE (Method.insert_tac facts 1 THEN tac thesis_ctxt) (Goal.init (cert thesis)) of
195 NONE => raise THM ("Obtain.result: tactic failed", 0, facts)
196 | SOME th => check_result ctxt thesis (Raw_Simplifier.norm_hhf (Goal.conclude th)));
198 val closed_rule = Thm.forall_intr (cert (Free thesis_var)) rule;
199 val ((_, [rule']), ctxt') = Variable.import false [closed_rule] ctxt;
200 val obtain_rule = Thm.forall_elim (cert (Logic.varify_global (Free thesis_var))) rule';
201 val ((params, stmt), fix_ctxt) = Variable.focus (Thm.cprem_of obtain_rule 1) ctxt';
202 val (prems, ctxt'') =
203 Assumption.add_assms (obtain_export fix_ctxt obtain_rule (map #2 params))
204 (Drule.strip_imp_prems stmt) fix_ctxt;
205 in ((params, prems), ctxt'') end;
213 fun unify_params vars thesis_var raw_rule ctxt =
215 val thy = Proof_Context.theory_of ctxt;
216 val certT = Thm.ctyp_of thy;
217 val cert = Thm.cterm_of thy;
218 val string_of_term = Syntax.string_of_term (Config.put show_types true ctxt);
220 fun err msg th = error (msg ^ ":\n" ^ Display.string_of_thm ctxt th);
222 val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
223 val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
225 val params = Rule_Cases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
227 val n = length params;
228 val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
230 fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
231 handle Type.TUNIFY =>
232 err ("Failed to unify variable " ^
233 string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
234 string_of_term (Syntax_Trans.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule;
235 val (tyenv, _) = fold unify (map #1 vars ~~ take m params)
236 (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
237 val norm_type = Envir.norm_type tyenv;
239 val xs = map (apsnd norm_type o fst) vars;
240 val ys = map (apsnd norm_type) (drop m params);
241 val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;
242 val terms = map (Drule.mk_term o cert o Free) (xs @ ys');
245 fold (Term.add_tvarsT o #2) params []
246 |> map (TVar #> (fn T => (certT T, certT (norm_type T))));
247 val closed_rule = rule
248 |> Thm.forall_intr (cert (Free thesis_var))
249 |> Thm.instantiate (instT, []);
251 val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt;
253 map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
254 (map snd vars @ replicate (length ys) NoSyn);
255 val rule'' = Thm.forall_elim (cert (Logic.varify_global (Free thesis_var))) rule';
256 in ((vars', rule''), ctxt') end;
258 fun inferred_type (binding, _, mx) ctxt =
260 val x = Variable.name binding;
261 val (T, ctxt') = Proof_Context.inferred_param x ctxt
262 in ((x, T, mx), ctxt') end;
264 fun polymorphic ctxt vars =
265 let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
266 in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
268 fun gen_guess prep_vars raw_vars int state =
270 val _ = Proof.assert_forward_or_chain state;
271 val thy = Proof.theory_of state;
272 val cert = Thm.cterm_of thy;
273 val ctxt = Proof.context_of state;
274 val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
276 val (thesis_var, thesis) = #1 (bind_judgment ctxt Auto_Bind.thesisN);
277 val vars = ctxt |> prep_vars raw_vars |-> fold_map inferred_type |> fst |> polymorphic ctxt;
279 fun guess_context raw_rule state' =
281 val ((parms, rule), ctxt') =
282 unify_params vars thesis_var raw_rule (Proof.context_of state');
283 val (bind, _) = Proof_Context.bind_fixes (map (#1 o #1) parms) ctxt';
284 val ts = map (bind o Free o #1) parms;
285 val ps = map dest_Free ts;
287 Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
288 |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), []));
289 val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
292 |> Proof.map_context (K ctxt')
293 |> Proof.fix (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms)
294 |> `Proof.context_of |-> (fn fix_ctxt => Proof.assm
295 (obtain_export fix_ctxt rule (map cert ts)) [(Thm.empty_binding, asms)])
296 |> Proof.bind_terms Auto_Bind.no_facts
299 val goal = Var (("guess", 0), propT);
300 fun print_result ctxt' (k, [(s, [_, th])]) =
301 Proof_Display.print_results int ctxt' (k, [(s, [th])]);
302 val before_qed = SOME (Method.primitive_text (Goal.conclude #> Raw_Simplifier.norm_hhf #>
303 (fn th => Goal.protect (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))));
304 fun after_qed [[_, res]] =
305 Proof.end_block #> guess_context (check_result ctxt thesis res);
308 |> Proof.enter_forward
310 |> Proof.fix [(Binding.name Auto_Bind.thesisN, NONE, NoSyn)]
311 |> Proof.chain_facts chain_facts
312 |> Proof.local_goal print_result (K I) (apsnd (rpair I))
313 "guess" before_qed after_qed [(Thm.empty_binding, [Logic.mk_term goal, goal])]
314 |> Proof.refine (Method.primitive_text (K (Goal.init (cert thesis)))) |> Seq.hd
319 val guess = gen_guess Proof_Context.cert_vars;
320 val guess_cmd = gen_guess Proof_Context.read_vars;