src/Pure/Isar/obtain.ML
 author wenzelm Wed Aug 02 22:27:02 2006 +0200 (2006-08-02) changeset 20308 ddb7e7129481 parent 20224 9c40a144ee0e child 20804 0e2591606867 permissions -rw-r--r--
simplified obtain_export: no Seq.seq, no lifting of result prems;
tuned;
```     1 (*  Title:      Pure/Isar/obtain.ML
```
```     2     ID:         \$Id\$
```
```     3     Author:     Markus Wenzel, TU Muenchen
```
```     4
```
```     5 The 'obtain' and 'guess' language elements -- generalized existence at
```
```     6 the level of proof texts: 'obtain' involves a proof that certain
```
```     7 fixes/assumes may be introduced into the present context; 'guess' is
```
```     8 similar, but derives these elements from the course of reasoning!
```
```     9
```
```    10   <chain_facts>
```
```    11   obtain x where "A x" <proof> ==
```
```    12
```
```    13   have "!!thesis. (!!x. A x ==> thesis) ==> thesis"
```
```    14   proof succeed
```
```    15     fix thesis
```
```    16     assume that [intro?]: "!!x. A x ==> thesis"
```
```    17     <chain_facts>
```
```    18     show thesis
```
```    19       apply (insert that)
```
```    20       <proof>
```
```    21   qed
```
```    22   fix x assm <<obtain_export>> "A x"
```
```    23
```
```    24
```
```    25   <chain_facts>
```
```    26   guess x <proof body> <proof end> ==
```
```    27
```
```    28   {
```
```    29     fix thesis
```
```    30     <chain_facts> have "PROP ?guess"
```
```    31       apply magic      -- {* turns goal into "thesis ==> #thesis" *}
```
```    32       <proof body>
```
```    33       apply_end magic  -- {* turns final "(!!x. P x ==> thesis) ==> #thesis" into
```
```    34         "#((!!x. A x ==> thesis) ==> thesis)" which is a finished goal state *}
```
```    35       <proof end>
```
```    36   }
```
```    37   fix x assm <<obtain_export>> "A x"
```
```    38 *)
```
```    39
```
```    40 signature OBTAIN =
```
```    41 sig
```
```    42   val obtain: string -> (string * string option * mixfix) list ->
```
```    43     ((string * Attrib.src list) * (string * string list) list) list ->
```
```    44     bool -> Proof.state -> Proof.state
```
```    45   val obtain_i: string -> (string * typ option * mixfix) list ->
```
```    46     ((string * attribute list) * (term * term list) list) list ->
```
```    47     bool -> Proof.state -> Proof.state
```
```    48   val result: (Proof.context -> tactic) -> thm list -> Proof.context ->
```
```    49     (cterm list * thm list) * Proof.context
```
```    50   val guess: (string * string option * mixfix) list -> bool -> Proof.state -> Proof.state
```
```    51   val guess_i: (string * typ option * mixfix) list -> bool -> Proof.state -> Proof.state
```
```    52   val statement: (string * ((string * 'typ option) list * 'term list)) list ->
```
```    53     (('typ, 'term, 'fact) Element.ctxt list *
```
```    54       ((string * Attrib.src list) * ('term * 'term list) list) list) *
```
```    55     (((string * Attrib.src list) * (term * term list) list) list -> Proof.context ->
```
```    56       (((string * Attrib.src list) * (term * term list) list) list * thm list) * Proof.context)
```
```    57 end;
```
```    58
```
```    59 structure Obtain: OBTAIN =
```
```    60 struct
```
```    61
```
```    62 (** obtain_export **)
```
```    63
```
```    64 (*
```
```    65   [x, A x]
```
```    66      :
```
```    67      B
```
```    68   --------
```
```    69      B
```
```    70 *)
```
```    71 fun obtain_export fix_ctxt rule xs _ As thm =
```
```    72   let
```
```    73     val thy = ProofContext.theory_of fix_ctxt;
```
```    74
```
```    75     val vs = map (dest_Free o Thm.term_of) xs;
```
```    76     val bads = Term.fold_aterms (fn t as Free v =>
```
```    77       if member (op =) vs v then insert (op aconv) t else I | _ => I) (Thm.prop_of thm) [];
```
```    78     val _ = null bads orelse
```
```    79       error ("Result contains obtained parameters: " ^
```
```    80         space_implode " " (map (ProofContext.string_of_term fix_ctxt) bads));
```
```    81     val _ = ObjectLogic.is_judgment thy (Thm.concl_of thm) orelse
```
```    82       error "Conclusion in obtained context must be object-logic judgment";
```
```    83
```
```    84     val ((_, [thm']), ctxt') = Variable.import true [thm] fix_ctxt;
```
```    85     val prems = Drule.strip_imp_prems (#prop (Thm.crep_thm thm'));
```
```    86   in
```
```    87     ((Drule.implies_elim_list thm' (map Thm.assume prems)
```
```    88         |> Drule.implies_intr_list (map Drule.norm_hhf_cterm As)
```
```    89         |> Drule.forall_intr_list xs)
```
```    90       COMP rule)
```
```    91     |> Drule.implies_intr_list prems
```
```    92     |> singleton (Variable.export ctxt' fix_ctxt)
```
```    93   end;
```
```    94
```
```    95
```
```    96
```
```    97 (** obtain **)
```
```    98
```
```    99 fun bind_judgment ctxt name =
```
```   100   let
```
```   101     val (bind, ctxt') = ProofContext.bind_fixes [name] ctxt;
```
```   102     val (t as _ \$ Free v) = bind (ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name);
```
```   103   in ((v, t), ctxt') end;
```
```   104
```
```   105 val thatN = "that";
```
```   106
```
```   107 local
```
```   108
```
```   109 fun gen_obtain prep_att prep_vars prep_propp
```
```   110     name raw_vars raw_asms int state =
```
```   111   let
```
```   112     val _ = Proof.assert_forward_or_chain state;
```
```   113     val thy = Proof.theory_of state;
```
```   114     val cert = Thm.cterm_of thy;
```
```   115     val ctxt = Proof.context_of state;
```
```   116     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
```
```   117
```
```   118     (*obtain vars*)
```
```   119     val (vars, vars_ctxt) = prep_vars raw_vars ctxt;
```
```   120     val (_, fix_ctxt) = vars_ctxt |> ProofContext.add_fixes_i vars;
```
```   121     val xs = map #1 vars;
```
```   122
```
```   123     (*obtain asms*)
```
```   124     val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);
```
```   125     val asm_props = maps (map fst) proppss;
```
```   126     val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;
```
```   127
```
```   128     val _ = Variable.warn_extra_tfrees fix_ctxt asms_ctxt;
```
```   129
```
```   130     (*obtain statements*)
```
```   131     val thesisN = Name.variant xs AutoBind.thesisN;
```
```   132     val (thesis_var, thesis) = #1 (bind_judgment fix_ctxt thesisN);
```
```   133
```
```   134     val asm_frees = fold Term.add_frees asm_props [];
```
```   135     val parms = xs |> map (fn x =>
```
```   136       let val x' = ProofContext.get_skolem fix_ctxt x
```
```   137       in (x', the_default propT (AList.lookup (op =) asm_frees x')) end);
```
```   138
```
```   139     val that_name = if name = "" then thatN else name;
```
```   140     val that_prop =
```
```   141       Term.list_all_free (parms, Logic.list_implies (asm_props, thesis))
```
```   142       |> Library.curry Logic.list_rename_params xs;
```
```   143     val obtain_prop =
```
```   144       Logic.list_rename_params ([AutoBind.thesisN],
```
```   145         Term.list_all_free ([thesis_var], Logic.mk_implies (that_prop, thesis)));
```
```   146
```
```   147     fun after_qed _ =
```
```   148       Proof.local_qed (NONE, false)
```
```   149       #> Seq.map (`Proof.the_fact #-> (fn rule =>
```
```   150         Proof.fix_i (map2 (fn x => fn (_, T, mx) => (x, T, mx)) xs vars)
```
```   151         #> Proof.assm_i (obtain_export fix_ctxt rule (map (cert o Free) parms)) asms));
```
```   152   in
```
```   153     state
```
```   154     |> Proof.enter_forward
```
```   155     |> Proof.have_i NONE (K Seq.single) [(("", []), [(obtain_prop, [])])] int
```
```   156     |> Proof.proof (SOME Method.succeed_text) |> Seq.hd
```
```   157     |> Proof.fix_i [(thesisN, NONE, NoSyn)]
```
```   158     |> Proof.assume_i [((that_name, [ContextRules.intro_query NONE]), [(that_prop, [])])]
```
```   159     |> `Proof.the_facts
```
```   160     ||> Proof.chain_facts chain_facts
```
```   161     ||> Proof.show_i NONE after_qed [(("", []), [(thesis, [])])] false
```
```   162     |-> Proof.refine_insert
```
```   163   end;
```
```   164
```
```   165 in
```
```   166
```
```   167 val obtain = gen_obtain Attrib.attribute ProofContext.read_vars ProofContext.read_propp;
```
```   168 val obtain_i = gen_obtain (K I) ProofContext.cert_vars ProofContext.cert_propp;
```
```   169
```
```   170 end;
```
```   171
```
```   172
```
```   173
```
```   174 (** tactical result **)
```
```   175
```
```   176 fun check_result ctxt thesis th =
```
```   177   (case Thm.prems_of th of
```
```   178     [prem] =>
```
```   179       if Thm.concl_of th aconv thesis andalso
```
```   180         Logic.strip_assums_concl prem aconv thesis then th
```
```   181       else error ("Guessed a different clause:\n" ^ ProofContext.string_of_thm ctxt th)
```
```   182   | [] => error "Goal solved -- nothing guessed."
```
```   183   | _ => error ("Guess split into several cases:\n" ^ ProofContext.string_of_thm ctxt th));
```
```   184
```
```   185 fun result tac facts ctxt =
```
```   186   let
```
```   187     val thy = ProofContext.theory_of ctxt;
```
```   188     val cert = Thm.cterm_of thy;
```
```   189
```
```   190     val ((thesis_var, thesis), thesis_ctxt) = bind_judgment ctxt AutoBind.thesisN;
```
```   191     val rule =
```
```   192       (case SINGLE (Method.insert_tac facts 1 THEN tac thesis_ctxt) (Goal.init (cert thesis)) of
```
```   193         NONE => raise THM ("Obtain.result: tactic failed", 0, facts)
```
```   194       | SOME th => check_result ctxt thesis (norm_hhf (Goal.conclude th)));
```
```   195
```
```   196     val closed_rule = Thm.forall_intr (cert (Free thesis_var)) rule;
```
```   197     val ((_, [rule']), ctxt') = Variable.import false [closed_rule] ctxt;
```
```   198     val obtain_rule = Thm.forall_elim (cert (Logic.varify (Free thesis_var))) rule';
```
```   199     val ((params, stmt), fix_ctxt) = Variable.focus (Thm.cprem_of obtain_rule 1) ctxt';
```
```   200     val (prems, ctxt'') =
```
```   201       Assumption.add_assms (obtain_export fix_ctxt obtain_rule params)
```
```   202         (Drule.strip_imp_prems stmt) fix_ctxt;
```
```   203   in ((params, prems), ctxt'') end;
```
```   204
```
```   205
```
```   206
```
```   207 (** guess **)
```
```   208
```
```   209 local
```
```   210
```
```   211 fun unify_params vars thesis_var raw_rule ctxt =
```
```   212   let
```
```   213     val thy = ProofContext.theory_of ctxt;
```
```   214     val certT = Thm.ctyp_of thy;
```
```   215     val cert = Thm.cterm_of thy;
```
```   216     val string_of_typ = ProofContext.string_of_typ ctxt;
```
```   217     val string_of_term = setmp show_types true (ProofContext.string_of_term ctxt);
```
```   218
```
```   219     fun err msg th = error (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th);
```
```   220
```
```   221     val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;
```
```   222     val rule = Thm.incr_indexes (maxidx + 1) raw_rule;
```
```   223
```
```   224     val params = RuleCases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));
```
```   225     val m = length vars;
```
```   226     val n = length params;
```
```   227     val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;
```
```   228
```
```   229     fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)
```
```   230       handle Type.TUNIFY =>
```
```   231         err ("Failed to unify variable " ^
```
```   232           string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^
```
```   233           string_of_term (Syntax.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule;
```
```   234     val (tyenv, _) = fold unify (map #1 vars ~~ Library.take (m, params))
```
```   235       (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));
```
```   236     val norm_type = Envir.norm_type tyenv;
```
```   237
```
```   238     val xs = map (apsnd norm_type o fst) vars;
```
```   239     val ys = map (apsnd norm_type) (Library.drop (m, params));
```
```   240     val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;
```
```   241     val terms = map (Drule.mk_term o cert o Free) (xs @ ys');
```
```   242
```
```   243     val instT =
```
```   244       fold (Term.add_tvarsT o #2) params []
```
```   245       |> map (TVar #> (fn T => (certT T, certT (norm_type T))));
```
```   246     val closed_rule = rule
```
```   247       |> Thm.forall_intr (cert (Free thesis_var))
```
```   248       |> Thm.instantiate (instT, []);
```
```   249
```
```   250     val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt;
```
```   251     val vars' =
```
```   252       map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~
```
```   253       (map snd vars @ replicate (length ys) NoSyn);
```
```   254     val rule'' = Thm.forall_elim (cert (Logic.varify (Free thesis_var))) rule';
```
```   255   in ((vars', rule''), ctxt') end;
```
```   256
```
```   257 fun inferred_type (x, _, mx) ctxt =
```
```   258   let val ((_, T), ctxt') = ProofContext.inferred_param x ctxt
```
```   259   in ((x, T, mx), ctxt') end;
```
```   260
```
```   261 fun polymorphic ctxt vars =
```
```   262   let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))
```
```   263   in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;
```
```   264
```
```   265 fun gen_guess prep_vars raw_vars int state =
```
```   266   let
```
```   267     val _ = Proof.assert_forward_or_chain state;
```
```   268     val thy = Proof.theory_of state;
```
```   269     val cert = Thm.cterm_of thy;
```
```   270     val ctxt = Proof.context_of state;
```
```   271     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];
```
```   272
```
```   273     val (thesis_var, thesis) = #1 (bind_judgment ctxt AutoBind.thesisN);
```
```   274     val vars = ctxt |> prep_vars raw_vars |-> fold_map inferred_type |> fst |> polymorphic ctxt;
```
```   275
```
```   276     fun guess_context raw_rule state' =
```
```   277       let
```
```   278         val ((parms, rule), ctxt') =
```
```   279           unify_params vars thesis_var raw_rule (Proof.context_of state');
```
```   280         val (bind, _) = ProofContext.bind_fixes (map (#1 o #1) parms) ctxt';
```
```   281         val ts = map (bind o Free o #1) parms;
```
```   282         val ps = map dest_Free ts;
```
```   283         val asms =
```
```   284           Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))
```
```   285           |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), []));
```
```   286         val _ = not (null asms) orelse error "Trivial result -- nothing guessed";
```
```   287       in
```
```   288         state'
```
```   289         |> Proof.map_context (K ctxt')
```
```   290         |> Proof.fix_i (map (fn ((x, T), mx) => (x, SOME T, mx)) parms)
```
```   291         |> `Proof.context_of |-> (fn fix_ctxt =>
```
```   292             Proof.assm_i (obtain_export fix_ctxt rule (map cert ts)) [(("", []), asms)])
```
```   293         |> Proof.add_binds_i AutoBind.no_facts
```
```   294       end;
```
```   295
```
```   296     val goal = Var (("guess", 0), propT);
```
```   297     fun print_result ctxt' (k, [(s, [_, th])]) =
```
```   298       ProofDisplay.print_results int ctxt' (k, [(s, [th])]);
```
```   299     val before_qed = SOME (Method.primitive_text (Goal.conclude #> norm_hhf #>
```
```   300         (fn th => Goal.protect (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))));
```
```   301     fun after_qed [[_, res]] =
```
```   302       Proof.end_block #> guess_context (check_result ctxt thesis res) #> Seq.single;
```
```   303   in
```
```   304     state
```
```   305     |> Proof.enter_forward
```
```   306     |> Proof.begin_block
```
```   307     |> Proof.fix_i [(AutoBind.thesisN, NONE, NoSyn)]
```
```   308     |> Proof.chain_facts chain_facts
```
```   309     |> Proof.local_goal print_result (K I) (apsnd (rpair I))
```
```   310       "guess" before_qed after_qed [(("", []), [Logic.mk_term goal, goal])]
```
```   311     |> Proof.refine (Method.primitive_text (K (Goal.init (cert thesis)))) |> Seq.hd
```
```   312   end;
```
```   313
```
```   314 in
```
```   315
```
```   316 val guess = gen_guess ProofContext.read_vars;
```
```   317 val guess_i = gen_guess ProofContext.cert_vars;
```
```   318
```
```   319 end;
```
```   320
```
```   321
```
```   322
```
```   323 (** statements with several cases **)
```
```   324
```
```   325 fun statement cases =
```
```   326   let
```
```   327     val names =
```
```   328       cases |> map_index (fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);
```
```   329     val elems = cases |> map (fn (_, (vars, _)) =>
```
```   330       Element.Constrains (vars |> map_filter (fn (x, SOME T) => SOME (x, T) | _ => NONE)));
```
```   331     val concl = cases |> map (fn (_, (_, props)) => (("", []), map (rpair []) props));
```
```   332
```
```   333     fun mk_stmt stmt ctxt =
```
```   334       let
```
```   335         val thesis =
```
```   336           ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;
```
```   337         val atts = map Attrib.internal
```
```   338           [RuleCases.consumes (~ (length cases)), RuleCases.case_names names];
```
```   339
```
```   340         fun assume_case ((name, (vars, _)), (_, propp)) ctxt' =
```
```   341           let
```
```   342             val xs = map fst vars;
```
```   343             val props = map fst propp;
```
```   344             val (parms, ctxt'') =
```
```   345               ctxt'
```
```   346               |> fold Variable.declare_term props
```
```   347               |> fold_map ProofContext.inferred_param xs;
```
```   348             val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));
```
```   349           in
```
```   350             ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));
```
```   351             ctxt' |> ProofContext.add_assms_i Assumption.assume_export
```
```   352               [((name, [ContextRules.intro_query NONE]), [(asm, [])])]
```
```   353             |>> (fn [(_, [th])] => th)
```
```   354           end;
```
```   355         val (ths, ctxt') = ctxt
```
```   356           |> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])
```
```   357           |> fold_map assume_case (cases ~~ stmt)
```
```   358           |-> (fn ths => ProofContext.note_thmss_i [((thatN, []), [(ths, [])])] #> #2 #> pair ths);
```
```   359       in (([(("", atts), [(thesis, [])])], ths), ctxt') end;
```
```   360   in ((elems, concl), mk_stmt) end;
```
```   361
```
```   362 end;
```