(*  Title:      Pure/Isar/obtain.ML

     Author:     Markus Wenzel, TU Muenchen

 The 'obtain' and 'guess' language elements -- generalized existence at

 the level of proof texts: 'obtain' involves a proof that certain

 fixes/assumes may be introduced into the present context; 'guess' is

 similar, but derives these elements from the course of reasoning!

   <chain_facts>

   obtain x where "A x" <proof> ==

   have "!!thesis. (!!x. A x ==> thesis) ==> thesis"

   proof succeed

     fix thesis

     assume that [intro?]: "!!x. A x ==> thesis"

     <chain_facts>

     show thesis

       apply (insert that)

       <proof>

   qed

   fix x assm <<obtain_export>> "A x"

   <chain_facts>

   guess x <proof body> <proof end> ==

   {

     fix thesis

     <chain_facts> have "PROP ?guess"

       apply magic      -- {* turns goal into "thesis ==> #thesis" *}

       <proof body>

       apply_end magic  -- {* turns final "(!!x. P x ==> thesis) ==> #thesis" into

         "#((!!x. A x ==> thesis) ==> thesis)" which is a finished goal state *}

       <proof end>

   }

   fix x assm <<obtain_export>> "A x"

 *)

 signature OBTAIN =

 sig

   val thatN: string

   val obtain: string -> (binding * string option * mixfix) list ->

     (Attrib.binding * (string * string list) list) list -> bool -> Proof.state -> Proof.state

   val obtain_i: string -> (binding * typ option * mixfix) list ->

     (Thm.binding * (term * term list) list) list -> bool -> Proof.state -> Proof.state

   val result: (Proof.context -> tactic) -> thm list -> Proof.context ->

     (cterm list * thm list) * Proof.context

   val guess: (binding * string option * mixfix) list -> bool -> Proof.state -> Proof.state

   val guess_i: (binding * typ option * mixfix) list -> bool -> Proof.state -> Proof.state

 end;

 structure Obtain: OBTAIN =

 struct

 (** obtain_export **)

 (*

   [x, A x]

      :

      B

   --------

      B

 *)

 fun eliminate_term ctxt xs tm =

   let

     val vs = map (dest_Free o Thm.term_of) xs;

     val bads = Term.fold_aterms (fn t as Free v =>

       if member (op =) vs v then insert (op aconv) t else I | _ => I) tm [];

     val _ = null bads orelse

       error ("Result contains obtained parameters: " ^

         space_implode " " (map (Syntax.string_of_term ctxt) bads));

   in tm end;

 fun eliminate fix_ctxt rule xs As thm =

   let

     val thy = ProofContext.theory_of fix_ctxt;

     val _ = eliminate_term fix_ctxt xs (Thm.full_prop_of thm);

     val _ = ObjectLogic.is_judgment thy (Thm.concl_of thm) orelse

       error "Conclusion in obtained context must be object-logic judgment";

     val ((_, [thm']), ctxt') = Variable.import true [thm] fix_ctxt;

     val prems = Drule.strip_imp_prems (#prop (Thm.crep_thm thm'));

   in

     ((Drule.implies_elim_list thm' (map Thm.assume prems)

         |> Drule.implies_intr_list (map Drule.norm_hhf_cterm As)

         |> Drule.forall_intr_list xs)

       COMP rule)

     |> Drule.implies_intr_list prems

     |> singleton (Variable.export ctxt' fix_ctxt)

   end;

 fun obtain_export ctxt rule xs _ As =

   (eliminate ctxt rule xs As, eliminate_term ctxt xs);

 (** obtain **)

 fun bind_judgment ctxt name =

   let

     val (bind, ctxt') = ProofContext.bind_fixes [name] ctxt;

     val (t as _ $ Free v) = bind (ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name);

   in ((v, t), ctxt') end;

 val thatN = "that";

 local

 fun gen_obtain prep_att prep_vars prep_propp

     name raw_vars raw_asms int state =

   let

     val _ = Proof.assert_forward_or_chain state;

     val thy = Proof.theory_of state;

     val cert = Thm.cterm_of thy;

     val ctxt = Proof.context_of state;

     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];

     (*obtain vars*)

     val (vars, vars_ctxt) = prep_vars raw_vars ctxt;

     val (_, fix_ctxt) = vars_ctxt |> ProofContext.add_fixes vars;

     val xs = map (Name.of_binding o #1) vars;

     (*obtain asms*)

     val (asms_ctxt, proppss) = prep_propp (fix_ctxt, map snd raw_asms);

     val asm_props = maps (map fst) proppss;

     val asms = map fst (Attrib.map_specs (prep_att thy) raw_asms) ~~ proppss;

     val _ = Variable.warn_extra_tfrees fix_ctxt asms_ctxt;

     (*obtain statements*)

     val thesisN = Name.variant xs AutoBind.thesisN;

     val (thesis_var, thesis) = #1 (bind_judgment fix_ctxt thesisN);

     val asm_frees = fold Term.add_frees asm_props [];

     val parms = xs |> map (fn x =>

       let val x' = ProofContext.get_skolem fix_ctxt x

       in (x', the_default propT (AList.lookup (op =) asm_frees x')) end);

     val that_name = if name = "" then thatN else name;

     val that_prop =

       Term.list_all_free (parms, Logic.list_implies (asm_props, thesis))

       |> Library.curry Logic.list_rename_params xs;

     val obtain_prop =

       Logic.list_rename_params ([AutoBind.thesisN],

         Term.list_all_free ([thesis_var], Logic.mk_implies (that_prop, thesis)));

     fun after_qed _ =

       Proof.local_qed (NONE, false)

       #> `Proof.the_fact #-> (fn rule =>

         Proof.fix_i vars

         #> Proof.assm_i (obtain_export fix_ctxt rule (map (cert o Free) parms)) asms);

   in

     state

     |> Proof.enter_forward

     |> Proof.have_i NONE (K I) [(Thm.empty_binding, [(obtain_prop, [])])] int

     |> Proof.proof (SOME Method.succeed_text) |> Seq.hd

     |> Proof.fix_i [(Binding.name thesisN, NONE, NoSyn)]

     |> Proof.assume_i

       [((Binding.name that_name, [ContextRules.intro_query NONE]), [(that_prop, [])])]

     |> `Proof.the_facts

     ||> Proof.chain_facts chain_facts

     ||> Proof.show_i NONE after_qed [(Thm.empty_binding, [(thesis, [])])] false

     |-> Proof.refine_insert

   end;

 in

 val obtain = gen_obtain Attrib.attribute ProofContext.read_vars ProofContext.read_propp;

 val obtain_i = gen_obtain (K I) ProofContext.cert_vars ProofContext.cert_propp;

 end;

 (** tactical result **)

 fun check_result ctxt thesis th =

   (case Thm.prems_of th of

     [prem] =>

       if Thm.concl_of th aconv thesis andalso

         Logic.strip_assums_concl prem aconv thesis then th

       else error ("Guessed a different clause:\n" ^ ProofContext.string_of_thm ctxt th)

   | [] => error "Goal solved -- nothing guessed."

   | _ => error ("Guess split into several cases:\n" ^ ProofContext.string_of_thm ctxt th));

 fun result tac facts ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     val cert = Thm.cterm_of thy;

     val ((thesis_var, thesis), thesis_ctxt) = bind_judgment ctxt AutoBind.thesisN;

     val rule =

       (case SINGLE (Method.insert_tac facts 1 THEN tac thesis_ctxt) (Goal.init (cert thesis)) of

         NONE => raise THM ("Obtain.result: tactic failed", 0, facts)

       | SOME th => check_result ctxt thesis (MetaSimplifier.norm_hhf (Goal.conclude th)));

     val closed_rule = Thm.forall_intr (cert (Free thesis_var)) rule;

     val ((_, [rule']), ctxt') = Variable.import false [closed_rule] ctxt;

     val obtain_rule = Thm.forall_elim (cert (Logic.varify (Free thesis_var))) rule';

     val ((params, stmt), fix_ctxt) = Variable.focus (Thm.cprem_of obtain_rule 1) ctxt';

     val (prems, ctxt'') =

       Assumption.add_assms (obtain_export fix_ctxt obtain_rule params)

         (Drule.strip_imp_prems stmt) fix_ctxt;

   in ((params, prems), ctxt'') end;

 (** guess **)

 local

 fun unify_params vars thesis_var raw_rule ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     val certT = Thm.ctyp_of thy;

     val cert = Thm.cterm_of thy;

     val string_of_typ = Syntax.string_of_typ ctxt;

     val string_of_term = setmp show_types true (Syntax.string_of_term ctxt);

     fun err msg th = error (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th);

     val maxidx = fold (Term.maxidx_typ o snd o fst) vars ~1;

     val rule = Thm.incr_indexes (maxidx + 1) raw_rule;

     val params = RuleCases.strip_params (Logic.nth_prem (1, Thm.prop_of rule));

     val m = length vars;

     val n = length params;

     val _ = m <= n orelse err "More variables than parameters in obtained rule" rule;

     fun unify ((x, T), (y, U)) (tyenv, max) = Sign.typ_unify thy (T, U) (tyenv, max)

       handle Type.TUNIFY =>

         err ("Failed to unify variable " ^

           string_of_term (Free (x, Envir.norm_type tyenv T)) ^ " against parameter " ^

           string_of_term (Syntax.mark_boundT (y, Envir.norm_type tyenv U)) ^ " in") rule;

     val (tyenv, _) = fold unify (map #1 vars ~~ Library.take (m, params))

       (Vartab.empty, Int.max (maxidx, Thm.maxidx_of rule));

     val norm_type = Envir.norm_type tyenv;

     val xs = map (apsnd norm_type o fst) vars;

     val ys = map (apsnd norm_type) (Library.drop (m, params));

     val ys' = map Name.internal (Name.variant_list (map fst xs) (map fst ys)) ~~ map #2 ys;

     val terms = map (Drule.mk_term o cert o Free) (xs @ ys');

     val instT =

       fold (Term.add_tvarsT o #2) params []

       |> map (TVar #> (fn T => (certT T, certT (norm_type T))));

     val closed_rule = rule

       |> Thm.forall_intr (cert (Free thesis_var))

       |> Thm.instantiate (instT, []);

     val ((_, rule' :: terms'), ctxt') = Variable.import false (closed_rule :: terms) ctxt;

     val vars' =

       map (dest_Free o Thm.term_of o Drule.dest_term) terms' ~~

       (map snd vars @ replicate (length ys) NoSyn);

     val rule'' = Thm.forall_elim (cert (Logic.varify (Free thesis_var))) rule';

   in ((vars', rule''), ctxt') end;

 fun inferred_type (binding, _, mx) ctxt =

   let

     val x = Name.of_binding binding;

     val (T, ctxt') = ProofContext.inferred_param x ctxt

   in ((x, T, mx), ctxt') end;

 fun polymorphic ctxt vars =

   let val Ts = map Logic.dest_type (Variable.polymorphic ctxt (map (Logic.mk_type o #2) vars))

   in map2 (fn (x, _, mx) => fn T => ((x, T), mx)) vars Ts end;

 fun gen_guess prep_vars raw_vars int state =

   let

     val _ = Proof.assert_forward_or_chain state;

     val thy = Proof.theory_of state;

     val cert = Thm.cterm_of thy;

     val ctxt = Proof.context_of state;

     val chain_facts = if can Proof.assert_chain state then Proof.the_facts state else [];

     val (thesis_var, thesis) = #1 (bind_judgment ctxt AutoBind.thesisN);

     val vars = ctxt |> prep_vars raw_vars |-> fold_map inferred_type |> fst |> polymorphic ctxt;

     fun guess_context raw_rule state' =

       let

         val ((parms, rule), ctxt') =

           unify_params vars thesis_var raw_rule (Proof.context_of state');

         val (bind, _) = ProofContext.bind_fixes (map (#1 o #1) parms) ctxt';

         val ts = map (bind o Free o #1) parms;

         val ps = map dest_Free ts;

         val asms =

           Logic.strip_assums_hyp (Logic.nth_prem (1, Thm.prop_of rule))

           |> map (fn asm => (Term.betapplys (Term.list_abs (ps, asm), ts), []));

         val _ = not (null asms) orelse error "Trivial result -- nothing guessed";

       in

         state'

         |> Proof.map_context (K ctxt')

         |> Proof.fix_i (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) parms)

         |> `Proof.context_of |-> (fn fix_ctxt => Proof.assm_i

           (obtain_export fix_ctxt rule (map cert ts)) [(Thm.empty_binding, asms)])

         |> Proof.bind_terms AutoBind.no_facts

       end;

     val goal = Var (("guess", 0), propT);

     fun print_result ctxt' (k, [(s, [_, th])]) =

       ProofDisplay.print_results int ctxt' (k, [(s, [th])]);

     val before_qed = SOME (Method.primitive_text (Goal.conclude #> MetaSimplifier.norm_hhf #>

         (fn th => Goal.protect (Conjunction.intr (Drule.mk_term (Thm.cprop_of th)) th))));

     fun after_qed [[_, res]] =

       Proof.end_block #> guess_context (check_result ctxt thesis res);

   in

     state

     |> Proof.enter_forward

     |> Proof.begin_block

     |> Proof.fix_i [(Binding.name AutoBind.thesisN, NONE, NoSyn)]

     |> Proof.chain_facts chain_facts

     |> Proof.local_goal print_result (K I) (apsnd (rpair I))

       "guess" before_qed after_qed [(Thm.empty_binding, [Logic.mk_term goal, goal])]

     |> Proof.refine (Method.primitive_text (K (Goal.init (cert thesis)))) |> Seq.hd

   end;

 in

 val guess = gen_guess ProofContext.read_vars;

 val guess_i = gen_guess ProofContext.cert_vars;

 end;

 end;