(*  Title:      Pure/Isar/obtain.ML

    ID:         $Id$

    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 "P x" <proof> ==

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

  proof succeed

    fix thesis

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

    <chain_facts> show thesis <proof (insert that)>

  qed

  fix x assm (obtained) "P x"

  <chain_facts>

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

  {

    fix thesis

    <chain_facts> have "PROP ?guess"

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

      <proof body>

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

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

      <proof end>

  }

  fix x assm (obtained) "P x"

*)

signature OBTAIN =

sig

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

    ((string * Attrib.src list) * (string * (string list * string list)) list) list

    -> bool -> Proof.state -> Proof.state

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

    ((string * Proof.context attribute list) * (term * (term list * term list)) list) list

    -> bool -> Proof.state -> Proof.state

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

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

end;

structure Obtain: OBTAIN =

struct

(** export_obtained **)

fun export_obtained state parms rule cprops thm =

  let

    val {thy, prop, maxidx, ...} = Thm.rep_thm thm;

    val cparms = map (Thm.cterm_of thy) parms;

    val thm' = thm

      |> Drule.implies_intr_protected cprops

      |> Drule.forall_intr_list cparms

      |> Drule.forall_elim_vars (maxidx + 1);

    val elim_tacs = replicate (length cprops) (Tactic.etac Drule.protectI);

    val concl = Logic.strip_assums_concl prop;

    val bads = parms inter (Term.term_frees concl);

  in

    if not (null bads) then

      raise Proof.STATE ("Conclusion contains obtained parameters: " ^

        space_implode " " (map (ProofContext.string_of_term (Proof.context_of state)) bads), state)

    else if not (ObjectLogic.is_judgment thy concl) then

      raise Proof.STATE ("Conclusion in obtained context must be object-logic judgments", state)

    else (Tactic.rtac thm' THEN' RANGE elim_tacs) 1 rule

  end;

(** obtain **)

fun bind_judgment ctxt name =

  let val (t as _ $ Free v) =

    ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) name

    |> ProofContext.bind_skolem ctxt [name]

  in (v, t) end;

local

val thatN = "that";

fun gen_obtain prep_att prep_vars prep_propp raw_vars raw_asms int state =

  let

    val _ = Proof.assert_forward_or_chain state;

    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) = fold_map prep_vars raw_vars ctxt;

    val fix_ctxt = vars_ctxt |> ProofContext.fix_i vars;

    val xs = List.concat (map fst vars);

    (*obtain asms*)

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

    val asm_props = List.concat (map (map fst) proppss);

    val asms = map fst (Attrib.map_specs (prep_att (Proof.theory_of state)) raw_asms) ~~ proppss;

    val _ = ProofContext.warn_extra_tfrees fix_ctxt asms_ctxt;

    (*obtain statements*)

    val thesisN = Term.variant xs AutoBind.thesisN;

    val (thesis_var, thesis) = bind_judgment fix_ctxt thesisN;

    fun occs_var x = Library.get_first (fn t =>

      Term.find_free t (ProofContext.get_skolem fix_ctxt x)) asm_props;

    val raw_parms = map occs_var xs;

    val parms = List.mapPartial I raw_parms;

    val parm_names =

      List.mapPartial (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (raw_parms ~~ xs);

    val that_prop =

      Term.list_all_free (map #1 parm_names, Logic.list_implies (asm_props, thesis))

      |> Library.curry Logic.list_rename_params (map #2 parm_names);

    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)

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

        Proof.fix_i vars

        #> Proof.assm_i (K (export_obtained state parms rule)) asms));

  in

    state

    |> Proof.enter_forward

    |> Proof.have_i NONE (K Seq.single) [(("", []), [(obtain_prop, ([], []))])] int

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

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

    |> Proof.assume_i [((thatN, [ContextRules.intro_query_local NONE]), [(that_prop, ([], []))])]

    |> `Proof.the_facts

    ||> Proof.chain_facts chain_facts

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

    |-> (Proof.refine o Method.Basic o K o Method.insert) |> Seq.hd

  end;

in

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

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

end;

(** guess **)

local

fun match_params state vars rule =

  let

    val ctxt = Proof.context_of state;

    val thy = Proof.theory_of state;

    val string_of_typ = ProofContext.string_of_typ ctxt;

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

    fun err msg th = raise Proof.STATE (msg ^ ":\n" ^ ProofContext.string_of_thm ctxt th, state);

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

    val m = length vars;

    val n = length params;

    val _ = conditional (m > n)

      (fn () => err "More variables than parameters in obtained rule" rule);

    fun match ((x, SOME T), (y, U)) tyenv =

        ((x, T), Sign.typ_match thy (U, T) tyenv handle Type.TYPE_MATCH =>

          err ("Failed to match variable " ^

            string_of_term (Free (x, T)) ^ " against parameter " ^

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

      | match ((x, NONE), (_, U)) tyenv = ((x, U), tyenv);

    val (xs, tyenv) = fold_map match (vars ~~ Library.take (m, params)) Vartab.empty;

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

    val norm_type = Envir.norm_type tyenv;

    val xs' = xs |> map (apsnd norm_type);

    val ys' =

      map Syntax.internal (Term.variantlist (map fst ys, map fst xs)) ~~

      map (norm_type o snd) ys;

    val instT =

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

      |> map (TVar #> (fn T => (Thm.ctyp_of thy T, Thm.ctyp_of thy (norm_type T))));

    val rule' = rule |> Thm.instantiate (instT, []);

    val tvars = Drule.tvars_of rule';

    val vars = fold (remove op =) (Term.add_vars (Thm.concl_of rule') []) (Drule.vars_of rule');

    val _ =

      if null tvars andalso null vars then ()

      else err ("Illegal schematic variable(s) " ^

        commas (map (string_of_typ o TVar) tvars @ map (string_of_term o Var) vars) ^ " in") rule';

  in (xs' @ ys', rule') 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 ctxt = Proof.context_of state;

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

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

    val varss = #1 (fold_map prep_vars raw_vars ctxt);

    val vars = List.concat (map (fn (xs, T) => map (rpair T) xs) varss);

    fun check_result th =

      (case Thm.prems_of th of

        [prem] =>

          if Thm.concl_of th aconv thesis andalso

            Logic.strip_assums_concl prem aconv thesis then ()

          else raise Proof.STATE ("Guessed a different clause:\n" ^

            ProofContext.string_of_thm ctxt th, state)

      | [] => raise Proof.STATE ("Goal solved -- nothing guessed.", state)

      | _ => raise Proof.STATE ("Guess split into several cases:\n" ^

        ProofContext.string_of_thm ctxt th, state));

    fun guess_context raw_rule =

      let

        val (parms, rule) = match_params state vars raw_rule;

        val ts = map (ProofContext.bind_skolem ctxt (map #1 parms) o Free) parms;

        val ps = map dest_Free ts;

        val asms =

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

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

        val _ = conditional (null asms) (fn () =>

          raise Proof.STATE ("Trivial result -- nothing guessed", state));

      in

        Proof.fix_i (map (fn (x, T) => ([x], SOME T)) parms)

        #> Proof.assm_i (K (export_obtained state ts rule)) [(("", []), asms)]

        #> Proof.add_binds_i AutoBind.no_facts

      end;

    val before_qed = SOME (Method.primitive_text (Goal.conclude #> Goal.protect));

    fun after_qed [[res]] =

      (check_result res; Proof.end_block #> Seq.map (`Proof.the_fact #-> guess_context));

  in

    state

    |> Proof.enter_forward

    |> Proof.begin_block

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

    |> Proof.chain_facts chain_facts

    |> Proof.local_goal (ProofDisplay.print_results int) (K I) (apsnd (rpair I))

      "guess" before_qed after_qed [(("", []), [Var (("guess", 0), propT)])]

    |> Proof.refine (Method.primitive_text (K (Goal.init (Thm.cterm_of thy thesis)))) |> Seq.hd

  end;

in

val guess = gen_guess ProofContext.read_vars;

val guess_i = gen_guess ProofContext.cert_vars;

end;

end;