(*  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 "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 obtain: string -> (string * string option * mixfix) list ->

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

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

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

    ((string * attribute list) * (term * term list) list) list

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

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

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

  val statement: (string * ((string * 'typ option) list * 'term list)) list ->

    (('typ, 'term, 'fact) Element.ctxt list *

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

    (((string * Attrib.src list) * (term * term list) list) list -> Proof.context ->

      (((string * Attrib.src list) * (term * term list) list) list * thm list) * Proof.context)

end;

structure Obtain: OBTAIN =

struct

(** obtain_export **)

(*

  [x, A x]

     :

     B

  --------

     B

*)

fun obtain_export ctxt parms rule cprops thm =

  let

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

    val concl = Logic.strip_assums_concl prop;

    val bads = Term.fold_aterms (fn v as Free (x, _) =>

      if member (op =) parms x then insert (op aconv) v else I | _ => I) concl [];

    val thm' = thm |> Drule.implies_intr_protected cprops |> Drule.generalize ([], parms);

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

  in

    if not (null bads) then

      error ("Conclusion contains obtained parameters: " ^

        space_implode " " (map (ProofContext.string_of_term ctxt) bads))

    else if not (ObjectLogic.is_judgment thy concl) then

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

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

  end;

(** obtain **)

fun bind_judgment ctxt name =

  let

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

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

  in (v, t) 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 ctxt = Proof.context_of state;

    val thy = Proof.theory_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_i vars;

    val xs = map #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 = 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 parms =

      map_filter (fn (SOME (Free a), x) => SOME (a, x) | _ => NONE) (map occs_var xs ~~ xs);

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

    val that_prop =

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

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

    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 (map2 (fn x => fn (_, T, mx) => (x, T, mx)) xs vars)

        #> Proof.assm_i (K (obtain_export ctxt (map (#1 o #1) 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, NoSyn)]

    |> Proof.assume_i [((that_name, [ContextRules.intro_query NONE]), [(that_prop, [])])]

    |> `Proof.the_facts

    ||> Proof.chain_facts chain_facts

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

(** guess **)

local

fun unify_params vars thesis_name 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 = ProofContext.string_of_typ ctxt;

    val string_of_term = setmp show_types true (ProofContext.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 Term.internal (Term.variantlist (map fst ys, map fst xs)) ~~ 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 (rule' :: terms', ctxt') =

      Variable.import false (Thm.instantiate (instT, []) 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'' = Drule.generalize ([], [thesis_name]) rule';

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

fun inferred_type (x, _, mx) ctxt =

  let 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 ctxt = Proof.context_of state;

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

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

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

    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 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 guess_context raw_rule state' =

      let

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

          unify_params vars thesis_name 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) => (x, SOME T, mx)) parms)

        |> Proof.assm_i (K (obtain_export ctxt' (map #1 ps) rule)) [(("", []), asms)]

        |> Proof.add_binds_i 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 #> (fn th =>

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

    fun after_qed [[_, res]] =

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

  in

    state

    |> Proof.enter_forward

    |> Proof.begin_block

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

    |> Proof.chain_facts chain_facts

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

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

    |> 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;

(** statements with several cases **)

fun statement cases =

  let

    val names =

      cases |> map_index (fn (i, ("", _)) => string_of_int (i + 1) | (_, (name, _)) => name);

    val elems = cases |> map (fn (_, (vars, _)) =>

      Element.Constrains (vars |> map_filter (fn (x, SOME T) => SOME (x, T) | _ => NONE)));

    val concl = cases |> map (fn (_, (_, props)) => (("", []), map (rpair []) props));

    fun mk_stmt stmt ctxt =

      let

        val thesis =

          ObjectLogic.fixed_judgment (ProofContext.theory_of ctxt) AutoBind.thesisN;

        val atts = map Attrib.internal

          [RuleCases.consumes (~ (length cases)), RuleCases.case_names names];

        fun assume_case ((name, (vars, _)), (_, propp)) ctxt' =

          let

            val xs = map fst vars;

            val props = map fst propp;

            val (parms, ctxt'') =

              ctxt'

              |> fold Variable.declare_term props

              |> fold_map ProofContext.inferred_param xs;

            val asm = Term.list_all_free (parms, Logic.list_implies (props, thesis));

          in

            ctxt' |> (snd o ProofContext.add_fixes_i (map (fn x => (x, NONE, NoSyn)) xs));

            ctxt' |> ProofContext.add_assms_i ProofContext.assume_export

              [((name, [ContextRules.intro_query NONE]), [(asm, [])])]

            |>> (fn [(_, [th])] => th)

          end;

        val (ths, ctxt') = ctxt

          |> (snd o ProofContext.add_fixes_i [(AutoBind.thesisN, NONE, NoSyn)])

          |> fold_map assume_case (cases ~~ stmt)

          |-> (fn ths => ProofContext.note_thmss_i [((thatN, []), [(ths, [])])] #> #2 #> pair ths);

      in (([(("", atts), [(thesis, [])])], ths), ctxt') end;

  in ((elems, concl), mk_stmt) end;

end;