(*  Title:      Pure/Isar/proof.ML

    Author:     Markus Wenzel, TU Muenchen

The Isar/VM proof language interpreter: maintains a structured flow of

context elements, goals, refinements, and facts.

*)

signature PROOF =

sig

  type context = Proof.context

  type method = Method.method

  type state

  val init: context -> state

  val level: state -> int

  val assert_bottom: bool -> state -> state

  val context_of: state -> context

  val theory_of: state -> theory

  val map_context: (context -> context) -> state -> state

  val map_context_result : (context -> 'a * context) -> state -> 'a * state

  val map_contexts: (context -> context) -> state -> state

  val propagate_ml_env: state -> state

  val report_improper: state -> unit

  val the_facts: state -> thm list

  val the_fact: state -> thm

  val set_facts: thm list -> state -> state

  val reset_facts: state -> state

  val improper_reset_facts: state -> state

  val assert_forward: state -> state

  val assert_chain: state -> state

  val assert_forward_or_chain: state -> state

  val assert_backward: state -> state

  val assert_no_chain: state -> state

  val enter_forward: state -> state

  val enter_chain: state -> state

  val enter_backward: state -> state

  val using_facts: thm list -> state -> state

  val pretty_state: state -> Pretty.T list

  val refine: Method.text -> state -> state Seq.result Seq.seq

  val refine_end: Method.text -> state -> state Seq.result Seq.seq

  val refine_singleton: Method.text -> state -> state

  val refine_insert: thm list -> state -> state

  val refine_primitive: (Proof.context -> thm -> thm) -> state -> state

  val raw_goal: state -> {context: context, facts: thm list, goal: thm}

  val goal: state -> {context: context, facts: thm list, goal: thm}

  val simple_goal: state -> {context: context, goal: thm}

  val let_bind: (term list * term) list -> state -> state

  val let_bind_cmd: (string list * string) list -> state -> state

  val write: Syntax.mode -> (term * mixfix) list -> state -> state

  val write_cmd: Syntax.mode -> (string * mixfix) list -> state -> state

  val fix: (binding * typ option * mixfix) list -> state -> state

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

  val assm: Assumption.export -> (binding * typ option * mixfix) list ->

    (term * term list) list list -> (Thm.binding * (term * term list) list) list ->

    state -> state

  val assm_cmd: Assumption.export -> (binding * string option * mixfix) list ->

    (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->

    state -> state

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

    (term * term list) list list -> (Thm.binding * (term * term list) list) list ->

    state -> state

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

    (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->

    state -> state

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

    (term * term list) list list -> (Thm.binding * (term * term list) list) list ->

    state -> state

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

    (string * string list) list list -> (Attrib.binding * (string * string list) list) list ->

    state -> state

  val chain: state -> state

  val chain_facts: thm list -> state -> state

  val note_thmss: (Thm.binding * (thm list * attribute list) list) list -> state -> state

  val note_thmss_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state

  val from_thmss: ((thm list * attribute list) list) list -> state -> state

  val from_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state

  val with_thmss: ((thm list * attribute list) list) list -> state -> state

  val with_thmss_cmd: ((Facts.ref * Token.src list) list) list -> state -> state

  val supply: (Thm.binding * (thm list * attribute list) list) list -> state -> state

  val supply_cmd: (Attrib.binding * (Facts.ref * Token.src list) list) list -> state -> state

  val using: ((thm list * attribute list) list) list -> state -> state

  val using_cmd: ((Facts.ref * Token.src list) list) list -> state -> state

  val unfolding: ((thm list * attribute list) list) list -> state -> state

  val unfolding_cmd: ((Facts.ref * Token.src list) list) list -> state -> state

  val case_: Thm.binding * ((string * Position.T) * binding option list) -> state -> state

  val case_cmd: Attrib.binding * ((string * Position.T) * binding option list) -> state -> state

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

    (binding * typ option * mixfix) list ->

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

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

    (binding * string option * mixfix) list ->

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

  val begin_block: state -> state

  val next_block: state -> state

  val end_block: state -> state

  val begin_notepad: context -> state

  val end_notepad: state -> context

  val is_notepad: state -> bool

  val reset_notepad: state -> state

  val proof: Method.text_range option -> state -> state Seq.result Seq.seq

  val defer: int -> state -> state

  val prefer: int -> state -> state

  val apply: Method.text_range -> state -> state Seq.result Seq.seq

  val apply_end: Method.text_range -> state -> state Seq.result Seq.seq

  val local_qed: Method.text_range option * bool -> state -> state

  val theorem: Method.text option -> (thm list list -> context -> context) ->

    (term * term list) list list -> context -> state

  val theorem_cmd: Method.text option -> (thm list list -> context -> context) ->

    (string * string list) list list -> context -> state

  val global_qed: Method.text_range option * bool -> state -> context

  val schematic_goal: state -> bool

  val is_relevant: state -> bool

  val local_terminal_proof: Method.text_range * Method.text_range option -> state -> state

  val local_default_proof: state -> state

  val local_immediate_proof: state -> state

  val local_skip_proof: bool -> state -> state

  val local_done_proof: state -> state

  val global_terminal_proof: Method.text_range * Method.text_range option -> state -> context

  val global_default_proof: state -> context

  val global_immediate_proof: state -> context

  val global_skip_proof: bool -> state -> context

  val global_done_proof: state -> context

  val internal_goal: (context -> (string * string) * (string * thm list) list -> unit) ->

    Proof_Context.mode -> bool -> string -> Method.text option ->

    (context * thm list list -> state -> state) ->

    (binding * typ option * mixfix) list ->

    (Thm.binding * (term * term list) list) list ->

    (Thm.binding * (term * term list) list) list -> state -> thm list * state

  val have: bool -> Method.text option -> (context * thm list list -> state -> state) ->

    (binding * typ option * mixfix) list ->

    (Thm.binding * (term * term list) list) list ->

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

  val have_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->

    (binding * string option * mixfix) list ->

    (Attrib.binding * (string * string list) list) list ->

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

  val show: bool -> Method.text option -> (context * thm list list -> state -> state) ->

    (binding * typ option * mixfix) list ->

    (Thm.binding * (term * term list) list) list ->

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

  val show_cmd: bool -> Method.text option -> (context * thm list list -> state -> state) ->

    (binding * string option * mixfix) list ->

    (Attrib.binding * (string * string list) list) list ->

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

  val future_proof: (state -> ('a * context) future) -> state -> 'a future * state

  val local_future_terminal_proof: Method.text_range * Method.text_range option -> state -> state

  val global_future_terminal_proof: Method.text_range * Method.text_range option -> state -> context

end;

structure Proof(**): PROOF(**) =

struct

type context = Proof.context;

type method = Method.method;

(** proof state **)

(* datatype state *)

datatype mode = Forward | Chain | Backward;

datatype state =

  State of node Stack.T

and node =

  Node of

   {context: context,

    facts: (thm list * bool) option,

    mode: mode,

    goal: goal option}

and goal =

  Goal of

   {statement: (string * Position.T) * term list list * term,

      (*goal kind and statement (starting with vars), initial proposition*)

    using: thm list,                      (*goal facts*)

    goal: thm,                            (*subgoals \<Longrightarrow> statement*)

    before_qed: Method.text option,

    after_qed:

      (context * thm list list -> state -> state) *

      (context * thm list list -> context -> context)};

val _ =

  ML_system_pp (fn _ => fn _ => fn _: state =>

    Pretty.to_polyml (Pretty.str "<Proof.state>"));

fun make_goal (statement, using, goal, before_qed, after_qed) =

  Goal {statement = statement, using = using, goal = goal,

    before_qed = before_qed, after_qed = after_qed};

fun make_node (context, facts, mode, goal) =

  Node {context = context, facts = facts, mode = mode, goal = goal};

fun map_node f (Node {context, facts, mode, goal}) =

  make_node (f (context, facts, mode, goal));

val init_context =

  Proof_Context.set_stmt true #>

  Proof_Context.map_naming (K Name_Space.local_naming);

fun init ctxt =

  State (Stack.init (make_node (init_context ctxt, NONE, Forward, NONE)));

fun top (State stack) = Stack.top stack |> (fn Node node => node);

fun map_top f (State stack) = State (Stack.map_top (map_node f) stack);

fun map_all f (State stack) = State (Stack.map_all (map_node f) stack);

(** basic proof state operations **)

(* block structure *)

fun open_block (State stack) = State (Stack.push stack);

fun close_block (State stack) = State (Stack.pop stack)

  handle List.Empty => error "Unbalanced block parentheses";

fun level (State stack) = Stack.level stack;

fun assert_bottom b state =

  let val b' = level state <= 2 in

    if b andalso not b' then error "Not at bottom of proof"

    else if not b andalso b' then error "Already at bottom of proof"

    else state

  end;

(* context *)

val context_of = #context o top;

val theory_of = Proof_Context.theory_of o context_of;

fun map_context f =

  map_top (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));

fun map_context_result f state =

  f (context_of state) ||> (fn ctxt => map_context (K ctxt) state);

fun map_contexts f = map_all (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal));

fun propagate_ml_env state = map_contexts

  (Context.proof_map (ML_Env.inherit [Context.Proof (context_of state)])) state;

(* facts *)

fun report_improper state =

  Context_Position.report (context_of state) (Position.thread_data ()) Markup.improper;

val get_facts = #facts o top;

fun the_facts state =

  (case get_facts state of

    SOME (facts, proper) => (if proper then () else report_improper state; facts)

  | NONE => error "No current facts available");

fun the_fact state =

  (case the_facts state of

    [thm] => thm

  | _ => error "Single theorem expected");

fun put_facts index facts =

  map_top (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) #>

  map_context (Proof_Context.put_thms index (Auto_Bind.thisN, Option.map #1 facts));

fun set_facts thms = put_facts false (SOME (thms, true));

val reset_facts = put_facts false NONE;

fun improper_reset_facts state =

  (case get_facts state of

    SOME (thms, _) => put_facts false (SOME (thms, false)) state

  | NONE => state);

fun these_factss more_facts (named_factss, state) =

  (named_factss, state |> set_facts (maps snd named_factss @ more_facts));

fun export_facts inner outer =

  (case get_facts inner of

    NONE => reset_facts outer

  | SOME (thms, proper) =>

      let val thms' = Proof_Context.export (context_of inner) (context_of outer) thms

      in put_facts true (SOME (thms', proper)) outer end);

(* mode *)

val get_mode = #mode o top;

fun put_mode mode = map_top (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal));

val mode_name = (fn Forward => "state" | Chain => "chain" | Backward => "prove");

fun assert_mode pred state =

  let val mode = get_mode state in

    if pred mode then state

    else error ("Illegal application of proof command in " ^ quote (mode_name mode) ^ " mode")

  end;

val assert_forward = assert_mode (fn mode => mode = Forward);

val assert_chain = assert_mode (fn mode => mode = Chain);

val assert_forward_or_chain = assert_mode (fn mode => mode = Forward orelse mode = Chain);

val assert_backward = assert_mode (fn mode => mode = Backward);

val assert_no_chain = assert_mode (fn mode => mode <> Chain);

val enter_forward = put_mode Forward;

val enter_chain = put_mode Chain;

val enter_backward = put_mode Backward;

(* current goal *)

fun current_goal state =

  (case top state of

    {context = ctxt, goal = SOME (Goal goal), ...} => (ctxt, goal)

  | _ => error "No current goal");

fun assert_current_goal g state =

  let val g' = can current_goal state in

    if g andalso not g' then error "No goal in this block"

    else if not g andalso g' then error "Goal present in this block"

    else state

  end;

fun put_goal goal = map_top (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal));

val set_goal = put_goal o SOME;

val reset_goal = put_goal NONE;

val before_qed = #before_qed o #2 o current_goal;

(* nested goal *)

fun map_goal f (State stack) =

  (case Stack.dest stack of

    (Node {context = ctxt, facts, mode, goal = SOME goal}, node :: nodes) =>

      let

        val Goal {statement, using, goal, before_qed, after_qed} = goal;

        val (ctxt', statement', using', goal', before_qed', after_qed') =

          f (ctxt, statement, using, goal, before_qed, after_qed);

        val goal' = make_goal (statement', using', goal', before_qed', after_qed');

      in State (Stack.make (make_node (ctxt', facts, mode, SOME goal')) (node :: nodes)) end

  | (top_node, node :: nodes) =>

      let

        val State stack' = map_goal f (State (Stack.make node nodes));

        val (node', nodes') = Stack.dest stack';

      in State (Stack.make top_node (node' :: nodes')) end

  | _ => State stack);

fun provide_goal goal =

  map_goal (fn (ctxt, statement, using, _, before_qed, after_qed) =>

    (ctxt, statement, using, goal, before_qed, after_qed));

fun using_facts using =

  map_goal (fn (ctxt, statement, _, goal, before_qed, after_qed) =>

    (ctxt, statement, using, goal, before_qed, after_qed));

fun find_goal state =

  (case try current_goal state of

    SOME ctxt_goal => ctxt_goal

  | NONE => find_goal (close_block state handle ERROR _ => error "No proof goal"));

fun get_goal state =

  let val (ctxt, {using, goal, ...}) = find_goal state

  in (ctxt, (using, goal)) end;

(** pretty_state **)

(*1*)local(*1*)

fun pretty_facts _ _ NONE = []

  | pretty_facts ctxt s (SOME ths) = [Proof_Display.pretty_goal_facts ctxt s ths];

fun pretty_sep prts [] = prts

  | pretty_sep [] prts = prts

  | pretty_sep prts1 prts2 = prts1 @ [Pretty.str ""] @ prts2;

(*1*)in(*1*)

fun pretty_state state =

  let

    val {context = ctxt, facts, mode, goal = _} = top state;

    val verbose = Config.get ctxt Proof_Context.verbose;

    fun prt_goal (SOME (_, {statement = _, using, goal, before_qed = _, after_qed = _})) =

          pretty_sep

            (pretty_facts ctxt "using"

              (if mode <> Backward orelse null using then NONE else SOME using))

            ([Proof_Display.pretty_goal_header goal] @ Goal_Display.pretty_goals ctxt goal)

      | prt_goal NONE = [];

    val prt_ctxt =

      if verbose orelse mode = Forward then Proof_Context.pretty_context ctxt

      else if mode = Backward then Proof_Context.pretty_ctxt ctxt

      else [];

    val position_markup = Position.markup (Position.thread_data ()) Markup.position;

(** )val _ = @{print} {a = "### Proof.pretty_state:"};( *..NOT yet available*)

(** )val _ = writeln "### Proof.pretty_state:";( **)

  in

    [Pretty.block

      [Pretty.mark_str (position_markup, "proof"), Pretty.str (" (" ^ mode_name mode ^ ")")]] @

    (if null prt_ctxt then [] else prt_ctxt @ [Pretty.str ""]) @

    (if verbose orelse mode = Forward then

       pretty_sep (pretty_facts ctxt "" (Option.map #1 facts)) (prt_goal (try find_goal state))

     else if mode = Chain then pretty_facts ctxt "picking" (Option.map #1 facts)

     else prt_goal (try find_goal state))

  end;

(*1*)end;(*1*)

(** proof steps **)

(* refine via method *)

(*2*)local(*2*)

fun apply_method text ctxt state =

  find_goal state |> (fn (goal_ctxt, {statement, using, goal, before_qed, after_qed}) =>

    Method.evaluate text ctxt using (goal_ctxt, goal)

    |> Seq.map_result (fn (goal_ctxt', goal') =>

        state |> map_goal (K (goal_ctxt', statement, using, goal', before_qed, after_qed))));

(*2*)in(*2*)

fun refine text state = apply_method text (context_of state) state;

fun refine_end text state = apply_method text (#1 (find_goal state)) state;

fun refine_singleton text = refine text #> Seq.the_result "";

fun refine_insert ths =

  refine_singleton (Method.Basic (K (Method.insert ths)));

fun refine_primitive r =

  refine_singleton (Method.Basic (fn ctxt => fn _ => CONTEXT_TACTIC (PRIMITIVE (r ctxt))));

(*2*)end;(*2*)

(* refine via sub-proof *)

(*3*)local(*3*)

fun finish_tac _ 0 = K all_tac

  | finish_tac ctxt n =

      Goal.norm_hhf_tac ctxt THEN'

      SUBGOAL (fn (goal, i) =>

        if can Logic.unprotect (Logic.strip_assums_concl goal) then

          eresolve_tac ctxt [Drule.protectI] i THEN finish_tac ctxt (n - 1) i

        else finish_tac ctxt (n - 1) (i + 1));

fun goal_tac ctxt rule =

  Goal.norm_hhf_tac ctxt THEN'

  resolve_tac ctxt [rule] THEN'

  finish_tac ctxt (Thm.nprems_of rule);

fun FINDGOAL tac st =

  let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)

  in find 1 (Thm.nprems_of st) st end;

fun protect_prem i th =

  Thm.bicompose NONE {flatten = false, match = false, incremented = true}

    (false, Drule.incr_indexes th Drule.protectD, 1) i th

  |> Seq.hd;

fun protect_prems th =

  fold_rev protect_prem (1 upto Thm.nprems_of th) th;

(*3*)in(*3*)

fun refine_goals print_rule result_ctxt result state =

  let

    val (goal_ctxt, (_, goal)) = get_goal state;

    fun refine rule st =

      (print_rule goal_ctxt rule; FINDGOAL (goal_tac goal_ctxt rule) st);

  in

    result

    |> map (Raw_Simplifier.norm_hhf result_ctxt #> protect_prems)

    |> Proof_Context.goal_export result_ctxt goal_ctxt

    |> (fn rules => Seq.lift provide_goal (EVERY (map refine rules) goal) state)

  end;

(*3*)end;(*3*)

(* conclude goal *)

fun conclude_goal ctxt goal propss =

  let

    val thy = Proof_Context.theory_of ctxt;

    val _ =

      Context.subthy_id (Thm.theory_id goal, Context.theory_id thy) orelse

        error "Bad background theory of goal state";

    val _ = Thm.no_prems goal orelse error (Proof_Display.string_of_goal ctxt goal);

    fun err_lost () = error ("Lost goal structure:\n" ^ Thm.string_of_thm ctxt goal);

    val th =

      (Goal.conclude (Thm.close_derivation \<^here> goal) handle THM _ => err_lost ())

      |> Drule.flexflex_unique (SOME ctxt)

      |> Thm.check_shyps ctxt

      |> Thm.check_hyps (Context.Proof ctxt);

    val goal_propss = filter_out null propss;

    val results =

      Conjunction.elim_balanced (length goal_propss) th

      |> map2 Conjunction.elim_balanced (map length goal_propss)

      handle THM _ => err_lost ();

    val _ =

      Unify.matches_list (Context.Proof ctxt)

        (map (Soft_Type_System.purge ctxt) (flat goal_propss)) (map Thm.prop_of (flat results))

        orelse error ("Proved a different theorem:\n" ^ Thm.string_of_thm ctxt th);

    fun recover_result ([] :: pss) thss = [] :: recover_result pss thss

      | recover_result (_ :: pss) (ths :: thss) = ths :: recover_result pss thss

      | recover_result [] [] = []

      | recover_result _ _ = err_lost ();

  in recover_result propss results end;

val finished_goal_error = "Failed to finish proof";

fun finished_goal pos state =

  let val (ctxt, (_, goal)) = get_goal state in

    if Thm.no_prems goal then Seq.Result state

    else

      Seq.Error (fn () =>

        finished_goal_error ^ Position.here pos ^ ":\n" ^

          Proof_Display.string_of_goal ctxt goal)

  end;

(* goal views -- corresponding to methods *)

fun raw_goal state =

  let val (ctxt, (using, goal)) = get_goal state

  in {context = ctxt, facts = using, goal = goal} end;

val goal = raw_goal o refine_insert [];

fun simple_goal state =

  let

    val (_, (using, _)) = get_goal state;

    val (ctxt, (_, goal)) = get_goal (refine_insert using state);

  in {context = ctxt, goal = goal} end;

fun method_error kind pos state =

  Seq.single (Proof_Display.method_error kind pos (raw_goal state));

(*** structured proof commands ***)

(** context elements **)

(* let bindings *)

(*4*)local(*4*)

fun gen_bind prep_terms raw_binds =

  assert_forward #> map_context (fn ctxt =>

    let

      fun prep_bind (raw_pats, t) ctxt1 =

        let

          val T = Term.fastype_of t;

          val ctxt2 = Variable.declare_term t ctxt1;

          val pats = prep_terms (Proof_Context.set_mode Proof_Context.mode_pattern ctxt2) T raw_pats;

          val binds = Proof_Context.simult_matches ctxt2 (t, pats);

        in (binds, ctxt2) end;

      val ts = prep_terms ctxt dummyT (map snd raw_binds);

      val (binds, ctxt') = apfst flat (fold_map prep_bind (map fst raw_binds ~~ ts) ctxt);

      val binds' = map #1 binds ~~ Variable.exportT_terms ctxt' ctxt (map #2 binds);

      val ctxt'' =

        ctxt

        |> fold Variable.declare_term (map #2 binds')

        |> fold Proof_Context.bind_term binds';

      val _ = Variable.warn_extra_tfrees ctxt ctxt'';

    in ctxt'' end)

  #> reset_facts;

(*val read_terms: context -> typ -> string list -> term list*)

fun read_terms ctxt T =

  map (Syntax.parse_term ctxt #> Type.constraint T) #> Syntax.check_terms ctxt;

(*4*)in(*4*)

(*val let_bind: (term list * term) list -> state -> state*)

val let_bind =

  ((** )writeln "#### Proof.let_bind";( **)

    gen_bind (fn ctxt => fn _ => map (Proof_Context.cert_term ctxt)));

(*val let_bind_cmd: (string list * string) list -> state -> state*)

val let_bind_cmd =

  ((** )writeln "#### Proof.let_bind_cmd";( **)

    gen_bind read_terms);

(*4*)end;(*4*)

(* concrete syntax *)

(*5*)local(*5*)

fun read_arg (c, mx) ctxt =

  (case Proof_Context.read_const {proper = false, strict = false} ctxt c of

    Free (x, _) =>

      let

        val ctxt' =

          ctxt |> is_none (Variable.default_type ctxt x) ?

            Variable.declare_constraints (Free (x, Mixfix.default_constraint mx));

        val t = Free (#1 (Proof_Context.inferred_param x ctxt'));

      in ((t, mx), ctxt') end

  | t => ((t, mx), ctxt));

fun gen_write prep_arg mode args =

  assert_forward

  #> map_context (fold_map prep_arg args #-> Proof_Context.notation true mode)

  #> reset_facts;

(*5*)in(*5*)

val write = gen_write pair;

val write_cmd = gen_write read_arg;

(*5*)end;(*5*)

(* fix *)

(*6*)local(*6*)

fun gen_fix add_fixes raw_fixes =

  assert_forward

  #> map_context (snd o add_fixes raw_fixes)

  #> reset_facts;

(*6*)in(*6*)

val fix = gen_fix Proof_Context.add_fixes;

val fix_cmd = gen_fix Proof_Context.add_fixes_cmd;

(*6*)end;(*6*)

(* assume *)

(*7*)local(*7*)

fun gen_assume prep_statement prep_att export raw_fixes raw_prems raw_concls state =

  let

    val ctxt = context_of state;

    val bindings = map (apsnd (map (prep_att ctxt)) o fst) raw_concls;

    val {fixes = params, assumes = prems_propss, shows = concl_propss, result_binds, text, ...} =

      #1 (prep_statement raw_fixes raw_prems (map snd raw_concls) ctxt);

    val propss = (map o map) (Logic.close_prop params (flat prems_propss)) concl_propss;

  in

    state

    |> assert_forward

    |> map_context_result (fn ctxt =>

      ctxt

      |> Proof_Context.augment text

      |> fold Variable.maybe_bind_term result_binds

      |> fold_burrow (Assumption.add_assms export o map (Thm.cterm_of ctxt)) propss

      |-> (fn premss =>

        Proof_Context.note_thmss "" (bindings ~~ (map o map) (fn th => ([th], [])) premss)))

    |> these_factss [] |> #2

  end;

(*7*)in(*7*)

val assm = gen_assume Proof_Context.cert_statement (K I);

val assm_cmd = gen_assume Proof_Context.read_statement Attrib.attribute_cmd;

val assume = assm Assumption.assume_export;

val assume_cmd = assm_cmd Assumption.assume_export;

val presume = assm Assumption.presume_export;

val presume_cmd = assm_cmd Assumption.presume_export;

(*7*)end;(*7*)

(** facts **)

(* chain *)

val chain =

  assert_forward

  #> (fn state => set_facts (Method.clean_facts (the_facts state)) state)

  #> enter_chain;

fun chain_facts facts =

  set_facts facts

  #> chain;

(* note etc. *)

fun empty_bindings args = map (pair Binding.empty_atts) args;

(*8*)local(*8*)

fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =

  state

  |> assert_forward

  |> map_context_result (fn ctxt => ctxt |> Proof_Context.note_thmss ""

    (Attrib.map_facts_refs (map (prep_atts ctxt)) (prep_fact ctxt) args))

  |> these_factss (more_facts state)

  ||> opt_chain

  |> opt_result;

(*8*)in(*8*)

val note_thmss = gen_thmss (K []) I #2 (K I) (K I);

val note_thmss_cmd = gen_thmss (K []) I #2 Attrib.attribute_cmd Proof_Context.get_fact;

val from_thmss = gen_thmss (K []) chain #2 (K I) (K I) o empty_bindings;

val from_thmss =

  ((**)writeln "####-# Proof.from_thmss";(**)

    gen_thmss (K []) chain #2 (K I) (K I) o empty_bindings);

val from_thmss_cmd =

  gen_thmss (K []) chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;

val from_thmss_cmd =

  ((**)writeln "####-# Proof.from_thmss_cmd";(**)

    gen_thmss (K []) chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings);

val with_thmss = gen_thmss the_facts chain #2 (K I) (K I) o empty_bindings;

val with_thmss =

  ((**)writeln "####-# Proof.with_thmss";(**)

    gen_thmss the_facts chain #2 (K I) (K I) o empty_bindings);

val with_thmss_cmd =

  gen_thmss the_facts chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings;

val with_thmss_cmd =

  ((**)writeln "####-# Proof.with_thmss_cmd";(**)

    gen_thmss the_facts chain #2 Attrib.attribute_cmd Proof_Context.get_fact o empty_bindings);

val local_results = gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact);

val local_results =

  (writeln "####-# Proof.local_results";

    gen_thmss (K []) I I (K I) (K I) o map (apsnd Thm.simple_fact));

(*8*)end;(*8*)

(* facts during goal refinement *)

(*9*)local(*9*)

fun gen_supply prep_att prep_fact args state =

  state

  |> assert_backward

  |> map_context (fn ctxt => ctxt |> Proof_Context.note_thmss ""

       (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) args) |> snd);

(*9*)in(*9*)

val supply = gen_supply (K I) (K I);

val supply_cmd = gen_supply Attrib.attribute_cmd Proof_Context.get_fact;

(*9*)end;(*9*)

(* using/unfolding *)

(*10*)local(*10*)

fun gen_using f g prep_att prep_fact args state =

  state

  |> assert_backward

  |> map_context_result

    (fn ctxt => ctxt |> Proof_Context.note_thmss ""

      (Attrib.map_facts_refs (map (prep_att ctxt)) (prep_fact ctxt) (empty_bindings args)))

  |> (fn (named_facts, state') =>

    state' |> map_goal (fn (goal_ctxt, statement, using, goal, before_qed, after_qed) =>

      let

        val ctxt = context_of state';

        val ths = maps snd named_facts;

      in (goal_ctxt, statement, f ctxt ths using, g ctxt ths goal, before_qed, after_qed) end));

fun append_using _ ths using = using @ filter_out Thm.is_dummy ths;

fun unfold_using ctxt ths = map (Local_Defs.unfold ctxt ths);

val unfold_goals = Local_Defs.unfold_goals;

(*10*)in(*10*)

val using = gen_using append_using (K (K I)) (K I) (K I);

val using_cmd = gen_using append_using (K (K I)) Attrib.attribute_cmd Proof_Context.get_fact;

val unfolding = gen_using unfold_using unfold_goals (K I) (K I);

val unfolding_cmd = gen_using unfold_using unfold_goals Attrib.attribute_cmd Proof_Context.get_fact;

(*10*)end;(*10*)

(* case *)

(*11*)local(*11*)

fun gen_case internal prep_att ((raw_binding, raw_atts), ((name, pos), xs)) state =

  let

    val ctxt = context_of state;

    val binding = if Binding.is_empty raw_binding then Binding.make (name, pos) else raw_binding;

    val atts = map (prep_att ctxt) raw_atts;

    val (asms, state') = state |> map_context_result (fn ctxt =>

      ctxt |> Proof_Context.apply_case (Proof_Context.check_case ctxt internal (name, pos) xs));

    val assumptions =

      asms |> map (fn (a, ts) => ((Binding.qualify_name true binding a, []), map (rpair []) ts));

  in

    state'

    |> assume [] [] assumptions

    |> map_context (fold Variable.unbind_term Auto_Bind.no_facts)

    |> `the_facts |-> (fn thms => note_thmss [((binding, atts), [(thms, [])])])

  end;

(*11*)in(*11*)

val case_ = gen_case true (K I);

val case_cmd = gen_case false Attrib.attribute_cmd;

(*11*)end;(*11*)

(* define *)

(*12*)local(*12*)

fun gen_define prep_stmt prep_att raw_decls raw_fixes raw_defs state =

  let

    val _ = writeln "###-# Proof.gen_define";

    val _ = assert_forward state;

    val ctxt = context_of state;

    (*vars*)

    val ({vars, propss, result_binds, ...}, vars_ctxt) =

      prep_stmt (raw_decls @ raw_fixes) (map snd raw_defs) ctxt;

    val (decls, fixes) = chop (length raw_decls) vars;

    val show_term = Syntax.string_of_term vars_ctxt;

    (*defs*)

    fun match_defs (((b, _, mx), (_, Free (x, T))) :: more_decls) ((((y, U), t), _) :: more_defs) =

          if x = y then ((b, mx), (Binding.empty_atts, t)) :: match_defs more_decls more_defs

          else

            error ("Mismatch of declaration " ^ show_term (Free (x, T)) ^ " wrt. definition " ^

              show_term (Free (y, U)))

      | match_defs [] [] = []

      | match_defs more_decls more_defs =

          error ("Mismatch of declarations " ^ commas (map (show_term o #2 o #2) more_decls) ^

            (if null more_decls then "" else " ") ^

            "wrt. definitions " ^ commas (map (show_term o Free o #1 o #1) more_defs));

    val derived_def = Local_Defs.derived_def ctxt (K  []) {conditional = false};

    val defs1 = map (derived_def o Logic.close_prop (map #2 fixes) []) (flat propss);

    val defs2 = match_defs decls defs1;

    val (defs3, defs_ctxt) = Local_Defs.define defs2 ctxt;

    (*notes*)

    val def_thmss =

      map (fn (((_, prove), ((b, _), _)), (_, (_, th))) => (b, prove defs_ctxt th))

        (defs1 ~~ defs2 ~~ defs3)

      |> unflat (map snd raw_defs);

    val notes =

      map2 (fn ((a, raw_atts), _) => fn def_thms =>

        ((Thm.def_binding_optional (Binding.conglomerate (map #1 def_thms)) a,

          map (prep_att defs_ctxt) raw_atts), map (fn (_, th) => ([th], [])) def_thms))

        raw_defs def_thmss;

  in

    state

    |> map_context (K defs_ctxt #> fold Variable.bind_term result_binds)

    |> note_thmss notes

  end;

(*12*)in(*12*)

val define = gen_define Proof_Context.cert_stmt (K I);

val define_cmd = gen_define Proof_Context.read_stmt Attrib.attribute_cmd;

(*12*)end;(*12*)

(** proof structure **)

(* blocks *)

val begin_block =

  assert_forward

  #> open_block

  #> reset_goal

  #> open_block;

val next_block =

  assert_forward

  #> close_block

  #> open_block

  #> reset_goal

  #> reset_facts;

fun end_block state =

  state

  |> assert_forward

  |> assert_bottom false

  |> close_block

  |> assert_current_goal false

  |> close_block

  |> export_facts state;

(* global notepad *)

val begin_notepad =

  init

  #> open_block

  #> map_context (Variable.set_body true)

  #> open_block;

val end_notepad =

  assert_forward

  #> assert_bottom true

  #> close_block

  #> assert_current_goal false

  #> close_block

  #> context_of;

fun get_notepad_context (State stack) =

  let

    fun escape [Node {goal = SOME _, ...}, Node {goal = NONE, ...}] = NONE

      | escape [Node {goal = SOME _, ...}] = NONE

      | escape [Node {goal = NONE, context = ctxt, ...}] = SOME ctxt

      | escape [] = NONE

      | escape (_ :: rest) = escape rest;

  in escape (op :: (Stack.dest stack)) end;

val is_notepad = is_some o get_notepad_context;

fun reset_notepad state =

  begin_notepad (the_default (context_of state) (get_notepad_context state));

(* sub-proofs *)

fun proof opt_text =

  Seq.APPEND

    (assert_backward

      #> refine (the_default Method.standard_text (Method.text opt_text))

      #> Seq.map_result

        (using_facts []

          #> enter_forward

          #> open_block

          #> reset_goal),

     method_error "initial" (Method.position opt_text));

fun end_proof bot (prev_pos, (opt_text, immed)) =

  let

    val (finish_text, terminal_pos, finished_pos) =

      (case opt_text of

        NONE => (Method.finish_text (NONE, immed), Position.none, prev_pos)

      | SOME (text, (pos, end_pos)) => (Method.finish_text (SOME text, immed), pos, end_pos));

  in

    Seq.APPEND (fn state =>

      state

      |> assert_forward

      |> assert_bottom bot

      |> close_block

      |> assert_current_goal true

      |> using_facts []

      |> `before_qed |-> (refine o the_default Method.succeed_text)

      |> Seq.maps_results (refine finish_text),

      method_error "terminal" terminal_pos)

    #> Seq.maps_results (Seq.single o finished_goal finished_pos)

  end;

fun check_result msg sq =

  (case Seq.pull sq of

    NONE => error msg

  | SOME (s, _) => s);

(* unstructured refinement *)

fun defer i =

  assert_no_chain #>

  refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL defer_tac i)));

fun prefer i =

  assert_no_chain #>

  refine_singleton (Method.Basic (fn _ => METHOD (fn _ => ASSERT_SUBGOAL prefer_tac i)));