(*  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_contexts: (context -> context) -> state -> state

   val bind_terms: (indexname * term option) list -> state -> state

   val put_thms: bool -> string * thm list option -> state -> state

   val the_facts: state -> thm list

   val the_fact: state -> thm

   val put_facts: thm list option -> 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 goal_message: (unit -> Pretty.T) -> state -> state

   val show_main_goal: bool Unsynchronized.ref

   val verbose: bool Unsynchronized.ref

   val pretty_state: int -> state -> Pretty.T list

   val pretty_goals: bool -> state -> Pretty.T list

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

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

   val refine_insert: thm list -> state -> state

   val goal_tac: thm -> int -> tactic

   val refine_goals: (context -> thm -> unit) -> context -> thm list -> state -> state Seq.seq

   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 match_bind: (term list * term) list -> state -> state

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

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

   val let_bind_cmd: (string list * string) 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 ->

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

   val assm_cmd: Assumption.export ->

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

   val assume: (Thm.binding * (term * term list) list) list -> state -> state

   val assume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state

   val presume: (Thm.binding * (term * term list) list) list -> state -> state

   val presume_cmd: (Attrib.binding * (string * string list) list) list -> state -> state

   val def: (Thm.binding * ((binding * mixfix) * (term * term list))) list -> state -> state

   val def_cmd: (Attrib.binding * ((binding * mixfix) * (string * string list))) list -> state -> state

   val chain: state -> state

   val chain_facts: thm list -> state -> state

   val get_thmss_cmd: state -> (Facts.ref * Attrib.src list) list -> thm list

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

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

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

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

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

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

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

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

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

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

   val invoke_case: string * string option list * attribute list -> state -> state

   val invoke_case_cmd: string * string option list * Attrib.src list -> state -> state

   val begin_block: state -> state

   val next_block: state -> state

   val end_block: state -> state

   val proof: Method.text option -> state -> state Seq.seq

   val defer: int option -> state -> state Seq.seq

   val prefer: int -> state -> state Seq.seq

   val apply: Method.text -> state -> state Seq.seq

   val apply_end: Method.text -> state -> state Seq.seq

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

     (theory -> 'a -> attribute) ->

     (context * 'b list -> context * (term list list * (context -> context))) ->

     string -> Method.text option -> (thm list list -> state -> state) ->

     ((binding * 'a list) * 'b) list -> state -> state

   val local_qed: Method.text 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 option * bool -> state -> context

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

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

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

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

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

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

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

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

   val schematic_goal: state -> bool

   val is_relevant: state -> bool

   val local_future_proof: (state -> ('a * state) Future.future) ->

     state -> 'a Future.future * state

   val global_future_proof: (state -> ('a * Proof.context) Future.future) ->

     state -> 'a Future.future * context

   val local_future_terminal_proof: Method.text * Method.text option -> bool -> state -> state

   val global_future_terminal_proof: Method.text * Method.text option -> bool -> 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 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*)

     messages: (unit -> Pretty.T) list,    (*persistent messages (hints etc.)*)

     using: thm list,                      (*goal facts*)

     goal: thm,                            (*subgoals ==> statement*)

     before_qed: Method.text option,

     after_qed:

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

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

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

   Goal {statement = statement, messages = messages, 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 =

   ProofContext.set_stmt true #>

   ProofContext.map_naming (K ProofContext.local_naming);

 fun init ctxt =

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

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

 fun map_current f (State st) = State (Stack.map_top (map_node f) st);

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

 (** basic proof state operations **)

 (* block structure *)

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

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

   handle Empty => error "Unbalanced block parentheses";

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

 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 current;

 val theory_of = ProofContext.theory_of o context_of;

 fun map_context f =

   map_current (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));

 val bind_terms = map_context o ProofContext.bind_terms;

 val put_thms = map_context oo ProofContext.put_thms;

 (* facts *)

 val get_facts = #facts o current;

 fun the_facts state =

   (case get_facts state of SOME facts => 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 facts =

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

   put_thms true (Auto_Bind.thisN, facts);

 fun these_factss more_facts (named_factss, state) =

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

 fun export_facts inner outer =

   (case get_facts inner of

     NONE => put_facts NONE outer

   | SOME thms =>

       thms

       |> ProofContext.export (context_of inner) (context_of outer)

       |> (fn ths => put_facts (SOME ths) outer));

 (* mode *)

 val get_mode = #mode o current;

 fun put_mode mode = map_current (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 current state of

     {context, goal = SOME (Goal goal), ...} => (context, 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_current (fn (ctxt, using, mode, _) => (ctxt, using, mode, goal));

 val before_qed = #before_qed o #2 o current_goal;

 (* nested goal *)

 fun map_goal f g (State (Node {context, facts, mode, goal = SOME goal}, nodes)) =

       let

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

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

       in State (make_node (f context, facts, mode, SOME goal'), nodes) end

   | map_goal f g (State (nd, node :: nodes)) =

       let val State (node', nodes') = map_goal f g (State (node, nodes))

       in map_context f (State (nd, node' :: nodes')) end

   | map_goal _ _ state = state;

 fun set_goal goal = map_goal I (fn (statement, _, using, _, before_qed, after_qed) =>

   (statement, [], using, goal, before_qed, after_qed));

 fun goal_message msg = map_goal I (fn (statement, messages, using, goal, before_qed, after_qed) =>

   (statement, msg :: messages, using, goal, before_qed, after_qed));

 fun using_facts using = map_goal I (fn (statement, _, _, goal, before_qed, after_qed) =>

   (statement, [], using, goal, before_qed, after_qed));

 local

   fun find i state =

     (case try current_goal state of

       SOME (ctxt, goal) => (ctxt, (i, goal))

     | NONE => find (i + 1) (close_block state handle ERROR _ => error "No goal present"));

 in val find_goal = find 0 end;

 fun get_goal state =

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

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

 (** pretty_state **)

 val show_main_goal = Unsynchronized.ref false;

 val verbose = ProofContext.verbose;

 fun pretty_facts _ _ NONE = []

   | pretty_facts s ctxt (SOME ths) =

       [Pretty.big_list (s ^ "this:") (map (Display.pretty_thm ctxt) ths), Pretty.str ""];

 fun pretty_state nr state =

   let

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

     fun levels_up 0 = ""

       | levels_up 1 = "1 level up"

       | levels_up i = string_of_int i ^ " levels up";

     fun subgoals 0 = ""

       | subgoals 1 = "1 subgoal"

       | subgoals n = string_of_int n ^ " subgoals";

     fun description strs =

       (case filter_out (fn s => s = "") strs of [] => ""

       | strs' => enclose " (" ")" (commas strs'));

     fun prt_goal (SOME (ctxt, (i,

       {statement = ((_, pos), _, _), messages, using, goal, before_qed = _, after_qed = _}))) =

           pretty_facts "using " ctxt

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

           [Pretty.str ("goal" ^

             description [levels_up (i div 2), subgoals (Thm.nprems_of goal)] ^ ":")] @

           Goal_Display.pretty_goals ctxt

             {total = true, main = ! show_main_goal, maxgoals = ! Display.goals_limit} goal @

           (map (fn msg => Position.setmp_thread_data pos msg ()) (rev messages))

       | prt_goal NONE = [];

     val prt_ctxt =

       if ! verbose orelse mode = Forward then ProofContext.pretty_context context

       else if mode = Backward then ProofContext.pretty_ctxt context

       else [];

   in

     [Pretty.str ("proof (" ^ mode_name mode ^ "): step " ^ string_of_int nr ^

       (if ! verbose then ", depth " ^ string_of_int (level state div 2 - 1) else "")),

       Pretty.str ""] @

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

     (if ! verbose orelse mode = Forward then

        pretty_facts "" context facts @ prt_goal (try find_goal state)

      else if mode = Chain then pretty_facts "picking " context facts

      else prt_goal (try find_goal state))

   end;

 fun pretty_goals main state =

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

     Goal_Display.pretty_goals ctxt

       {total = false, main = main, maxgoals = ! Display.goals_limit} goal

   end;

 (** proof steps **)

 (* refine via method *)

 local

 fun goalN i = "goal" ^ string_of_int i;

 fun goals st = map goalN (1 upto Thm.nprems_of st);

 fun no_goal_cases st = map (rpair NONE) (goals st);

 fun goal_cases st =

   Rule_Cases.make_common (Thm.theory_of_thm st, Thm.prop_of st) (map (rpair []) (goals st));

 fun apply_method current_context meth state =

   let

     val (goal_ctxt, (_, {statement, messages = _, using, goal, before_qed, after_qed})) =

       find_goal state;

     val ctxt = if current_context then context_of state else goal_ctxt;

   in

     Method.apply meth ctxt using goal |> Seq.map (fn (meth_cases, goal') =>

       state

       |> map_goal

           (ProofContext.add_cases false (no_goal_cases goal @ goal_cases goal') #>

            ProofContext.add_cases true meth_cases)

           (K (statement, [], using, goal', before_qed, after_qed)))

   end;

 fun select_goals n meth state =

   state

   |> (#2 o #2 o get_goal)

   |> ALLGOALS Goal.conjunction_tac

   |> Seq.maps (fn goal =>

     state

     |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Goal.conjunction_tac 1))

     |> Seq.maps meth

     |> Seq.maps (fn state' => state'

       |> Seq.lift set_goal (Goal.retrofit 1 n (#2 (#2 (get_goal state'))) goal))

     |> Seq.maps (apply_method true (K Method.succeed)));

 fun apply_text cc text state =

   let

     val thy = theory_of state;

     fun eval (Method.Basic m) = apply_method cc m

       | eval (Method.Source src) = apply_method cc (Method.method thy src)

       | eval (Method.Source_i src) = apply_method cc (Method.method_i thy src)

       | eval (Method.Then txts) = Seq.EVERY (map eval txts)

       | eval (Method.Orelse txts) = Seq.FIRST (map eval txts)

       | eval (Method.Try txt) = Seq.TRY (eval txt)

       | eval (Method.Repeat1 txt) = Seq.REPEAT1 (eval txt)

       | eval (Method.SelectGoals (n, txt)) = select_goals n (eval txt);

   in eval text state end;

 in

 val refine = apply_text true;

 val refine_end = apply_text false;

 fun refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths)));

 end;

 (* refine via sub-proof *)

 fun finish_tac 0 = K all_tac

   | finish_tac n =

       Goal.norm_hhf_tac THEN'

       SUBGOAL (fn (goal, i) =>

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

           Tactic.etac Drule.protectI i THEN finish_tac (n - 1) i

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

 fun goal_tac rule =

   Goal.norm_hhf_tac THEN'

   Tactic.rtac rule THEN'

   finish_tac (Thm.nprems_of rule);

 fun refine_goals print_rule inner raw_rules state =

   let

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

     fun refine rule st = (print_rule outer rule; FINDGOAL (goal_tac rule) st);

   in

     raw_rules

     |> ProofContext.goal_export inner outer

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

   end;

 (* conclude_goal *)

 fun conclude_goal ctxt goal propss =

   let

     val thy = ProofContext.theory_of ctxt;

     val string_of_term = Syntax.string_of_term ctxt;

     val string_of_thm = Display.string_of_thm ctxt;

     val ngoals = Thm.nprems_of goal;

     val _ = ngoals = 0 orelse error (Pretty.string_of (Pretty.chunks

       (Goal_Display.pretty_goals ctxt

           {total = true, main = ! show_main_goal, maxgoals = ! Display.goals_limit} goal @

         [Pretty.str (string_of_int ngoals ^ " unsolved goal(s)!")])));

     val extra_hyps = Assumption.extra_hyps ctxt goal;

     val _ = null extra_hyps orelse

       error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term extra_hyps));

     fun lost_structure () = error ("Lost goal structure:\n" ^ string_of_thm goal);

     val th = Goal.conclude

       (if length (flat propss) > 1 then Thm.norm_proof goal else goal)

       handle THM _ => lost_structure ();

     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 _ => lost_structure ();

     val _ = Unify.matches_list thy (flat goal_propss) (map Thm.prop_of (flat results)) orelse

       error ("Proved a different theorem:\n" ^ string_of_thm th);

     val _ = Thm.check_shyps (Variable.sorts_of 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 _ _ = lost_structure ();

   in recover_result propss results end;

 (* goal views -- corresponding to methods *)

 fun raw_goal state =

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

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

 val goal = raw_goal o refine_insert [];

 fun simple_goal state =

   let

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

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

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

 (*** structured proof commands ***)

 (** context elements **)

 (* bindings *)

 local

 fun gen_bind bind args state =

   state

   |> assert_forward

   |> map_context (bind args #> snd)

   |> put_facts NONE;

 in

 val match_bind = gen_bind (ProofContext.match_bind_i false);

 val match_bind_cmd = gen_bind (ProofContext.match_bind false);

 val let_bind = gen_bind (ProofContext.match_bind_i true);

 val let_bind_cmd = gen_bind (ProofContext.match_bind true);

 end;

 (* fix *)

 local

 fun gen_fix prep_vars args =

   assert_forward

   #> map_context (fn ctxt => snd (ProofContext.add_fixes (prep_vars ctxt args) ctxt))

   #> put_facts NONE;

 in

 val fix = gen_fix (K I);

 val fix_cmd = gen_fix (fn ctxt => fn args => fst (ProofContext.read_vars args ctxt));

 end;

 (* assume etc. *)

 local

 fun gen_assume asm prep_att exp args state =

   state

   |> assert_forward

   |> map_context_result (asm exp (Attrib.map_specs (prep_att (theory_of state)) args))

   |> these_factss [] |> #2;

 in

 val assm = gen_assume ProofContext.add_assms_i (K I);

 val assm_cmd = gen_assume ProofContext.add_assms Attrib.attribute;

 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;

 end;

 (* def *)

 local

 fun gen_def prep_att prep_vars prep_binds args state =

   let

     val _ = assert_forward state;

     val thy = theory_of state;

     val (raw_name_atts, (raw_vars, raw_rhss)) = args |> split_list ||> split_list;

     val name_atts = map (apsnd (map (prep_att thy))) raw_name_atts;

   in

     state

     |> map_context_result (prep_vars (map (fn (x, mx) => (x, NONE, mx)) raw_vars))

     |>> map (fn (x, _, mx) => (x, mx))

     |-> (fn vars =>

       map_context_result (prep_binds false (map swap raw_rhss))

       #-> (fn rhss => map_context_result (Local_Defs.add_defs (vars ~~ (name_atts ~~ rhss)))))

     |-> (put_facts o SOME o map (#2 o #2))

   end;

 in

 val def = gen_def (K I) ProofContext.cert_vars ProofContext.match_bind_i;

 val def_cmd = gen_def Attrib.attribute ProofContext.read_vars ProofContext.match_bind;

 end;

 (** facts **)

 (* chain *)

 fun clean_facts ctxt =

   put_facts (SOME (filter_out Thm.is_dummy (the_facts ctxt))) ctxt;

 val chain =

   assert_forward

   #> clean_facts

   #> enter_chain;

 fun chain_facts facts =

   put_facts (SOME facts)

   #> chain;

 (* note etc. *)

 fun no_binding args = map (pair (Binding.empty, [])) args;

 local

 fun gen_thmss more_facts opt_chain opt_result prep_atts prep_fact args state =

   state

   |> assert_forward

   |> map_context_result (ProofContext.note_thmss ""

     (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state)) args))

   |> these_factss (more_facts state)

   ||> opt_chain

   |> opt_result;

 in

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

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

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

 val from_thmss_cmd = gen_thmss (K []) chain #2 Attrib.attribute ProofContext.get_fact o no_binding;

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

 val with_thmss_cmd = gen_thmss the_facts chain #2 Attrib.attribute ProofContext.get_fact o no_binding;

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

 fun get_thmss_cmd state srcs = the_facts (note_thmss_cmd [((Binding.empty, []), srcs)] state);

 end;

 (* using/unfolding *)

 local

 fun gen_using f g prep_atts prep_fact args state =

   state

   |> assert_backward

   |> map_context_result

     (ProofContext.note_thmss ""

       (Attrib.map_facts_refs (prep_atts (theory_of state)) (prep_fact (context_of state))

         (no_binding args)))

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

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

       let

         val ctxt = context_of state';

         val ths = maps snd named_facts;

       in (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;

 in

 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 ProofContext.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 ProofContext.get_fact;

 end;

 (* case *)

 local

 fun qualified_binding a =

   Binding.qualify true (Long_Name.qualifier a) (Binding.name (Long_Name.base_name a));

 fun gen_invoke_case prep_att (name, xs, raw_atts) state =

   let

     val atts = map (prep_att (theory_of state)) raw_atts;

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

       ctxt |> ProofContext.apply_case (ProofContext.get_case ctxt name xs));

     val assumptions = asms |> map (fn (a, ts) => ((qualified_binding a, atts), map (rpair []) ts));

   in

     state'

     |> assume assumptions

     |> bind_terms Auto_Bind.no_facts

     |> `the_facts |-> (fn thms => note_thmss [((Binding.name name, []), [(thms, [])])])

   end;

 in

 val invoke_case = gen_invoke_case (K I);

 val invoke_case_cmd = gen_invoke_case Attrib.attribute;

 end;

 (** proof structure **)

 (* blocks *)

 val begin_block =

   assert_forward

   #> open_block

   #> put_goal NONE

   #> open_block;

 val next_block =

   assert_forward

   #> close_block

   #> open_block

   #> put_goal NONE

   #> put_facts NONE;

 fun end_block state =

   state

   |> assert_forward

   |> close_block

   |> assert_current_goal false

   |> close_block

   |> export_facts state;

 (* sub-proofs *)

 fun proof opt_text =

   assert_backward

   #> refine (the_default Method.default_text opt_text)

   #> Seq.map (using_facts [] #> enter_forward);

 fun end_proof bot txt 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 (refine (Method.finish_text txt));

 fun check_result msg sq =

   (case Seq.pull sq of

     NONE => error msg

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

 fun check_finish sq = check_result "Failed to finish proof" sq;

 (* unstructured refinement *)

 fun defer i = assert_no_chain #> refine (Method.Basic (K (Method.defer i)));

 fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i)));

 fun apply text = assert_backward #> refine text #> Seq.map (using_facts []);

 fun apply_end text = assert_forward #> refine_end text;

 (** goals **)

 (* generic goals *)

 local

 val is_var =

   can (dest_TVar o Logic.dest_type o Logic.dest_term) orf

   can (dest_Var o Logic.dest_term);

 fun implicit_vars props =

   let

     val (var_props, props') = take_prefix is_var props;

     val explicit_vars = fold Term.add_vars var_props [];

     val vars = filter_out (member (op =) explicit_vars) (fold Term.add_vars props []);

   in map (Logic.mk_term o Var) vars end;

 fun refine_terms n =

   refine (Method.Basic (K (RAW_METHOD

     (K (HEADGOAL (PRECISE_CONJUNCTS n

       (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI))))))))))

   #> Seq.hd;

 in

 fun generic_goal prepp kind before_qed after_qed raw_propp state =

   let

     val thy = theory_of state;

     val cert = Thm.cterm_of thy;

     val chaining = can assert_chain state;

     val pos = Position.thread_data ();

     val ((propss, after_ctxt), goal_state) =

       state

       |> assert_forward_or_chain

       |> enter_forward

       |> open_block

       |> map_context_result (fn ctxt => swap (prepp (ctxt, raw_propp)));

     val props = flat propss;

     val vars = implicit_vars props;

     val propss' = vars :: propss;

     val goal_propss = filter_out null propss';

     val goal =

       cert (Logic.mk_conjunction_balanced (map Logic.mk_conjunction_balanced goal_propss))

       |> Thm.weaken_sorts (Variable.sorts_of (context_of goal_state));

     val statement = ((kind, pos), propss', Thm.term_of goal);

     val after_qed' = after_qed |>> (fn after_local =>

       fn results => map_context after_ctxt #> after_local results);

   in

     goal_state

     |> map_context (init_context #> Variable.set_body true)

     |> put_goal (SOME (make_goal (statement, [], [], Goal.init goal, before_qed, after_qed')))

     |> map_context (ProofContext.auto_bind_goal props)

     |> chaining ? (`the_facts #-> using_facts)

     |> put_facts NONE

     |> open_block

     |> put_goal NONE

     |> enter_backward

     |> not (null vars) ? refine_terms (length goal_propss)

     |> null props ? (refine (Method.Basic Method.assumption) #> Seq.hd)

   end;

 fun generic_qed after_ctxt state =

   let

     val (goal_ctxt, {statement, goal, after_qed, ...}) = current_goal state;

     val outer_state = state |> close_block;

     val outer_ctxt = context_of outer_state;

     val ((_, pos), stmt, _) = statement;

     val props =

       flat (tl stmt)

       |> Variable.exportT_terms goal_ctxt outer_ctxt;

     val results =

       tl (conclude_goal goal_ctxt goal stmt)

       |> burrow (ProofContext.export goal_ctxt outer_ctxt);

   in

     outer_state

     |> map_context (after_ctxt props)

     |> pair (after_qed, results)

   end;

 end;

 (* local goals *)

 fun local_goal print_results prep_att prepp kind before_qed after_qed stmt state =

   let

     val thy = theory_of state;

     val ((names, attss), propp) =

       Attrib.map_specs (prep_att thy) stmt |> split_list |>> split_list;

     fun after_qed' results =

       local_results ((names ~~ attss) ~~ results)

       #-> (fn res => tap (fn st => print_results (context_of st) ((kind, ""), res) : unit))

       #> after_qed results;

   in

     state

     |> generic_goal prepp kind before_qed (after_qed', K I) propp

     |> tap (Variable.warn_extra_tfrees (context_of state) o context_of)

   end;

 fun local_qeds txt =

   end_proof false txt

   #> Seq.map (generic_qed ProofContext.auto_bind_facts #->

     (fn ((after_qed, _), results) => after_qed results));

 fun local_qed txt = local_qeds txt #> check_finish;

 (* global goals *)

 fun global_goal prepp before_qed after_qed propp ctxt =

   init ctxt

   |> generic_goal (prepp #> ProofContext.auto_fixes) "" before_qed (K I, after_qed) propp;

 val theorem = global_goal ProofContext.bind_propp_schematic_i;

 val theorem_cmd = global_goal ProofContext.bind_propp_schematic;

 fun global_qeds txt =

   end_proof true txt

   #> Seq.map (generic_qed (K I) #> (fn (((_, after_qed), results), state) =>

     after_qed results (context_of state)));

 fun global_qed txt = global_qeds txt #> check_finish;

 (* concluding steps *)

 fun terminal_proof qed initial terminal =

   proof (SOME initial) #> Seq.maps (qed terminal) #> check_finish;

 fun local_terminal_proof (text, opt_text) = terminal_proof local_qeds text (opt_text, true);

 val local_default_proof = local_terminal_proof (Method.default_text, NONE);

 val local_immediate_proof = local_terminal_proof (Method.this_text, NONE);

 fun local_skip_proof int = local_terminal_proof (Method.sorry_text int, NONE);

 val local_done_proof = terminal_proof local_qeds Method.done_text (NONE, false);

 fun global_terminal_proof (text, opt_text) = terminal_proof global_qeds text (opt_text, true);

 val global_default_proof = global_terminal_proof (Method.default_text, NONE);

 val global_immediate_proof = global_terminal_proof (Method.this_text, NONE);

 fun global_skip_proof int = global_terminal_proof (Method.sorry_text int, NONE);

 val global_done_proof = terminal_proof global_qeds Method.done_text (NONE, false);

 (* common goal statements *)

 local

 fun gen_have prep_att prepp before_qed after_qed stmt int =

   local_goal (Proof_Display.print_results int) prep_att prepp "have" before_qed after_qed stmt;

 fun gen_show prep_att prepp before_qed after_qed stmt int state =

   let

     val testing = Unsynchronized.ref false;

     val rule = Unsynchronized.ref (NONE: thm option);

     fun fail_msg ctxt =

       "Local statement will fail to refine any pending goal" ::

       (case ! rule of NONE => [] | SOME th => [Proof_Display.string_of_rule ctxt "Failed" th])

       |> cat_lines;

     fun print_results ctxt res =

       if ! testing then () else Proof_Display.print_results int ctxt res;

     fun print_rule ctxt th =

       if ! testing then rule := SOME th

       else if int then priority (Proof_Display.string_of_rule ctxt "Successful" th)

       else ();

     val test_proof =

       try (local_skip_proof true)

       |> setmp_noncritical testing true

       |> Exn.capture;

     fun after_qed' results =

       refine_goals print_rule (context_of state) (flat results)

       #> check_result "Failed to refine any pending goal"

       #> after_qed results;

   in

     state

     |> local_goal print_results prep_att prepp "show" before_qed after_qed' stmt

     |> int ? (fn goal_state =>

       (case test_proof goal_state of

         Exn.Result (SOME _) => goal_state

       | Exn.Result NONE => error (fail_msg (context_of goal_state))

       | Exn.Exn Exn.Interrupt => raise Exn.Interrupt

       | Exn.Exn exn => raise Exn.EXCEPTIONS ([exn, ERROR (fail_msg (context_of goal_state))])))

   end;

 in

 val have = gen_have (K I) ProofContext.bind_propp_i;

 val have_cmd = gen_have Attrib.attribute ProofContext.bind_propp;

 val show = gen_show (K I) ProofContext.bind_propp_i;

 val show_cmd = gen_show Attrib.attribute ProofContext.bind_propp;

 end;

 (** future proofs **)

 (* relevant proof states *)

 fun is_schematic t =

   Term.exists_subterm Term.is_Var t orelse

   Term.exists_type (Term.exists_subtype Term.is_TVar) t;

 fun schematic_goal state =

   let val (_, (_, {statement = (_, _, prop), ...})) = find_goal state

   in is_schematic prop end;

 fun is_relevant state =

   (case try find_goal state of

     NONE => true

   | SOME (_, (_, {statement = (_, _, prop), goal, ...})) =>

       is_schematic prop orelse not (Logic.protect prop aconv Thm.concl_of goal));

 (* full proofs *)

 local

 fun future_proof done get_context fork_proof state =

   let

     val _ = assert_backward state;

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

     val {statement as (kind, _, prop), messages, using, goal, before_qed, after_qed} = goal;

     val goal_txt = prop :: map Thm.term_of (Assumption.all_assms_of goal_ctxt);

     val _ = is_relevant state andalso error "Cannot fork relevant proof";

     val prop' = Logic.protect prop;

     val statement' = (kind, [[], [prop']], prop');

     val goal' = Thm.adjust_maxidx_thm (Thm.maxidx_of goal)

       (Drule.comp_no_flatten (goal, Thm.nprems_of goal) 1 Drule.protectI);

     fun after_local' [[th]] = put_thms false (Auto_Bind.thisN, SOME [th]);

     fun after_global' [[th]] = ProofContext.put_thms false (Auto_Bind.thisN, SOME [th]);

     val after_qed' = (after_local', after_global');

     val this_name = ProofContext.full_name goal_ctxt (Binding.name Auto_Bind.thisN);

     val result_ctxt =

       state

       |> map_contexts (fold Variable.declare_term goal_txt)

       |> map_goal I (K (statement', messages, using, goal', before_qed, after_qed'))

       |> fork_proof;

     val future_thm = result_ctxt |> Future.map (fn (_, x) =>

       ProofContext.get_fact_single (get_context x) (Facts.named this_name));

     val finished_goal = Goal.future_result goal_ctxt future_thm prop';

     val state' =

       state

       |> map_goal I (K (statement, messages, using, finished_goal, NONE, after_qed))

       |> done;

   in (Future.map #1 result_ctxt, state') end;

 in

 fun local_future_proof x = future_proof local_done_proof context_of x;

 fun global_future_proof x = future_proof global_done_proof I x;

 end;

 (* terminal proofs *)

 local

 fun future_terminal_proof proof1 proof2 meths int state =

   if int orelse is_relevant state orelse not (Goal.local_future_enabled ())

   then proof1 meths state

   else snd (proof2 (fn state' => Future.fork_pri ~1 (fn () => ((), proof1 meths state'))) state);

 in

 fun local_future_terminal_proof x =

   future_terminal_proof local_terminal_proof local_future_proof x;

 fun global_future_terminal_proof x =

   future_terminal_proof global_terminal_proof global_future_proof x;

 end;

 end;