(*  Title:      Pure/Isar/proof.ML

    ID:         $Id$

    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 (*= Context.proof*)

  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 sign_of: state -> theory    (*obsolete*)

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

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

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

  val put_thms_internal: 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 get_goal: state -> context * (thm list * thm)

  val show_main_goal: bool ref

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

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

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

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

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

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

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

  val assm: ProofContext.export ->

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

  val assm_i: ProofContext.export ->

    ((string * attribute list) * (term * term list) list) list -> state -> state

  val assume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state

  val assume_i: ((string * attribute list) * (term * term list) list) list -> state -> state

  val presume: ((string * Attrib.src list) * (string * string list) list) list -> state -> state

  val presume_i: ((string * attribute list) * (term * term list) list) list -> state -> state

  val def: ((string * Attrib.src list) *

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

  val def_i: ((string * attribute list) *

    ((string * mixfix) * (term * term list))) list -> state -> state

  val chain: state -> state

  val chain_facts: thm list -> state -> state

  val get_thmss: state -> (thmref * Attrib.src list) list -> thm list

  val simple_note_thms: string -> thm list -> state -> state

  val note_thmss: ((string * Attrib.src list) *

    (thmref * Attrib.src list) list) list -> state -> state

  val note_thmss_i: ((string * attribute list) *

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

  val from_thmss: ((thmref * Attrib.src list) list) list -> state -> state

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

  val with_thmss: ((thmref * Attrib.src list) list) list -> state -> state

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

  val using: ((thmref * Attrib.src list) list) list -> state -> state

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

  val unfolding: ((thmref * Attrib.src list) list) list -> state -> state

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

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

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

  val begin_block: state -> state

  val next_block: state -> state

  val end_block: state -> state Seq.seq

  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 goal_names: string option -> string -> string list -> string

  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 Seq.seq) ->

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

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

  val global_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 -> theory -> theory) ->

    string option -> string * 'a list -> ((string * 'a list) * 'b) list -> context -> state

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

  val local_terminal_proof: Method.text * Method.text option -> state -> state Seq.seq

  val local_default_proof: state -> state Seq.seq

  val local_immediate_proof: state -> state Seq.seq

  val local_done_proof: state -> state Seq.seq

  val local_skip_proof: bool -> state -> state Seq.seq

  val global_terminal_proof: Method.text * Method.text option -> state -> context * theory

  val global_default_proof: state -> context * theory

  val global_immediate_proof: state -> context * theory

  val global_done_proof: state -> context * theory

  val global_skip_proof: bool -> state -> context * theory

  val have: Method.text option -> (thm list list -> state -> state Seq.seq) ->

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

  val have_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->

    ((string * attribute list) * (term * term list) list) list -> bool -> state -> state

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

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

  val show_i: Method.text option -> (thm list list -> state -> state Seq.seq) ->

    ((string * attribute list) * (term * term list) list) list -> bool -> state -> state

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

    string option -> string * Attrib.src list ->

    ((string * Attrib.src list) * (string * string list) list) list -> context -> state

  val theorem_i: string -> Method.text option -> (thm list list -> theory -> theory) ->

    string option -> string * attribute list ->

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

end;

structure Proof: PROOF =

struct

type context = ProofContext.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 * term list list,     (*goal kind and statement, starting with vars*)

    using: thm list,                        (*goal facts*)

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

    before_qed: Method.text option,

    after_qed:

      (thm list list -> state -> state Seq.seq) *

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

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));

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

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

fun map_current f (State st) = State (Stack.map (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;

val sign_of = theory_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);

val add_binds_i = map_context o ProofContext.add_binds_i;

val put_thms = map_context oo ProofContext.put_thms;

val put_thms_internal = map_context o ProofContext.put_thms_internal;

(* 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_internal (AutoBind.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 => Seq.single (put_facts NONE outer)

  | SOME thms =>

      thms

      |> Seq.map_list (ProofContext.exports (context_of inner) (context_of outer))

      |> Seq.map (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, using, goal, before_qed, after_qed} = goal;

        val goal' = make_goal (g (statement, 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 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 = ref false;

val verbose = ProofContext.verbose;

val pretty_goals_local = Display.pretty_goals_aux o ProofContext.pp;

fun pretty_facts _ _ NONE = []

  | pretty_facts s ctxt (SOME ths) =

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

fun pretty_state nr state =

  let

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

    val ref (_, _, bg) = Display.current_goals_markers;

    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 (equal "") strs of [] => ""

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

    fun prt_goal (SOME (ctxt, (i, {statement = (kind, _), 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 [kind, levels_up (i div 2),

              subgoals (Thm.nprems_of goal)] ^ ":")] @

          pretty_goals_local ctxt bg (true, ! show_main_goal) (! Display.goals_limit) goal

      | 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 pretty_goals_local ctxt "" (false, main) (! 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 =

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

fun check_theory thy state =

  if subthy (thy, theory_of state) then state

  else error ("Bad theory of method result: " ^ Context.str_of_thy thy);

fun apply_method current_context meth_fun state =

  let

    val (goal_ctxt, (_, {statement, using, goal, before_qed, after_qed})) = find_goal state;

    val meth = meth_fun (if current_context then context_of state else goal_ctxt);

  in

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

      state

      |> check_theory (Thm.theory_of_thm goal')

      |> 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 Tactic.conjunction_tac

  |> Seq.maps (fn goal =>

    state

    |> Seq.lift set_goal (Goal.extract 1 n goal |> Seq.maps (Tactic.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.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 [] = I

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

end;

(* refine via sub-proof *)

local

fun refine_tac rule =

  Tactic.norm_hhf_tac THEN' Tactic.rtac rule THEN_ALL_NEW

    (Tactic.norm_hhf_tac THEN' (SUBGOAL (fn (goal, i) =>

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

        Tactic.etac Drule.protectI i

      else all_tac)));

fun refine_goal print_rule inner raw_rule state =

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

    raw_rule

    |> ProofContext.goal_exports inner outer

    |> Seq.maps (fn rule =>

      (print_rule outer rule;

        Seq.lift set_goal (FINDGOAL (refine_tac rule) goal) state))

  end;

in

fun refine_goals print_rule inner raw_rules =

  Seq.EVERY (map (refine_goal print_rule inner) raw_rules);

end;

(* conclude_goal *)

fun conclude_goal state goal propss =

  let

    val thy = theory_of state;

    val ctxt = context_of state;

    val string_of_term = ProofContext.string_of_term ctxt;

    val string_of_thm = ProofContext.string_of_thm ctxt;

    val ngoals = Thm.nprems_of goal;

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

        (pretty_goals_local ctxt "" (true, ! show_main_goal) (! Display.goals_limit) goal @

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

    val _ =

      (case subtract (op aconv) (ProofContext.assms_of ctxt) (#hyps (Thm.rep_thm goal)) of

        [] => ()

      | hyps => error ("Additional hypotheses:\n" ^ cat_lines (map string_of_term hyps)));

    val (results, th) = `(Conjunction.elim_precise (map length propss)) (Goal.conclude goal)

      handle THM _ => error ("Lost goal structure:\n" ^ string_of_thm goal);

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

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

  in results 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 false);

val match_bind_i = gen_bind (ProofContext.match_bind_i false);

val let_bind = gen_bind (ProofContext.match_bind true);

val let_bind_i = gen_bind (ProofContext.match_bind_i true);

end;

(* fix *)

local

fun gen_fix add_fixes args =

  assert_forward

  #> map_context (snd o add_fixes args)

  #> put_facts NONE;

in

val fix = gen_fix ProofContext.add_fixes;

val fix_i = gen_fix ProofContext.add_fixes_i;

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 Attrib.attribute;

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

val assume    = assm ProofContext.assume_export;

val assume_i  = assm_i ProofContext.assume_export;

val presume   = assm ProofContext.presume_export;

val presume_i = assm_i ProofContext.presume_export;

end;

(* def *)

local

fun gen_def gen_fix prep_att prep_binds args state =

  let

    val _ = assert_forward state;

    val thy = theory_of state;

    val ((raw_names, raw_atts), (vars, raw_rhss)) =

      args |> split_list |>> split_list ||> split_list;

    val xs = map #1 vars;

    val names = map (fn ("", x) => Thm.def_name x | (name, _) => name) (raw_names ~~ xs);

    val atts = map (map (prep_att thy)) raw_atts;

    val (rhss, state') = state |> map_context_result (prep_binds false (map swap raw_rhss));

    val eqs = LocalDefs.mk_def (context_of state') (xs ~~ rhss);

  in

    state'

    |> gen_fix (map (fn (x, mx) => (x, NONE, mx)) vars)

    |> assm_i LocalDefs.def_export ((names ~~ atts) ~~ map (fn eq => [(eq, [])]) eqs)

  end;

in

val def = gen_def fix Attrib.attribute ProofContext.match_bind;

val def_i = gen_def fix_i (K I) ProofContext.match_bind_i;

end;

(** facts **)

(* chain *)

val chain =

  assert_forward

  #> tap the_facts

  #> enter_chain;

fun chain_facts facts =

  put_facts (SOME facts)

  #> chain;

(* note etc. *)

fun no_binding args = map (pair ("", [])) args;

local

fun gen_thmss note_ctxt more_facts opt_chain opt_result prep_atts args state =

  state

  |> assert_forward

  |> map_context_result (note_ctxt (Attrib.map_facts (prep_atts (theory_of state)) args))

  |> these_factss (more_facts state)

  ||> opt_chain

  |> opt_result;

in

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

val note_thmss_i = gen_thmss ProofContext.note_thmss_i (K []) I #2 (K I);

val from_thmss =

  gen_thmss ProofContext.note_thmss (K []) chain #2 Attrib.attribute o no_binding;

val from_thmss_i = gen_thmss ProofContext.note_thmss_i (K []) chain #2 (K I) o no_binding;

val with_thmss =

  gen_thmss ProofContext.note_thmss the_facts chain #2 Attrib.attribute o no_binding;

val with_thmss_i = gen_thmss ProofContext.note_thmss_i the_facts chain #2 (K I) o no_binding;

val local_results =

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

fun global_results kind = PureThy.note_thmss_i kind o map (apsnd Thm.simple_fact);

fun get_thmss state srcs = the_facts (note_thmss [(("", []), srcs)] state);

fun simple_note_thms name thms = note_thmss_i [((name, []), [(thms, [])])];

end;

(* using/unfolding *)

local

fun gen_using f g note prep_atts args state =

  state

  |> assert_backward

  |> map_context_result (note (Attrib.map_facts (prep_atts (theory_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 @ ths;

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

val unfold_goals = LocalDefs.unfold_goals;

in

val using = gen_using append_using (K (K I)) ProofContext.note_thmss Attrib.attribute;

val using_i = gen_using append_using (K (K I)) ProofContext.note_thmss_i (K I);

val unfolding = gen_using unfold_using unfold_goals ProofContext.note_thmss Attrib.attribute;

val unfolding_i = gen_using unfold_using unfold_goals ProofContext.note_thmss_i (K I);

end;

(* case *)

local

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) => ((a, atts), map (rpair []) ts));

  in

    state'

    |> map_context (ProofContext.qualified_names #> ProofContext.no_base_names)

    |> assume_i assumptions

    |> add_binds_i AutoBind.no_facts

    |> map_context (ProofContext.restore_naming (context_of state))

    |> `the_facts |-> simple_note_thms name

  end;

in

val invoke_case = gen_invoke_case Attrib.attribute;

val invoke_case_i = gen_invoke_case (K I);

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 =

  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));

(* 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 **)

(* goal names *)

fun prep_names prep_att stmt =

  let

    val (names_attss, propp) = split_list (Attrib.map_specs prep_att stmt);

    val (names, attss) = split_list names_attss;

  in ((names, attss), propp) end;

fun goal_names target name names =

  (case target of NONE => "" | SOME "" => "" | SOME loc => " (in " ^ loc ^ ")") ^

  (if name = "" then "" else " " ^ name) ^

  (case filter_out (equal "") names of [] => ""

  | nms => " " ^ enclose "(" ")" (space_implode " and " (Library.take (7, nms) @

      (if length nms > 7 then ["..."] else []))));

(* generic goals *)

local

fun implicit_vars dest add props =

  let

    val (explicit_vars, props') = take_prefix (can dest) props |>> map dest;

    val vars = rev (subtract (op =) explicit_vars (fold add props []));

    val _ =

      if null vars then ()

      else warning ("Goal statement contains unbound schematic variable(s): " ^

        commas_quote (map (Term.string_of_vname o fst) vars));

  in (rev vars, props') end;

fun refine_terms n =

  refine (Method.Basic (K (Method.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 chaining = can assert_chain state;

    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 (_, props') =

      implicit_vars (dest_TVar o Logic.dest_type o Logic.dest_term) Term.add_tvars props;

    val (vars, _) = implicit_vars (dest_Var o Logic.dest_term) Term.add_vars props';

    val propss' = map (Logic.mk_term o Var) vars :: propss;

    val goal = Goal.init (Thm.cterm_of thy (Logic.mk_conjunction_list2 propss'));

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

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

  in

    goal_state

    |> map_context (Variable.set_body true)

    |> put_goal (SOME (make_goal ((kind, propss'), [], goal, before_qed, after_qed')))

    |> map_context (ProofContext.add_cases false (AutoBind.cases thy props))

    |> map_context (ProofContext.auto_bind_goal props)

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

    |> put_facts NONE

    |> open_block

    |> put_goal NONE

    |> enter_backward

    |> K (not (null vars)) ? refine_terms (length propss')

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

  end;

fun generic_qed state =

  let

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

      current_goal state;

    val outer_state = state |> close_block;

    val outer_ctxt = context_of outer_state;

    val props =

      flat (tl stmt)

      |> Variable.generalize goal_ctxt outer_ctxt;

    val results =

      tl (conclude_goal state goal stmt)

      |> (Seq.map_list o Seq.map_list) (ProofContext.exports goal_ctxt outer_ctxt);

  in

    outer_state

    |> map_context (ProofContext.auto_bind_facts 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 ((names, attss), propp) = prep_names (prep_att (theory_of state)) stmt;

    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 ^ goal_names NONE "" names) before_qed (after_qed', K I) propp

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

  end;

fun local_qed txt =

  end_proof false txt

  #> Seq.map generic_qed

  #> Seq.maps (uncurry (fn ((after_qed, _), results) => Seq.lifts after_qed results));

(* global goals *)

fun global_goal print_results prep_att prepp

    kind before_qed after_qed target (name, raw_atts) stmt ctxt =

  let

    val thy = ProofContext.theory_of ctxt;

    val thy_ctxt = ProofContext.init thy;

    val atts = map (prep_att thy) raw_atts;

    val ((names, attss), propp) = prep_names (prep_att thy) stmt;

    fun store_results prfx res =

      K (prfx <> "") ? (Sign.add_path prfx #> Sign.no_base_names)

      #> global_results kind ((names ~~ attss) ~~ res)

      #-> (fn res' =>

        (print_results thy_ctxt ((kind, name), res') : unit;

          #2 o global_results kind [((name, atts), maps #2 res')]))

      #> Sign.restore_naming thy;

    fun after_qed' results =

      (case target of NONE => I

      | SOME prfx => store_results (NameSpace.base prfx)

          (map (map (ProofContext.export_standard ctxt thy_ctxt

            #> Drule.strip_shyps_warning)) results))

      #> after_qed results;

  in

    init ctxt

    |> generic_goal (prepp #> ProofContext.auto_fixes) (kind ^ goal_names target name names)

      before_qed (K Seq.single, after_qed') propp

  end;

fun check_result msg sq =

  (case Seq.pull sq of

    NONE => error msg

  | SOME (s', sq') => Seq.cons s' sq');

fun global_qeds txt =

  end_proof true txt

  #> Seq.map generic_qed

  #> Seq.maps (fn (((_, after_qed), results), state) =>

    Seq.lift after_qed results (theory_of state)

    |> Seq.map (fn thy => (ProofContext.transfer thy (context_of state), thy)))

  |> Seq.DETERM;   (*backtracking may destroy theory!*)

fun global_qed txt =

  global_qeds txt

  #> check_result "Failed to finish proof"

  #> Seq.hd;

(* concluding steps *)

fun local_terminal_proof (text, opt_text) =

  proof (SOME text) #> Seq.maps (local_qed (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);

val local_done_proof = proof (SOME Method.done_text) #> Seq.maps (local_qed (NONE, false));

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

fun global_term_proof immed (text, opt_text) =

  proof (SOME text)

  #> check_result "Terminal proof method failed"

  #> Seq.maps (global_qeds (opt_text, immed))

  #> check_result "Failed to finish proof (after successful terminal method)"

  #> Seq.hd;

val global_terminal_proof = global_term_proof true;

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

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

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

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

(* common goal statements *)

local

fun gen_have prep_att prepp before_qed after_qed stmt int =

  local_goal (ProofDisplay.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 = ref false;

    val rule = ref (NONE: thm option);

    fun fail_msg ctxt =

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

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

      |> cat_lines;

    fun print_results ctxt res =

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

    fun print_rule ctxt th =

      if ! testing then rule := SOME th

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

      else ();

    val test_proof =

      (Seq.pull oo local_skip_proof) true

      |> setmp testing true

      |> setmp proofs 0

      |> capture;

    fun after_qed' results =

      refine_goals print_rule (context_of state) (flat results)

      #> Seq.maps (after_qed results);

  in

    state

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

    |> K int ? (fn goal_state =>

      (case test_proof goal_state of

        Result (SOME _) => goal_state

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

      | Exn Interrupt => raise Interrupt

      | Exn exn => raise EXCEPTION (exn, fail_msg (context_of goal_state))))

  end;

fun gen_theorem prep_att prepp kind before_qed after_qed target a =

  global_goal ProofDisplay.present_results prep_att prepp kind before_qed after_qed target a;

in

val have = gen_have Attrib.attribute ProofContext.bind_propp;

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

val show = gen_show Attrib.attribute ProofContext.bind_propp;

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

val theorem = gen_theorem Attrib.attribute ProofContext.bind_propp_schematic;

val theorem_i = gen_theorem (K I) ProofContext.bind_propp_schematic_i;

end;