(*  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 = 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 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 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 goal_tac: thm -> int -> tactic

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

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

  val assm: Assumption.export ->

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

  val assm_i: Assumption.export ->

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

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

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

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

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

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

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

  val chain: state -> state

  val chain_facts: thm list -> state -> state

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

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

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

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

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

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

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

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

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

  val unfolding: ((Facts.ref * 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

  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) ->

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

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

    (term * term 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) ->

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

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

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

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

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

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

    (Thm.binding * (term * term 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 = Context.proof;

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.reset_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 (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 => 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 = ref false;

val verbose = ProofContext.verbose;

val pretty_goals_local = Display.pretty_goals_aux o Syntax.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;

    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)] ^ ":")] @

          pretty_goals_local ctxt Markup.subgoal

            (true, ! show_main_goal) (! 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 pretty_goals_local ctxt Markup.none (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 apply_method current_context pos 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 pos 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 Position.none (K Method.succeed)));

fun apply_text cc text state =

  let

    val thy = theory_of state;

    val pos_of = #2 o Args.dest_src;

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

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

      | eval (Method.Source_i src) = apply_method cc (pos_of src) (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 [] = I

  | refine_insert ths = Seq.hd o refine (Method.Basic (K (Method.insert ths), Position.none));

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 = 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 Markup.none (true, ! show_main_goal) (! 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;

(*** 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 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 (fn ctxt => fn args => fst (ProofContext.read_vars args ctxt));

val fix_i = gen_fix (K 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 Assumption.assume_export;

val assume_i  = assm_i Assumption.assume_export;

val presume   = assm Assumption.presume_export;

val presume_i = assm_i 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 ctxt = context_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 (LocalDefs.add_defs (vars ~~ (name_atts ~~ rhss)))))

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

  end;

in

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

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

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 Attrib.attribute ProofContext.get_fact;

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

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

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

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

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

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

fun get_thmss state srcs = the_facts (note_thmss [((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 (LocalDefs.unfold ctxt ths);

val unfold_goals = LocalDefs.unfold_goals;

in

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

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

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

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

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_i assumptions

    |> bind_terms AutoBind.no_facts

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

  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 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 (Position.thread_data ())));

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), Position.none));

fun prefer i = assert_no_chain #> refine (Method.Basic (K (Method.prefer i), Position.none));

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

fun apply_end text = assert_forward #> refine_end text;

(** goals **)

(* 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 (RAW_METHOD

    (K (HEADGOAL (PRECISE_CONJUNCTS n

      (HEADGOAL (CONJUNCTS (ALLGOALS (rtac Drule.termI)))))))), Position.none))

  #> 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 (_, 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_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, Position.none)) #> 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);

    val (after_local, after_global) = after_qed;

    fun after_local' x y = Position.setmp_thread_data pos (fn () => after_local x y) ();

    fun after_global' x y = Position.setmp_thread_data pos (fn () => after_global x y) ();

  in

    outer_state

    |> map_context (after_ctxt props)

    |> pair ((after_local', after_global'), 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;

val theorem_i = global_goal ProofContext.bind_propp_schematic_i;

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 (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 refine 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 =

      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 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;

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));